{"group":{"id":1,"name":"Community","lockable":false,"created_at":"2012-01-18T18:02:15.000Z","updated_at":"2025-12-14T01:33:56.000Z","description":"Problems submitted by members of the MATLAB Central community.","is_default":true,"created_by":161519,"badge_id":null,"featured":false,"trending":false,"solution_count_in_trending_period":0,"trending_last_calculated":"2025-12-14T00:00:00.000Z","image_id":null,"published":true,"community_created":false,"status_id":2,"is_default_group_for_player":false,"deleted_by":null,"deleted_at":null,"restored_by":null,"restored_at":null,"description_opc":null,"description_html":null,"published_at":null},"problems":[{"id":44880,"title":"Angle between two vectors","description":"Given 2 pairs of _cartesian co-ordinates_, determine the angle between the 2 vectors formed by the _points_ and the _origin_. Angle must be in [0,180] and in degrees.\r\n\r\ne.g. \r\n\r\n* Input (3 separate inputs)\r\n\r\n  [0 1;2 0]\r\n  [1 1;-2 0]\r\n  [1 1;2 2]\r\n\r\n* Output (3 separate outputs):\r\n\r\n  90\r\n  135\r\n  0","description_html":"\u003cp\u003eGiven 2 pairs of \u003ci\u003ecartesian co-ordinates\u003c/i\u003e, determine the angle between the 2 vectors formed by the \u003ci\u003epoints\u003c/i\u003e and the \u003ci\u003eorigin\u003c/i\u003e. Angle must be in [0,180] and in degrees.\u003c/p\u003e\u003cp\u003ee.g.\u003c/p\u003e\u003cul\u003e\u003cli\u003eInput (3 separate inputs)\u003c/li\u003e\u003c/ul\u003e\u003cpre class=\"language-matlab\"\u003e[0 1;2 0]\r\n[1 1;-2 0]\r\n[1 1;2 2]\r\n\u003c/pre\u003e\u003cul\u003e\u003cli\u003eOutput (3 separate outputs):\u003c/li\u003e\u003c/ul\u003e\u003cpre class=\"language-matlab\"\u003e90\r\n135\r\n0\r\n\u003c/pre\u003e","function_template":"function y = angle(x)\r\n  y = x;\r\nend","test_suite":"%%\r\nx = [1 1;-1 -1];\r\ny_correct = 180;\r\nassert(isequal(angle(x),y_correct))\r\n\r\n%%\r\nx = [-1 1;-1 -1];\r\ny_correct = 90;\r\nassert(isequal(angle(x),y_correct))\r\n\r\n%%\r\nx = [0.5 sqrt(3)/2;0.2 0];\r\ny_correct = 60;\r\nassert(isequal(angle(x),y_correct))\r\n\r\n%%\r\nx = [-1 1;0.5 sqrt(3)/2];\r\ny_correct = 75;\r\nassert(isequal(angle(x),y_correct))\r\n\r\n%%\r\nx = [0 1;0 5];\r\ny_correct = 0;\r\nassert(isequal(angle(x),y_correct))","published":true,"deleted":false,"likes_count":1,"comments_count":1,"created_by":290843,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":34,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2019-04-02T11:16:36.000Z","updated_at":"2026-02-28T08:22:03.000Z","published_at":"2019-04-02T11:17:50.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGiven 2 pairs of\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ecartesian co-ordinates\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, determine the angle between the 2 vectors formed by the\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003epoints\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e and the\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eorigin\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e. Angle must be in [0,180] and in degrees.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ee.g.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eInput (3 separate inputs)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[[0 1;2 0]\\n[1 1;-2 0]\\n[1 1;2 2]]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eOutput (3 separate outputs):\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[90\\n135\\n0]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":2772,"title":"Find out phase angle of second order system. ","description":"Find out the phase angle of a second order system. \r\n\r\nIn a control system, the phase angle is given by the inverse of cos. ","description_html":"\u003cp\u003eFind out the phase angle of a second order system.\u003c/p\u003e\u003cp\u003eIn a control system, the phase angle is given by the inverse of cos.\u003c/p\u003e","function_template":"function y = phase_angle(x)\r\n  \r\nend","test_suite":"%%\r\nx = 1;\r\ny_correct = 0;\r\nassert(isequal(phase_angle(x),y_correct))\r\n%%\r\nx = 0.5;\r\ny_correct = 1.0472;\r\nassert(abs(phase_angle(x)-y_correct)\u003c0.0001)\r\n%%\r\nx = 0.25;\r\ny_correct =  1.3181;\r\nassert(abs(phase_angle(x)-y_correct)\u003c0.0001)\r\n%%\r\nx = 0.7;\r\ny_correct =   0.7954;\r\nassert(abs(phase_angle(x)-y_correct)\u003c0.0001)","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":27760,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":73,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2014-12-13T10:41:27.000Z","updated_at":"2026-03-02T14:05:34.000Z","published_at":"2014-12-13T10:41:27.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFind out the phase angle of a second order system.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eIn a control system, the phase angle is given by the inverse of cos.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":44271,"title":"0\u003c=x\u003c=pi?","description":"Check whether the given angle is between zero and pi.\r\nReturn logical true or false.","description_html":"\u003cp\u003eCheck whether the given angle is between zero and pi.\r\nReturn logical true or false.\u003c/p\u003e","function_template":"function y = ang(x)\r\n  y = (x==pi/2);\r\nend","test_suite":"%%\r\nx = rand*pi;\r\ny_correct = (200\u003e=100);\r\nassert(isequal(ang(x),y_correct))\r\n%%\r\nx = -rand*pi;\r\ny_correct = (100\u003e=200);\r\nassert(isequal(ang(x),y_correct))\r\n\r\n","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":166,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":140,"test_suite_updated_at":"2017-08-01T23:22:04.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2017-08-01T23:13:05.000Z","updated_at":"2026-02-16T12:15:51.000Z","published_at":"2017-08-01T23:13:38.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eCheck whether the given angle is between zero and pi. Return logical true or false.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":2518,"title":"Find out value of sine given by  degree. ","description":"Find out value of sine given by  degree. \r\nIf theta=30, it's value must be 0.5. ","description_html":"\u003cp\u003eFind out value of sine given by  degree. \r\nIf theta=30, it's value must be 0.5.\u003c/p\u003e","function_template":"function y = your_fcn_name(x)\r\n  y =  x;\r\nend","test_suite":"%%\r\nx = 30;\r\ny_correct =  0.5000;\r\nassert(abs(your_fcn_name(x)-y_correct)\u003c0.0001)\r\n%%\r\nx = 60;\r\ny_correct = 0.8660;\r\nassert(abs(your_fcn_name(x)-y_correct)\u003c0.0001)\r\n%%\r\nx = 90;\r\ny_correct = 1;\r\nassert(isequal(your_fcn_name(x),y_correct))","published":true,"deleted":false,"likes_count":2,"comments_count":0,"created_by":27760,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":356,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2014-08-20T07:02:02.000Z","updated_at":"2026-03-03T22:17:43.000Z","published_at":"2014-08-20T07:02:02.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFind out value of sine given by degree. If theta=30, it's value must be 0.5.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":43563,"title":"Calculate cosine without cos(x)","description":"Solve cos(x).\r\n\r\nThe use of the function cos() and sin() is not allowed.","description_html":"\u003cp\u003eSolve cos(x).\u003c/p\u003e\u003cp\u003eThe use of the function cos() and sin() is not allowed.\u003c/p\u003e","function_template":"function y = my_func(x)\r\n  y = cos(x);\r\nend","test_suite":"%%\r\nx = 0;\r\ny_correct = 1;\r\nassert(abs(my_func(x)-y_correct)\u003c0.0001)\r\n\r\n%%\r\nx = pi/2;\r\ny_correct = 0;\r\nassert(abs(my_func(x)-y_correct)\u003c0.0001)\r\n\r\n%%\r\nx = rand(1)*2*pi;\r\ny_correct = cos(x);\r\nassert(abs(my_func(x)-y_correct)\u003c0.0001)\r\n\r\n%%\r\nassessFunctionAbsence({'sin','cos'}, 'FileName', 'my_func.m')\r\n\r\n","published":true,"deleted":false,"likes_count":1,"comments_count":1,"created_by":14644,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":125,"test_suite_updated_at":"2016-12-01T18:38:29.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2016-10-16T10:35:20.000Z","updated_at":"2026-04-03T02:52:46.000Z","published_at":"2016-10-16T10:42:54.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eSolve cos(x).\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe use of the function cos() and sin() is not allowed.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":44282,"title":"Minimum possible M of the maximum side of a triangle of given area A.","description":"Suppose a triangle has area A.\r\nSuppose it has three sides S1, S2, and S3.\r\nSuppose M = max([S1 S2 S3]).\r\nWhat is the minimum possible value of M?\r\n","description_html":"\u003cp\u003eSuppose a triangle has area A.\r\nSuppose it has three sides S1, S2, and S3.\r\nSuppose M = max([S1 S2 S3]).\r\nWhat is the minimum possible value of M?\u003c/p\u003e","function_template":"function m = tri(a)\r\n  m = max(a/7);\r\nend","test_suite":"%%\r\na = 0.4331;\r\nm = 1.0001;\r\nassert(tri(a)\u003em*0.99)\r\n\r\n%%\r\na = 43.31;\r\nm = 10.001;\r\nassert(tri(a)\u003cm*1.01)\r\n\r\n%%\r\na = 4331;\r\nm = 100.01;\r\nassert(tri(a)\u003em*0.99)\r\n\r\n%%\r\na = 4331;\r\nm = 100.01;\r\nassert(tri(a)\u003cm*1.01)\r\n","published":true,"deleted":false,"likes_count":2,"comments_count":0,"created_by":166,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":62,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2017-08-10T11:39:30.000Z","updated_at":"2026-03-14T18:37:39.000Z","published_at":"2017-08-10T11:39:53.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eSuppose a triangle has area A. Suppose it has three sides S1, S2, and S3. Suppose M = max([S1 S2 S3]). What is the minimum possible value of M?\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":43564,"title":"Calculate sin(x) without sin(x)","description":"Calculate\r\ny = sin(x)\r\n\r\nx = 0 -\u003e y= 0\r\n\r\nwithout the use of sin(x) or cos(x)\r\n","description_html":"\u003cp\u003eCalculate\r\ny = sin(x)\u003c/p\u003e\u003cp\u003ex = 0 -\u0026gt; y= 0\u003c/p\u003e\u003cp\u003ewithout the use of sin(x) or cos(x)\u003c/p\u003e","function_template":"function y = my_func(x)\r\n  y = sin(x);\r\nend","test_suite":"x = 0;\r\ny_correct = 0;\r\nassert(abs(my_func(x)-y_correct)\u003c0.0001)\r\n\r\n%%\r\nx = -pi/2;\r\ny_correct = sin(x);\r\nassert(abs(my_func(x)-y_correct)\u003c0.0001)\r\n\r\n%%\r\nx = rand(1)*2*pi;\r\ny_correct = sin(x);\r\nassert(abs(my_func(x)-y_correct)\u003c0.0001)\r\n\r\n%%\r\nassessFunctionAbsence({'cos', 'sin'}, 'FileName', 'my_func.m');\r\n","published":true,"deleted":false,"likes_count":1,"comments_count":2,"created_by":14644,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":119,"test_suite_updated_at":"2016-12-01T18:41:33.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2016-10-16T10:50:54.000Z","updated_at":"2026-04-03T02:51:49.000Z","published_at":"2016-10-16T10:50:54.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eCalculate y = sin(x)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ex = 0 -\u0026gt; y= 0\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ewithout the use of sin(x) or cos(x)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":45345,"title":"Grazing-01","description":"A cow is tied to an outside corner of a rectangular barn of size (a,b) with a rope of length l. What is the maximum area the cow can graze outside the barn?\r\n\r\n\u003chttps://serving.photos.photobox.com/495639807b8e93bb90ab3c212fe921e51fefc77e0b8756d28871096f5482839b5e5d4bb8.jpg\u003e\r\n\r\nNb.the test cases are simpler for this problem. They'll be enhanced in the next case.","description_html":"\u003cp\u003eA cow is tied to an outside corner of a rectangular barn of size (a,b) with a rope of length l. What is the maximum area the cow can graze outside the barn?\u003c/p\u003e\u003cp\u003e\u003ca href = \"https://serving.photos.photobox.com/495639807b8e93bb90ab3c212fe921e51fefc77e0b8756d28871096f5482839b5e5d4bb8.jpg\"\u003ehttps://serving.photos.photobox.com/495639807b8e93bb90ab3c212fe921e51fefc77e0b8756d28871096f5482839b5e5d4bb8.jpg\u003c/a\u003e\u003c/p\u003e\u003cp\u003eNb.the test cases are simpler for this problem. They'll be enhanced in the next case.\u003c/p\u003e","function_template":"function y = grazing_01(a,b,l)\r\n  y = x;\r\nend","test_suite":"%%\r\nassert(abs(grazing_01(10,20,5)-58.9049)\u003c0.001)\r\n%%\r\nassert(abs(grazing_01(5,25,2)-9.4248)\u003c0.001)\r\n%%\r\nassert(abs(grazing_01(5,25,8)-157.8650)\u003c0.001)\r\n%%\r\nassert(abs(grazing_01(20,20,20)- 942.4778)\u003c0.001)\r\n%%\r\nassert(abs(grazing_01(10,20,0)-0)\u003c0.001)\r\n%%\r\nassert(abs(grazing_01(12,20,25)-1624.9888)\u003c0.001)\r\n\r\n","published":true,"deleted":false,"likes_count":2,"comments_count":3,"created_by":363598,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":19,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2020-02-20T10:45:47.000Z","updated_at":"2026-01-29T12:35:16.000Z","published_at":"2020-02-20T11:20:35.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eA cow is tied to an outside corner of a rectangular barn of size (a,b) with a rope of length l. What is the maximum area the cow can graze outside the barn?\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:hyperlink w:docLocation=\\\"https://serving.photos.photobox.com/495639807b8e93bb90ab3c212fe921e51fefc77e0b8756d28871096f5482839b5e5d4bb8.jpg\\\"\u003e\u003cw:r\u003e\u003cw:t\u003e\u0026lt;https://serving.photos.photobox.com/495639807b8e93bb90ab3c212fe921e51fefc77e0b8756d28871096f5482839b5e5d4bb8.jpg\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e\u0026gt;\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eNb.the test cases are simpler for this problem. They'll be enhanced in the next case.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":401,"title":"cos for boss?","description":"a programmer had too much coffee and his boss needs cos(alpha+beta) correctly, especially when alpha or beta are close to pi/2 and the coffee is close to ninety degrees. A hint: sin() may be appropriate for some input, without committing any sin!! ","description_html":"\u003cp\u003ea programmer had too much coffee and his boss needs cos(alpha+beta) correctly, especially when alpha or beta are close to pi/2 and the coffee is close to ninety degrees. A hint: sin() may be appropriate for some input, without committing any sin!!\u003c/p\u003e","function_template":"function coffee = cos_for_boss(alfa,bita)\r\n  coffee=cos(alfalfa+bitabita);\r\nend","test_suite":"%%\r\nalfa=pi/2;\r\nbita=-1/10^20;\r\ncos_correct = 1/10^20;\r\nassert(abs(cos_for_boss(alfa,bita)-cos_correct)\u003ceps/10)\r\n%%\r\nbita=pi/2;\r\nalfa=-1/11^20;\r\ncos_correct = 1/11^20;\r\nassert(abs(cos_for_boss(alfa,bita)-cos_correct)\u003ceps/10)\r\n%%\r\nbita=pi/6;\r\nalfa=pi/6;\r\ncos_correct = 1/2;\r\nassert(abs(cos_for_boss(alfa,bita)-cos_correct)\u003ceps*10)\r\n%%\r\nbita=pi/8;\r\nalfa=pi/8;\r\ncos_correct = 1/sqrt(2);\r\nassert(abs(cos_for_boss(alfa,bita)-cos_correct)\u003ceps*10)\r\n%%\r\nbita=pi/12;\r\nalfa=pi/4;\r\ncos_correct = 1/2;\r\nassert(abs(cos_for_boss(alfa,bita)-cos_correct)\u003ceps*10)\r\n","published":true,"deleted":false,"likes_count":2,"comments_count":2,"created_by":166,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":64,"test_suite_updated_at":"2012-02-26T08:30:12.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2012-02-24T22:49:02.000Z","updated_at":"2025-12-14T23:19:46.000Z","published_at":"2012-02-26T08:36:11.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ea programmer had too much coffee and his boss needs cos(alpha+beta) correctly, especially when alpha or beta are close to pi/2 and the coffee is close to ninety degrees. A hint: sin() may be appropriate for some input, without committing any sin!!\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":336,"title":"Similar Triangles - find the height of the tree","description":"Given the height, h1, of a power pole, shorter than a tree, a given distance, x2 away, please find h2, height of the tree. Please note that the angle, phi, is the acute angle measured from the ground to an observer's line of sight aimed to the sucessive peaks of the power pole and the tree, in that order. Also the distance from the observer to the power pole is x1, also a given. x2 is the distance between the tree and the power pole. In all tests x1 is always a multiple of x2.\r\n\r\n\r\nInputs: h1, x1, x2\r\n\r\nOutput: h2\r\n\r\nHINT: find phi, given h1 and x1. Phi may be measured in degrees or radians. Note that default trig functions in MATLAB operate in radians.\r\n\r\nEX:\r\nx1 = 4;\r\nx2 = 4;\r\nh1 = 3;\r\n\r\n\u003e\u003eh2=findHeight(x1,x2,h1)\r\n\r\nh2=6\r\n\r\n\u003e\u003e","description_html":"\u003cp\u003eGiven the height, h1, of a power pole, shorter than a tree, a given distance, x2 away, please find h2, height of the tree. Please note that the angle, phi, is the acute angle measured from the ground to an observer's line of sight aimed to the sucessive peaks of the power pole and the tree, in that order. Also the distance from the observer to the power pole is x1, also a given. x2 is the distance between the tree and the power pole. In all tests x1 is always a multiple of x2.\u003c/p\u003e\u003cp\u003eInputs: h1, x1, x2\u003c/p\u003e\u003cp\u003eOutput: h2\u003c/p\u003e\u003cp\u003eHINT: find phi, given h1 and x1. Phi may be measured in degrees or radians. Note that default trig functions in MATLAB operate in radians.\u003c/p\u003e\u003cp\u003eEX:\r\nx1 = 4;\r\nx2 = 4;\r\nh1 = 3;\u003c/p\u003e\u003cp\u003e\u003e\u003eh2=findHeight(x1,x2,h1)\u003c/p\u003e\u003cp\u003eh2=6\u003c/p\u003e\u003cp\u003e\u003e\u003e\u003c/p\u003e","function_template":"function h2 = findHeight(x1,x2,h1)\r\n  h2 = heightoftree\r\nend","test_suite":"%%\r\nx1 = 4;\r\nx2 = 4;\r\nh1 = 3;\r\ny_correct = 6;\r\nassert(isequal(findHeight(x1,x2,h1),y_correct))\r\n%%\r\nx1 = 4;\r\nx2 = 8;\r\nh1 = 3;\r\ny_correct = 9;\r\nassert(isequal(findHeight(x1,x2,h1),y_correct))\r\n%%\r\nx1 = 4;\r\nx2 = 12;\r\nh1 = 3;\r\ny_correct = 12;\r\nassert(isequal(findHeight(x1,x2,h1),y_correct))\r\n%%\r\nx1 = 4;\r\nx2 = 16;\r\nh1 = 3;\r\ny_correct = 15;\r\nassert(isequal(findHeight(x1,x2,h1),y_correct))\r\n%%\r\nx1 = 4;\r\nx2 = 20;\r\nh1 = 3;\r\ny_correct = 18;\r\nassert(isequal(findHeight(x1,x2,h1),y_correct))\r\n%%\r\nx1 = 4;\r\nx2 = 24;\r\nh1 = 3;\r\ny_correct = 21;\r\nassert(isequal(findHeight(x1,x2,h1),y_correct))\r\n%%\r\nx1 = 4;\r\nx2 = 12;\r\nh1 = 5;\r\ny_correct = 20;\r\nassert(isequal(findHeight(x1,x2,h1),y_correct))\r\n%%\r\nx1 = 4;\r\nx2 = 16;\r\nh1 = 10;\r\ny_correct = 50;\r\nassert(isequal(findHeight(x1,x2,h1),y_correct))\r\n%%\r\nx1 = 2;\r\nx2 = 4;\r\nh1 = 5;\r\ny_correct = 15;\r\nassert(isequal(findHeight(x1,x2,h1),y_correct))\r\n%%\r\nx1 = 3;\r\nx2 = 6;\r\nh1 = 4;\r\ny_correct = 12;\r\nassert(isequal(findHeight(x1,x2,h1),y_correct))\r\n\r\n\r\n","published":true,"deleted":false,"likes_count":4,"comments_count":6,"created_by":1103,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":469,"test_suite_updated_at":"2012-02-18T04:42:47.000Z","rescore_all_solutions":false,"group_id":17,"created_at":"2012-02-17T22:52:21.000Z","updated_at":"2026-03-13T05:26:44.000Z","published_at":"2012-02-18T04:42:47.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGiven the height, h1, of a power pole, shorter than a tree, a given distance, x2 away, please find h2, height of the tree. Please note that the angle, phi, is the acute angle measured from the ground to an observer's line of sight aimed to the sucessive peaks of the power pole and the tree, in that order. Also the distance from the observer to the power pole is x1, also a given. x2 is the distance between the tree and the power pole. In all tests x1 is always a multiple of x2.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eInputs: h1, x1, x2\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eOutput: h2\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eHINT: find phi, given h1 and x1. Phi may be measured in degrees or radians. Note that default trig functions in MATLAB operate in radians.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eEX: x1 = 4; x2 = 4; h1 = 3;\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003e\u003eh2=findHeight(x1,x2,h1)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eh2=6\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003e\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":837,"title":"Find all the zeros of sinus , cosinus and tangent in a given interval","description":"The aim is to find all the zeros of a function within an interval.\r\n\r\n*Input* : \r\n\r\n* fcn : an anonymous function (@sin, @cos...)\r\n* \r\n* lb : lower bound\r\n* \r\n* ub :upper bound\r\n\r\n\r\n*Output* :\r\n\r\n* output :  vector with unique values for which the input function return zero\r\nThe values must be sorted in ascending order. \r\n\r\n*Example* \r\n\r\n\r\n\r\n  output = find_zeros(@sin,0,2*pi) will return :\r\n\r\n  output = [0.0000    3.1416    6.2832]\r\n\r\nsince the sinus function between [0 2pi] is zero for [0 pi 2pi]\r\n","description_html":"\u003cdiv style = \"text-align: start; line-height: 20px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: normal; text-decoration: none; white-space: normal; \"\u003e\u003cdiv style=\"display: block; min-width: 0px; padding-top: 0px; transform-origin: 332px 197px; vertical-align: baseline; perspective-origin: 332px 197px; \"\u003e\u003cdiv style=\"font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-bottom: 9px; margin-left: 4px; margin-right: 10px; margin-top: 2px; text-align: left; transform-origin: 309px 10.5px; white-space: pre-wrap; perspective-origin: 309px 10.5px; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"display: inline; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; transform-origin: 0px 0px; perspective-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eThe aim is to find all the zeros of a function within an interval.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-bottom: 9px; margin-left: 4px; margin-right: 10px; margin-top: 2px; text-align: left; transform-origin: 309px 10.5px; white-space: pre-wrap; perspective-origin: 309px 10.5px; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"display: inline; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; transform-origin: 0px 0px; perspective-origin: 0px 0px; \"\u003e\u003cspan style=\"font-weight: bold; \"\u003eInput\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"display: inline; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; transform-origin: 0px 0px; perspective-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e :\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cul style=\"font-family: Helvetica, Arial, sans-serif; list-style-type: square; margin-bottom: 20px; margin-top: 10px; transform-origin: 316px 50px; perspective-origin: 316px 50px; margin-top: 10px; margin-bottom: 20px; \"\u003e\u003cli style=\"display: list-item; margin-bottom: 0px; margin-left: 56px; margin-top: 0px; text-align: left; transform-origin: 288px 10px; white-space: pre-wrap; perspective-origin: 288px 10px; margin-left: 56px; \"\u003e\u003cspan style=\"display: inline; margin-left: 0px; transform-origin: 0px 0px; perspective-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003efcn : an anonymous function (@sin, @cos...)\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"display: list-item; margin-bottom: 0px; margin-left: 56px; margin-top: 0px; text-align: left; transform-origin: 288px 10px; white-space: pre-wrap; perspective-origin: 288px 10px; margin-left: 56px; \"\u003e\u003c/li\u003e\u003cli style=\"display: list-item; margin-bottom: 0px; margin-left: 56px; margin-top: 0px; text-align: left; transform-origin: 288px 10px; white-space: pre-wrap; perspective-origin: 288px 10px; margin-left: 56px; \"\u003e\u003cspan style=\"display: inline; margin-left: 0px; transform-origin: 0px 0px; perspective-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003elb : lower bound\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"display: list-item; margin-bottom: 0px; margin-left: 56px; margin-top: 0px; text-align: left; transform-origin: 288px 10px; white-space: pre-wrap; perspective-origin: 288px 10px; margin-left: 56px; \"\u003e\u003c/li\u003e\u003cli style=\"display: list-item; margin-bottom: 0px; margin-left: 56px; margin-top: 0px; text-align: left; transform-origin: 288px 10px; white-space: pre-wrap; perspective-origin: 288px 10px; margin-left: 56px; \"\u003e\u003cspan style=\"display: inline; margin-left: 0px; transform-origin: 0px 0px; perspective-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eub :upper bound\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ul\u003e\u003cdiv style=\"font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-bottom: 9px; margin-left: 4px; margin-right: 10px; margin-top: 2px; text-align: left; transform-origin: 309px 10.5px; white-space: pre-wrap; perspective-origin: 309px 10.5px; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"display: inline; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; transform-origin: 0px 0px; perspective-origin: 0px 0px; \"\u003e\u003cspan style=\"font-weight: bold; \"\u003eOutput\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"display: inline; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; transform-origin: 0px 0px; perspective-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e :\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cul style=\"font-family: Helvetica, Arial, sans-serif; list-style-type: square; margin-bottom: 20px; margin-top: 10px; transform-origin: 316px 20px; perspective-origin: 316px 20px; margin-top: 10px; margin-bottom: 20px; \"\u003e\u003cli style=\"display: list-item; margin-bottom: 0px; margin-left: 56px; margin-top: 0px; text-align: left; transform-origin: 288px 20px; white-space: pre-wrap; perspective-origin: 288px 20px; margin-left: 56px; \"\u003e\u003cspan style=\"display: inline; margin-left: 0px; transform-origin: 0px 0px; perspective-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eoutput : vector with unique values for which the input function return zeroThe values must be sorted in ascending order.\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ul\u003e\u003cdiv style=\"font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-bottom: 9px; margin-left: 4px; margin-right: 10px; margin-top: 2px; text-align: left; transform-origin: 309px 10.5px; white-space: pre-wrap; perspective-origin: 309px 10.5px; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"display: inline; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; transform-origin: 0px 0px; perspective-origin: 0px 0px; \"\u003e\u003cspan style=\"font-weight: bold; \"\u003eExample\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgb(247, 247, 247); border-bottom-left-radius: 4px; border-bottom-right-radius: 4px; border-top-left-radius: 4px; border-top-right-radius: 4px; margin-bottom: 10px; margin-left: 3px; margin-right: 3px; margin-top: 10px; transform-origin: 329px 30px; perspective-origin: 329px 30px; margin-left: 3px; margin-top: 10px; margin-bottom: 10px; margin-right: 3px; \"\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-height: 18px; padding-left: 4px; transform-origin: 329px 10px; white-space: nowrap; perspective-origin: 329px 10px; \"\u003e\u003cspan style=\"border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-right: 45px; min-height: 0px; padding-left: 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; perspective-origin: 0px 0px; margin-right: 45px; \"\u003e\u003cspan style=\"margin-right: 0px; \"\u003eoutput = find_zeros(@sin,0,2*pi) will \u003c/span\u003e\u003cspan style=\"border-bottom-color: rgb(170, 4, 249); border-left-color: rgb(170, 4, 249); border-right-color: rgb(170, 4, 249); border-top-color: rgb(170, 4, 249); caret-color: rgb(170, 4, 249); color: rgb(170, 4, 249); margin-right: 0px; outline-color: rgb(170, 4, 249); text-decoration-color: rgb(170, 4, 249); column-rule-color: rgb(170, 4, 249); \"\u003ereturn :\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-height: 18px; padding-left: 4px; transform-origin: 329px 10px; white-space: nowrap; perspective-origin: 329px 10px; \"\u003e\u003cspan style=\"border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-right: 45px; min-height: 0px; padding-left: 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; perspective-origin: 0px 0px; margin-right: 45px; \"\u003e\u003cspan style=\"margin-right: 0px; \"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-height: 18px; padding-left: 4px; transform-origin: 329px 10px; white-space: nowrap; perspective-origin: 329px 10px; \"\u003e\u003cspan style=\"border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-right: 45px; min-height: 0px; padding-left: 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; perspective-origin: 0px 0px; margin-right: 45px; \"\u003e\u003cspan style=\"margin-right: 0px; \"\u003eoutput = [0.0000    3.1416    6.2832]\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003cdiv style=\"font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-bottom: 9px; margin-left: 4px; margin-right: 10px; margin-top: 10px; text-align: left; transform-origin: 309px 10.5px; white-space: pre-wrap; perspective-origin: 309px 10.5px; margin-left: 4px; margin-top: 10px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"display: inline; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; transform-origin: 0px 0px; perspective-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003esince the sinus function between [0 2pi] is zero for [0 pi 2pi]\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function output = find_zeros(fcn,lb,ub)\r\noutput = lb*up;","test_suite":"%% Test sinus between [0 2pi]\r\nassert(all(abs(find_zeros(@sin,0,2*pi) -[0 pi 2*pi])\u003c1e-9))\r\n\r\n%% [0 pi]\r\nassert(all(abs(find_zeros(@sin,0,pi) -[0 pi ])\u003c1e-9))\r\n\r\n%% [0 pi/3] \r\nassert(all(abs(find_zeros(@sin,0,pi/3) -0) \u003c1e-9))\r\n\r\n%% Test cos between [0 2pi]\r\nassert(all(abs(find_zeros(@cos,0,2*pi) -[pi/2 3*pi/2])\u003c1e-9))\r\n\r\n%% Test tan between [0 pi/4]\r\nassert(all(abs(find_zeros(@tan,0,pi/4) -0)\u003c1e-9))","published":true,"deleted":false,"likes_count":1,"comments_count":7,"created_by":639,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":24,"test_suite_updated_at":"2020-09-29T14:30:54.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2012-07-17T07:42:46.000Z","updated_at":"2026-01-03T12:33:06.000Z","published_at":"2012-07-17T08:10:10.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe aim is to find all the zeros of a function within an interval.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eInput\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e :\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003efcn : an anonymous function (@sin, @cos...)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003elb : lower bound\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eub :upper bound\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eOutput\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e :\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eoutput : vector with unique values for which the input function return zeroThe values must be sorted in ascending order.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eExample\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[output = find_zeros(@sin,0,2*pi) will return :\\n\\noutput = [0.0000    3.1416    6.2832]]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003esince the sinus function between [0 2pi] is zero for [0 pi 2pi]\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":44070,"title":"Under the sea: Snell's law \u0026 total internal reflection","description":"\u003chttps://en.wikipedia.org/wiki/Snell's_law\u003e\r\n\r\nWhen a light travels from one medium to another medium, depending on the refractive index, the light will bend with a certain angle. For certain combination of materials, it might be that light cannot escape one medium at all from a certain angle (greater than critical angle). It is called total internal reflection. If you point a flashlight from \"under the sea\" the light won't leave the water at all. \r\n\r\nFor given refractive indices, find critical angle where total internal reflection happens. If total internal reflection does not happen for any angle, then return \"-1\".\r\n\r\nExample1: n_in = 1.333, n_out = 1, theta_crit = 48.6 degrees;\r\nExample2: n_out = 1, n_in = 1.333, theta_crit = -1 (total internal reflection does not occur, if you are in the air, and beaming light at the water.)\r\n\r\nInput of function: n_in, n_out (refractive index, positive) \r\nOutput: critical angle (rounded to nearest integer), if total internal reflection occurs. Else return -1.","description_html":"\u003cp\u003e\u003ca href = \"https://en.wikipedia.org/wiki/Snell's_law\"\u003ehttps://en.wikipedia.org/wiki/Snell's_law\u003c/a\u003e\u003c/p\u003e\u003cp\u003eWhen a light travels from one medium to another medium, depending on the refractive index, the light will bend with a certain angle. For certain combination of materials, it might be that light cannot escape one medium at all from a certain angle (greater than critical angle). It is called total internal reflection. If you point a flashlight from \"under the sea\" the light won't leave the water at all.\u003c/p\u003e\u003cp\u003eFor given refractive indices, find critical angle where total internal reflection happens. If total internal reflection does not happen for any angle, then return \"-1\".\u003c/p\u003e\u003cp\u003eExample1: n_in = 1.333, n_out = 1, theta_crit = 48.6 degrees;\r\nExample2: n_out = 1, n_in = 1.333, theta_crit = -1 (total internal reflection does not occur, if you are in the air, and beaming light at the water.)\u003c/p\u003e\u003cp\u003eInput of function: n_in, n_out (refractive index, positive) \r\nOutput: critical angle (rounded to nearest integer), if total internal reflection occurs. Else return -1.\u003c/p\u003e","function_template":"function theta_crit = totalInternalReflection(n_in,n_out)\r\n  theta_crit = -1;\r\nend","test_suite":"%%\r\nn_in = 3; n_out = 3;\r\ntheta_crit_correct = -1;\r\nassert(isequal(totalInternalReflection(n_in,n_out),theta_crit_correct))\r\n\r\n%%\r\nn_in = 1; n_out = 1.333;\r\ntheta_crit_correct = -1;\r\nassert(isequal(totalInternalReflection(n_in,n_out),theta_crit_correct))\r\n\r\n%%\r\nn_in = 1.333; n_out = 1;\r\ntheta_crit_correct = 49;\r\nassert(isequal(totalInternalReflection(n_in,n_out),theta_crit_correct))\r\n\r\n%%\r\nn_in = 4; n_out = 3;\r\ntheta_crit_correct = 49;\r\nassert(isequal(totalInternalReflection(n_in,n_out),theta_crit_correct))\r\n\r\n%%\r\nn_in = 4; n_out = 2;\r\ntheta_crit_correct = 30;\r\nassert(isequal(totalInternalReflection(n_in,n_out),theta_crit_correct))","published":true,"deleted":false,"likes_count":2,"comments_count":6,"created_by":115733,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":58,"test_suite_updated_at":"2017-02-16T21:45:07.000Z","rescore_all_solutions":false,"group_id":37,"created_at":"2017-02-14T00:59:14.000Z","updated_at":"2026-02-08T13:00:17.000Z","published_at":"2017-02-14T00:59:14.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:hyperlink w:docLocation=\\\"https://en.wikipedia.org/wiki/Snell's_law\\\"\u003e\u003cw:r\u003e\u003cw:t\u003e\u0026lt;https://en.wikipedia.org/wiki/Snell's_law\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e\u0026gt;\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWhen a light travels from one medium to another medium, depending on the refractive index, the light will bend with a certain angle. For certain combination of materials, it might be that light cannot escape one medium at all from a certain angle (greater than critical angle). It is called total internal reflection. If you point a flashlight from \\\"under the sea\\\" the light won't leave the water at all.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFor given refractive indices, find critical angle where total internal reflection happens. If total internal reflection does not happen for any angle, then return \\\"-1\\\".\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eExample1: n_in = 1.333, n_out = 1, theta_crit = 48.6 degrees; Example2: n_out = 1, n_in = 1.333, theta_crit = -1 (total internal reflection does not occur, if you are in the air, and beaming light at the water.)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eInput of function: n_in, n_out (refractive index, positive) Output: critical angle (rounded to nearest integer), if total internal reflection occurs. Else return -1.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":44936,"title":"Float like a cannonball","description":"Given gravity on earth (g=9.81 [m/s/s]) find the distance s [m] by a cannonball propelled at a speed of u [m/s] from the origin at an angle theta [deg] measured from the horizontal. Assume no air resistance or bouncing. The altitude of the release of the cannon ball is 0 m and the travel should have the appropriate sign (i.e. behind the release point would be negative).\r\nHint: Consider logical reasoning when the orientation of the firing vector would be into the ground!!","description_html":"\u003cp\u003eGiven gravity on earth (g=9.81 [m/s/s]) find the distance s [m] by a cannonball propelled at a speed of u [m/s] from the origin at an angle theta [deg] measured from the horizontal. Assume no air resistance or bouncing. The altitude of the release of the cannon ball is 0 m and the travel should have the appropriate sign (i.e. behind the release point would be negative).\r\nHint: Consider logical reasoning when the orientation of the firing vector would be into the ground!!\u003c/p\u003e","function_template":"function s = CannonBall(u,theta)\r\n%Stones taught me to fly...\r\n  s = u*theta;\r\nend","test_suite":"%%\r\nu= 100;\r\ntheta=85;\r\ny_correct = 177;\r\nassert(isequal(round(CannonBall(u,theta)),y_correct))\r\n\r\n%%\r\nu= 31.42;\r\ntheta=45;\r\ny_correct = 101;\r\nassert(isequal(round(CannonBall(u,theta)),y_correct))\r\n\r\n%%\r\nu= 31.42;\r\ntheta=-41;\r\ny_correct = 0;\r\nassert(isequal(round(CannonBall(u,theta)),y_correct))\r\n\r\n%%\r\nu= 100;\r\ntheta=30;\r\ny_correct = 883;\r\nassert(isequal(round(CannonBall(u,theta)),y_correct))\r\n\r\n%%\r\nu= -100;\r\ntheta=30;\r\ny_correct = 0;\r\nassert(isequal(round(CannonBall(u,theta)),y_correct))\r\n\r\n\r\n%%\r\nu= -100;\r\ntheta=210;\r\ny_correct = 883;\r\nassert(isequal(round(CannonBall(u,theta)),y_correct))\r\n\r\n\r\n%%\r\nu= 100;\r\ntheta=210;\r\ny_correct = 0;\r\nassert(isequal(round(CannonBall(u,theta)),y_correct))\r\n\r\n%%\r\nu= 0;\r\ntheta=40;\r\ny_correct = 0;\r\nassert(isequal(round(CannonBall(u,theta)),y_correct))\r\n\r\n%%\r\nu= 100;\r\ntheta=90;\r\ny_correct = 0;\r\nassert(isequal(round(CannonBall(u,theta)),y_correct))\r\n\r\n%%\r\nu= 100;\r\ntheta=0;\r\ny_correct = 0;\r\nassert(isequal(round(CannonBall(u,theta)),y_correct))\r\n\r\n%%\r\nfiletext = fileread('CannonBall.m');\r\nassert(isempty(strfind(filetext, 'regexp'))); assert(isempty(strfind(filetext, 'eval'))) \r\n\r\n","published":true,"deleted":false,"likes_count":3,"comments_count":0,"created_by":170350,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":26,"test_suite_updated_at":"2019-08-02T09:56:25.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2019-08-02T09:45:02.000Z","updated_at":"2026-01-02T13:04:50.000Z","published_at":"2019-08-02T09:45:02.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGiven gravity on earth (g=9.81 [m/s/s]) find the distance s [m] by a cannonball propelled at a speed of u [m/s] from the origin at an angle theta [deg] measured from the horizontal. Assume no air resistance or bouncing. The altitude of the release of the cannon ball is 0 m and the travel should have the appropriate sign (i.e. behind the release point would be negative). Hint: Consider logical reasoning when the orientation of the firing vector would be into the ground!!\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":2495,"title":"Find the first N zeros of the 666 function","description":"Using the following definition of the 666 function for this problem: _f(n)=sin('nnn')-cos(n*n*n)_, write a function that returns the first N integer zeros of the 666 function, formatted as 'nnn'.\r\n\r\nFor example:\r\n\r\nsixsixsix(1) = should return 666\r\n\r\nsixsixsix(7) should return 666 151515 181818 272727 424242 636363 666666\r\n\r\nNote 1: Consider a 'zero' to occur when f(n)\u003c1e-8\r\n\r\nNote 2: The sin and cosine functions must be in degrees, not radians.","description_html":"\u003cp\u003eUsing the following definition of the 666 function for this problem: \u003ci\u003ef(n)=sin('nnn')-cos(n*n*n)\u003c/i\u003e, write a function that returns the first N integer zeros of the 666 function, formatted as 'nnn'.\u003c/p\u003e\u003cp\u003eFor example:\u003c/p\u003e\u003cp\u003esixsixsix(1) = should return 666\u003c/p\u003e\u003cp\u003esixsixsix(7) should return 666 151515 181818 272727 424242 636363 666666\u003c/p\u003e\u003cp\u003eNote 1: Consider a 'zero' to occur when f(n)\u0026lt;1e-8\u003c/p\u003e\u003cp\u003eNote 2: The sin and cosine functions must be in degrees, not radians.\u003c/p\u003e","function_template":"function M = sixsixsix(N)\r\n\r\nend","test_suite":"%%\r\nN = 1;\r\nM_correct = 666;\r\nassert(isequal(sixsixsix(N),M_correct))\r\n%%\r\nN = 7;\r\nM_correct = [666   151515   181818   272727   424242   636363   666666];\r\nassert(isequal(sixsixsix(N),M_correct))\r\n%%\r\nN = 25;\r\nM_correct=[666 151515 181818 272727 424242 636363 666666 757575 878787 909090 105105105 114114114 117117117 138138138 153153153 162162162 165165165 177177177 186186186 210210210 213213213 225225225 234234234 237237237 258258258];\r\nassert(isequal(sixsixsix(N),M_correct))\r\n%%\r\nN = 63;\r\nM_correct = [666 151515 181818 272727 424242 636363 666666 757575 878787 909090 105105105 114114114 117117117 138138138 153153153 162162162 165165165 177177177 186186186 210210210 213213213 225225225 234234234 237237237 258258258 273273273 282282282 285285285 297297297 306306306 330330330 333333333 345345345 354354354 357357357 378378378 393393393 402402402 405405405 417417417 426426426 450450450 453453453 465465465 474474474 477477477 498498498 513513513 522522522 525525525 537537537 546546546 570570570 573573573 585585585 594594594 597597597 618618618 633633633 642642642 645645645 657657657 666666666];\r\nassert(isequal(sixsixsix(N),M_correct))\r\n","published":true,"deleted":false,"likes_count":2,"comments_count":3,"created_by":379,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":24,"test_suite_updated_at":"2014-08-09T09:21:11.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2014-08-09T09:16:38.000Z","updated_at":"2026-01-03T12:55:27.000Z","published_at":"2014-08-09T09:21:11.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eUsing the following definition of the 666 function for this problem:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ef(n)=sin('nnn')-cos(n*n*n)\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, write a function that returns the first N integer zeros of the 666 function, formatted as 'nnn'.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFor example:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003esixsixsix(1) = should return 666\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003esixsixsix(7) should return 666 151515 181818 272727 424242 636363 666666\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eNote 1: Consider a 'zero' to occur when f(n)\u0026lt;1e-8\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eNote 2: The sin and cosine functions must be in degrees, not radians.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":61081,"title":"Slicing the area of a regular polygon","description":"Given the area, A, of a regular polygon with n sides, each of length s, consider its decomposition in congruent isosceles triangles of base s and heigth h. Find the rectangle, with dimensions L×h, which covers all n triangles in their adjacent positions (n\u003e3, cf. figure below). Complete the problem by determining the area, A_r, of the rectangle.\r\nHint: Consider that we are slicing the polygon into triangular slices and put them into the rectangle.\r\ninput: (A, n)\r\noutput: y = [L h A_r]\r\n","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none; white-space: normal; \"\u003e\u003cdiv style=\"block-size: 575.8px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 408px 287.9px; transform-origin: 408px 287.9px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 31.5px; text-align: left; transform-origin: 385px 31.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eGiven the area, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eA\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, of a regular polygon with \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003en\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e sides, each of length \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003es\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, consider its decomposition in congruent isosceles triangles of base \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003es\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and heigth \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eh\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. Find the rectangle, with dimensions \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eL\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e×\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eh\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, which covers all \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003en\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e triangles in their adjacent positions (\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003en\u0026gt;3,\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e cf. figure below). Complete the problem by determining the area, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eA_r\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, of the rectangle.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eHint: Consider that we are slicing the polygon into triangular slices and put them into the rectangle.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003einput:\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e(A, n)\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003eoutput:\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003ey = [L h A_r]\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 413.8px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 206.9px; text-align: left; transform-origin: 385px 206.9px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cimg class=\"imageNode\" width=\"501\" height=\"408\" style=\"vertical-align: baseline;width: 501px;height: 408px\" src=\"data:image/png;base64,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\" alt=\"Slicing square (n=4)\" data-image-state=\"image-loaded\"\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = slicing(A,n)\r\n  y = [L h A_r];\r\nend","test_suite":"%%\r\nA = 16;\r\nn = 4;\r\ny_correct = [10 2 20];\r\nassert(isequal(slicing(A,n),y_correct))\r\n\r\n%%\r\nA = 20;\r\nn = 5; \r\ny_correct = [10.22849568767431 2.34638608968871 24];\r\ntolerance = 1e-13;\r\nassert(all(abs(slicing(A,n)-y_correct)\u003ctolerance))\r\n\r\n%%\r\nfiletext = fileread('slicing.m');\r\nillegal = contains(filetext, 'assignin') || contains(filetext, 'regexp') || ...\r\n          contains(filetext, 'str2num'); \r\nassert(~illegal)\r\n\r\n%%\r\nA = 20;\r\nn = 6; \r\ny_correct = [7*sqrt(10*3^(-3/2)) sqrt(10*3^(-1/2)) 70/3];\r\ntolerance = 1e-13;\r\nassert(all(abs(slicing(A,n)-y_correct)\u003ctolerance))\r\n\r\n%%\r\nA = 32;\r\nn = 8; \r\ny_correct = [18*sqrt(sqrt(2)-1) 2/sqrt(sqrt(2)-1) 36];\r\ntolerance = 1e-13;\r\nassert(all(abs(slicing(A,n)-y_correct)\u003ctolerance))\r\n","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":4993982,"edited_by":4993982,"edited_at":"2025-11-19T14:59:52.000Z","deleted_by":null,"deleted_at":null,"solvers_count":8,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2025-11-18T11:18:12.000Z","updated_at":"2026-03-20T13:59:51.000Z","published_at":"2025-11-19T14:59:52.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGiven the area, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eA\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, of a regular polygon with \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e sides, each of length \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003es\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, consider its decomposition in congruent isosceles triangles of base \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003es\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e and heigth \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eh\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e. Find the rectangle, with dimensions \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eL\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e×\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eh\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, which covers all \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e triangles in their adjacent positions (\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003en\u0026gt;3,\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e cf. figure below). Complete the problem by determining the area, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eA_r\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, of the rectangle.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eHint: Consider that we are slicing the polygon into triangular slices and put them into the rectangle.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003einput:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e(A, n)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eoutput:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ey = [L h A_r]\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"408\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"501\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"baseline\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"Slicing square (n=4)\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId1\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/image\",\"target\":\"/media/image1.png\",\"relationshipId\":\"rId1\"}]},{\"partUri\":\"/media/image1.png\",\"contentType\":\"image/png\",\"content\":\"data:image/png;base64,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\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":60311,"title":"Travel a path","description":"In Cody Problem 60251, minnolina asks us to determine the end point given a string indicating unit movements forward, backward, left, and right. For example, ‘fflff’ brings the marker to the point (-1,4). \r\nThis problem extends that one by specifying a heading (H)—i.e., an angle in degrees measured clockwise from north, or the positive y-direction—and a distance (D) to move. The movement string corresponding to the example above would be ‘H0 D1 H0 D1 H270 D1 H0 D1 H0 D1’.\r\nWrite a function that determines the points, starting at an initial point with coordinates in x0y0, resulting from a movement string. The output should be an nx2 matrix with the x and y coordinates of the points in the columns.","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 165px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 82.5px; transform-origin: 407px 82.5px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 7.775px 8px; transform-origin: 7.775px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eIn \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/60251\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"text-decoration-line: underline; \"\u003eCody Problem 60251\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 298.35px 8px; transform-origin: 298.35px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, minnolina asks us to determine the end point given a string indicating unit movements forward, backward, left, and right. For example, ‘fflff’ brings the marker to the point (-1,4). \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 31.5px; text-align: left; transform-origin: 384px 31.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 384px 8px; transform-origin: 384px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThis problem extends that one by specifying a heading (H)—i.e., an angle in degrees measured clockwise from north, or the positive y-direction—and a distance (D) to move. The movement string corresponding to the example above would be ‘H0 D1 H0 D1 H270 D1 H0 D1 H0 D1’.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 272.15px 8px; transform-origin: 272.15px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function that determines the points, starting at an initial point with coordinates in \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 15.4px 8px; transform-origin: 15.4px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003ex0y0\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 88.675px 8px; transform-origin: 88.675px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, resulting from a movement string. The output should be an nx2 matrix with the x and y coordinates of the points in the columns.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function xy = travelPath(s,x0y0)\r\n% s = movement string of the form 'Hx Dy...', which moves y units with heading x degrees\r\n% x0y0 = [x0 y0], starting point\r\n  xy = x0y0+[cos(s) sin(s)];\r\nend","test_suite":"%% \r\ns = 'H0 D1 H0 D1 H270 D1 H0 D1 H0 D1';\r\nx0y0 = [0,0];\r\nxy = travelPath(s,x0y0);\r\nxy_correct = [0 0; 0 1; 0 2; -1 2; -1 3; -1 4];\r\nassert(all(abs(xy-xy_correct)\u003c1e-12,'all'))\r\n\r\n%% \r\ns = 'H0 D1 H0 D1 H90 D1 H0 D1 H0 D1';\r\nx0y0 = [0,0];\r\nxy = travelPath(s,x0y0);\r\nxy_correct = [0 0; 0 1; 0 2; 1 2; 1 3; 1 4];\r\nassert(all(abs(xy-xy_correct)\u003c1e-12,'all'))\r\n\r\n%% \r\ns = 'H0 D1 H180 D1 H270 D1 H90 D1';\r\nx0y0 = [0,0];\r\nxy = travelPath(s,x0y0);\r\nxy_correct = [0 0; 0 1; 0 0; -1 0; 0 0];\r\nassert(all(abs(xy-xy_correct)\u003c1e-12,'all'))\r\n\r\n%% \r\ns = 'H45 D3 H315 D3 H225 D3 H135 D3';\r\nx0y0 = [1,5];\r\nxy = travelPath(s,x0y0);\r\nxy_correct = [1 5; 3.121320343559643 7.121320343559643; 1 9.242640687119286; -1.121320343559643 7.121320343559643; 1 5];\r\nassert(all(abs(xy-xy_correct)\u003c1e-12,'all'))\r\n\r\n%% \r\ns = 'H10 D5 H20 D4 H30 D3 H40 D2 H50 D1';\r\nx0y0 = [-1 -4];\r\nxy = travelPath(s,x0y0);\r\nxy_correct = [-1 -4; -0.131759111665348 0.924038765061040; 1.236321461637326 4.682809248204673; 2.736321461637326 7.280885459557989; 4.021896681010405 8.812974345795945; 4.787941124129383 9.455761955482485];\r\nassert(all(abs(xy-xy_correct)\u003c1e-12,'all'))\r\n\r\n%% \r\ns = 'H27 D5 H153 D5 H27 D4 H153 D4 H27 D3 H153 D3 H27 D2 H153 D2 H27 D1 H153 D1';\r\nx0y0 = [0 0];\r\nxy = travelPath(s,x0y0);\r\nxy_correct = [0 0; 2.269952498697734 4.455032620941839; 4.539904997395468 0; 6.355866996353655 3.564026096753472; 8.171828995311843 0; 9.533800494530484 2.673019572565104; 10.895771993749124 0; 11.803752993228217 1.782013048376736; 12.711733992707311 0; 13.165724492446857 0.891006524188368; 13.619714992186404 0];\r\nassert(all(abs(xy-xy_correct)\u003c1e-12,'all'))\r\n\r\n%%\r\nx0y0 = 6*rand(1,2);\r\nr = round(8*rand,2);\r\nn = 2+2*randi(5); \r\nth = 360/n;\r\ntheta = th*(0:n-1);\r\ns = '';\r\nfor k = 1:n\r\n    s = [s 'H' num2str(theta(k)) ' D' num2str(r) ' '];\r\nend\r\ns = s(1:end-1);\r\nxy = travelPath(s,x0y0);\r\nassert(all(abs(xy(1,:)-xy(end,:))\u003c1e-12))\r\naxis equal\r\nk = randi(n/2);\r\n[x1,y1,x2,y2] = deal(xy(k,1),xy(k,2),xy(k+n/2,1),xy(k+n/2,2));\r\nassert(abs(hypot(x1-x2,y1-y2)-r/cosd(90*(n-2)/n))\u003c1e-12)\r\n\r\n%%\r\nfiletext = fileread('travelPath.m');\r\nillegal = contains(filetext, 'assignin') || contains(filetext, 'assert'); \r\nassert(~illegal)\r\n","published":true,"deleted":false,"likes_count":0,"comments_count":1,"created_by":46909,"edited_by":46909,"edited_at":"2024-05-15T02:50:53.000Z","deleted_by":null,"deleted_at":null,"solvers_count":4,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2024-05-15T02:48:52.000Z","updated_at":"2024-05-15T02:50:53.000Z","published_at":"2024-05-15T02:50:53.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eIn \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/60251\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eCody Problem 60251\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e, minnolina asks us to determine the end point given a string indicating unit movements forward, backward, left, and right. For example, ‘fflff’ brings the marker to the point (-1,4). \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThis problem extends that one by specifying a heading (H)—i.e., an angle in degrees measured clockwise from north, or the positive y-direction—and a distance (D) to move. The movement string corresponding to the example above would be ‘H0 D1 H0 D1 H270 D1 H0 D1 H0 D1’.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a function that determines the points, starting at an initial point with coordinates in \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ex0y0\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, resulting from a movement string. The output should be an nx2 matrix with the x and y coordinates of the points in the columns.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":1460,"title":"Cosine frequency doubler","description":"Given an input vector containing a cosine wave of unknown frequency, produce an output vector of the same length containing a cosine wave of twice the input frequency.  The output should have the same mean and amplitude as the input.  ","description_html":"\u003cp\u003eGiven an input vector containing a cosine wave of unknown frequency, produce an output vector of the same length containing a cosine wave of twice the input frequency.  The output should have the same mean and amplitude as the input.\u003c/p\u003e","function_template":"function y = SineDublr(x)\r\n  y = x;\r\nend","test_suite":"%%\r\nt = 0:0.001:1;\r\nx = cos(2*pi*5*t);\r\ny_correct = cos(2*pi*10*t);\r\n%assert(isequal(SineDublr(x),y_correct));\r\nassert(sqrt(sum((y_correct-SineDublr(x)).^2))\u003c0.1);\r\n\r\n%%\r\nt = 0:0.002:1;\r\nx = cos(2*pi*15*t)+2;\r\ny_correct = cos(2*pi*30*t)+2;\r\n%assert(isequal(SineDublr(x),y_correct));\r\nassert(sqrt(sum((y_correct-SineDublr(x)).^2))\u003c0.1);\r\n\r\n%%\r\nt = 0:0.001:1;\r\nx = 3*cos(2*pi*35*t)-2;\r\ny_correct = 3*cos(2*pi*70*t)-2;\r\n%assert(isequal(SineDublr(x),y_correct));\r\nassert(sqrt(sum((y_correct-SineDublr(x)).^2))\u003c0.1);\r\n\r\n%%\r\nt = 0:0.001:1;\r\nfreq = floor(rand*100);\r\noffset = floor(rand*10);\r\namp = floor(rand*10);\r\nx = amp*cos(2*pi*freq*t)-offset;\r\ny_correct = amp*cos(2*pi*2*freq*t)-offset;\r\n%assert(isequal(SineDublr(x),y_correct));\r\nassert(sqrt(sum((y_correct-SineDublr(x)).^2))\u003c0.1);","published":true,"deleted":false,"likes_count":2,"comments_count":0,"created_by":13007,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":21,"test_suite_updated_at":"2013-04-25T21:13:33.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2013-04-25T20:47:42.000Z","updated_at":"2026-01-20T14:22:54.000Z","published_at":"2013-04-25T20:47:47.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGiven an input vector containing a cosine wave of unknown frequency, produce an output vector of the same length containing a cosine wave of twice the input frequency. The output should have the same mean and amplitude as the input.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":42306,"title":"Esoteric Trigonometry","description":"From Wikipedia: \"All of the trigonometric functions of an angle θ can be constructed geometrically in terms of a unit circle centered at O. Many of these terms are no longer in common use.\"\r\n\r\n\u003c\u003chttps://i.imgur.com/vVIFB1x.png\u003e\u003e\r\n\r\nNonetheless, suppose you do need to use one of these esoteric trigonometric functions that is not built into Matlab. Write a function that takes an angle as the first input (radians) and the trigonometric function name as the second input (string, function name will be completely spelled out). Make sure your function covers both the esoteric and commonly used functions; then it's a more useful tool. In particular, include sine, cosine, tangent, cosecant, secant, cotangent, versine, vercosine, coversine, covercosine, haversine, havercosine, hacoversine, hacovercosine, exsecant, excosecant, and chord. Formulas for each function are available \u003chttp://en.wikipedia.org/wiki/List_of_trigonometric_identities here\u003e.","description_html":"\u003cp\u003eFrom Wikipedia: \"All of the trigonometric functions of an angle θ can be constructed geometrically in terms of a unit circle centered at O. Many of these terms are no longer in common use.\"\u003c/p\u003e\u003cimg src = \"https://i.imgur.com/vVIFB1x.png\"\u003e\u003cp\u003eNonetheless, suppose you do need to use one of these esoteric trigonometric functions that is not built into Matlab. Write a function that takes an angle as the first input (radians) and the trigonometric function name as the second input (string, function name will be completely spelled out). Make sure your function covers both the esoteric and commonly used functions; then it's a more useful tool. In particular, include sine, cosine, tangent, cosecant, secant, cotangent, versine, vercosine, coversine, covercosine, haversine, havercosine, hacoversine, hacovercosine, exsecant, excosecant, and chord. Formulas for each function are available \u003ca href = \"http://en.wikipedia.org/wiki/List_of_trigonometric_identities\"\u003ehere\u003c/a\u003e.\u003c/p\u003e","function_template":"function y = trig_func_tool(theta,f_name)\r\n \r\nend","test_suite":"%%\r\ntheta = pi/3;\r\nf_name = 'sine';\r\nassert(isequal(trig_func_tool(theta,f_name),sin(theta)))\r\n\r\n%%\r\ntheta = pi/3;\r\nf_name = 'cosine';\r\nassert(isequal(trig_func_tool(theta,f_name),cos(theta)))\r\n\r\n%%\r\ntheta = pi/3;\r\nf_name = 'tangent';\r\nassert(isequal(trig_func_tool(theta,f_name),tan(theta)))\r\n\r\n%%\r\ntheta = pi/3;\r\nf_name = 'cosecant';\r\nassert(isequal(trig_func_tool(theta,f_name),csc(theta)))\r\n\r\n%%\r\ntheta = pi/3;\r\nf_name = 'secant';\r\nassert(isequal(trig_func_tool(theta,f_name),sec(theta)))\r\n\r\n%%\r\ntheta = pi/3;\r\nf_name = 'cotangent';\r\nassert(isequal(trig_func_tool(theta,f_name),cot(theta)))\r\n\r\n%%\r\ntheta = pi/3;\r\nf_name = 'versine';\r\nassert(isequal(trig_func_tool(theta,f_name),1-cos(theta)))\r\n\r\n%%\r\ntheta = pi/3;\r\nf_name = 'vercosine';\r\nassert(isequal(trig_func_tool(theta,f_name),1+cos(theta)))\r\n\r\n%%\r\ntheta = pi/3;\r\nf_name = 'coversine';\r\nassert(isequal(trig_func_tool(theta,f_name),1-sin(theta)))\r\n\r\n%%\r\ntheta = pi/3;\r\nf_name = 'covercosine';\r\nassert(isequal(trig_func_tool(theta,f_name),1+sin(theta)))\r\n\r\n%%\r\ntheta = pi/3;\r\nf_name = 'haversine';\r\nassert(isequal(trig_func_tool(theta,f_name),(1-cos(theta))/2))\r\n\r\n%%\r\ntheta = pi/3;\r\nf_name = 'havercosine';\r\nassert(isequal(trig_func_tool(theta,f_name),(1+cos(theta))/2))\r\n\r\n%%\r\ntheta = pi/3;\r\nf_name = 'hacoversine';\r\nassert(isequal(trig_func_tool(theta,f_name),(1-sin(theta))/2))\r\n\r\n%%\r\ntheta = pi/3;\r\nf_name = 'hacovercosine';\r\nassert(isequal(trig_func_tool(theta,f_name),(1+sin(theta))/2))\r\n\r\n%%\r\ntheta = pi/3;\r\nf_name = 'exsecant';\r\nassert(isequal(trig_func_tool(theta,f_name),sec(theta)-1))\r\n\r\n%%\r\ntheta = pi/3;\r\nf_name = 'excosecant';\r\nassert(isequal(trig_func_tool(theta,f_name),csc(theta)-1))\r\n\r\n%%\r\ntheta = pi/3;\r\nf_name = 'chord';\r\nassert(isequal(trig_func_tool(theta,f_name),2*sin(theta/2)))\r\n\r\n%%\r\ntheta = pi/5;\r\nf_name = 'sine';\r\nassert(isequal(trig_func_tool(theta,f_name),sin(theta)))\r\n\r\n%%\r\ntheta = pi/10;\r\nf_name = 'cosine';\r\nassert(isequal(trig_func_tool(theta,f_name),cos(theta)))\r\n\r\n%%\r\ntheta = pi/2.5;\r\nf_name = 'tangent';\r\nassert(isequal(trig_func_tool(theta,f_name),tan(theta)))\r\n\r\n%%\r\ntheta = 2*pi/3;\r\nf_name = 'cosecant';\r\nassert(isequal(trig_func_tool(theta,f_name),csc(theta)))\r\n\r\n%%\r\ntheta = pi/7;\r\nf_name = 'secant';\r\nassert(isequal(trig_func_tool(theta,f_name),sec(theta)))\r\n\r\n%%\r\ntheta = pi/13;\r\nf_name = 'cotangent';\r\nassert(isequal(trig_func_tool(theta,f_name),cot(theta)))\r\n\r\n%%\r\ntheta = pi/31;\r\nf_name = 'versine';\r\nassert(isequal(trig_func_tool(theta,f_name),1-cos(theta)))\r\n\r\n%%\r\ntheta = pi/1.3;\r\nf_name = 'vercosine';\r\nassert(isequal(trig_func_tool(theta,f_name),1+cos(theta)))\r\n\r\n%%\r\ntheta = pi/3.3;\r\nf_name = 'coversine';\r\nassert(isequal(trig_func_tool(theta,f_name),1-sin(theta)))\r\n\r\n%%\r\ntheta = pi/33;\r\nf_name = 'covercosine';\r\nassert(isequal(trig_func_tool(theta,f_name),1+sin(theta)))\r\n\r\n%%\r\ntheta = pi/0.7;\r\nf_name = 'haversine';\r\nassert(isequal(trig_func_tool(theta,f_name),(1-cos(theta))/2))\r\n\r\n%%\r\ntheta = pi/0.3;\r\nf_name = 'havercosine';\r\nassert(isequal(trig_func_tool(theta,f_name),(1+cos(theta))/2))\r\n\r\n%%\r\ntheta = pi/13;\r\nf_name = 'hacoversine';\r\nassert(isequal(trig_func_tool(theta,f_name),(1-sin(theta))/2))\r\n\r\n%%\r\ntheta = pi/31;\r\nf_name = 'hacovercosine';\r\nassert(isequal(trig_func_tool(theta,f_name),(1+sin(theta))/2))\r\n\r\n%%\r\ntheta = pi/30;\r\nf_name = 'exsecant';\r\nassert(isequal(trig_func_tool(theta,f_name),sec(theta)-1))\r\n\r\n%%\r\ntheta = pi/1.3;\r\nf_name = 'excosecant';\r\nassert(isequal(trig_func_tool(theta,f_name),csc(theta)-1))\r\n\r\n%%\r\ntheta = pi/13;\r\nf_name = 'chord';\r\nassert(isequal(trig_func_tool(theta,f_name),2*sin(theta/2)))","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":26769,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":41,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":26,"created_at":"2015-05-12T17:53:15.000Z","updated_at":"2026-02-19T10:17:18.000Z","published_at":"2015-05-12T17:53:15.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/image\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/media/image1.JPEG\"}],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFrom Wikipedia: \\\"All of the trigonometric functions of an angle θ can be constructed geometrically in terms of a unit circle centered at O. Many of these terms are no longer in common use.\\\"\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"-1\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"-1\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId1\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eNonetheless, suppose you do need to use one of these esoteric trigonometric functions that is not built into Matlab. Write a function that takes an angle as the first input (radians) and the trigonometric function name as the second input (string, function name will be completely spelled out). Make sure your function covers both the esoteric and commonly used functions; then it's a more useful tool. In particular, include sine, cosine, tangent, cosecant, secant, cotangent, versine, vercosine, coversine, covercosine, haversine, havercosine, hacoversine, hacovercosine, exsecant, excosecant, and chord. Formulas for each function are available\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"http://en.wikipedia.org/wiki/List_of_trigonometric_identities\\\"\u003e\u003cw:r\u003e\u003cw:t\u003ehere\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"},{\"partUri\":\"/media/image1.JPEG\",\"contentType\":\"image/JPEG\",\"content\":\"data:image/JPEG;base64,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\"}]}"},{"id":59249,"title":"Compute the total length of lines between all vertices of a regular polygon","description":"Write a function to compute the total length of between all vertices of a regular polygon inscribed in a unit circle. For example, a square in a unit circle would have side length of  and each of the two diagonals would have a length of 2. Therefore, for  the total length is . In the hexagon below, there are 6 lines of length 1 connecting adjacent points, 3 lines of length 2 connecting opposite points, and 6 lines of length  connecting points two away; therefore, for , the total length is . \r\n","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 442.4px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 221.2px; transform-origin: 407px 221.2px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 105.4px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 52.7px; text-align: left; transform-origin: 384px 52.7px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 358.892px 8px; transform-origin: 358.892px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function to compute the total length of between all vertices of a regular polygon inscribed in a unit circle. For example, a square in a unit circle would have side length of \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"23\" height=\"20\" alt=\"sqrt(2)\" style=\"width: 23px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 176.6px 8px; transform-origin: 176.6px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and each of the two diagonals would have a length of 2. Therefore, for \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"36.5\" height=\"18\" alt=\"n = 4\" style=\"width: 36.5px; height: 18px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 56.7833px 8px; transform-origin: 56.7833px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e the total length is \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"66.5\" height=\"20.5\" alt=\"4(1+sqrt(2))\" style=\"width: 66.5px; height: 20.5px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 224.833px 8px; transform-origin: 224.833px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. In the hexagon below, there are 6 lines of length 1 connecting adjacent points, 3 lines of length 2 connecting opposite points, and 6 lines of length \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"23\" height=\"20\" alt=\"sqrt(3)\" style=\"width: 23px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 133.408px 8px; transform-origin: 133.408px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e connecting points two away; therefore, for \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"36.5\" height=\"18\" alt=\"n = 6\" style=\"width: 36.5px; height: 18px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 58.725px 8px; transform-origin: 58.725px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, the total length is \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"66.5\" height=\"20.5\" alt=\"6(2+sqrt(3))\" style=\"width: 66.5px; height: 20.5px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.88333px 8px; transform-origin: 3.88333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 328px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 164px; text-align: left; transform-origin: 384px 164px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cimg class=\"imageNode\" width=\"438\" height=\"328\" style=\"vertical-align: middle;width: 438px;height: 328px\" src=\"data:image/png;base64,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\" alt=\"hexagon\" data-image-state=\"image-loaded\"\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = totalLength(n)\r\n  y = n*(n/2-1+sqrt(n/2));\r\nend","test_suite":"%% Point\r\nn = 1;\r\nassert(abs(totalLength(n))\u003ceps)\r\n\r\n%% Line\r\nn = 2;\r\ny_correct = 2;\r\nassert(abs(totalLength(n)-y_correct)./y_correct\u003c1e-12)\r\n\r\n%% Triangle\r\nn = 3;\r\ny_correct = 3^(3/2);\r\nassert(abs(totalLength(n)-y_correct)./y_correct\u003c1e-12)\r\n\r\n%% Square\r\nn = 4;\r\ny_correct = 4*(1+sqrt(2));\r\nassert(abs(totalLength(n)-y_correct)./y_correct\u003c1e-12)\r\n\r\n%% Hexagon\r\nn = 6;\r\ny_correct = 22.392304845413271;\r\nassert(abs(totalLength(n)-y_correct)./y_correct\u003c1e-12)\r\n\r\n%% Octagon\r\nn = 8;\r\ny_correct = 40.218715937006777;\r\nassert(abs(totalLength(n)-y_correct)./y_correct\u003c1e-12)\r\n\r\n%% Dodecagon\r\nn = 12;\r\ny_correct = 91.149049352701866;\r\nassert(abs(totalLength(n)-y_correct)./y_correct\u003c1e-12)\r\n\r\n%% Heptadecagon\r\nn = 17;\r\ny_correct = 183.4592171734470;\r\nassert(abs(totalLength(n)-y_correct)./y_correct\u003c1e-12)\r\n\r\n%% Icosikaitetragon\r\nn = 24;\r\ny_correct = 366.1692405183716;\r\nassert(abs(totalLength(n)-y_correct)./y_correct\u003c1e-12)\r\n\r\n%% Icosidodecagon\r\nn = 32;\r\ny_correct = 651.3749639995958;\r\nassert(abs(totalLength(n)-y_correct)./y_correct\u003c1e-12)\r\n\r\n%% Heptacontatetragon\r\nn = 74;\r\ny_correct = 3485.606258980444;\r\nassert(abs(totalLength(n)-y_correct)./y_correct\u003c1e-12)\r\n\r\n%% Hectogon\r\nn = 100;\r\ny_correct = 6365.674116287712;\r\nassert(abs(totalLength(n)-y_correct)./y_correct\u003c1e-12)\r\n\r\n%% ?-gon\r\nn = floor(totalLength(21));\r\ny_correct = 49910.46655373736;\r\nassert(abs(totalLength(n)-y_correct)./y_correct\u003c1e-12)\r\n\r\n%%\r\na = floor(totalLength(1:1000));\r\nassert(isequal(sum(a),212524005))\r\nassert(isequal(max(a),636619))\r\nassert(isequal(sum(a(isprime(a))),15303427))\r\nassert(isequal(a(mod(a,171)==0),[0 66006 119358 191178 225378 393300]))\r\n\r\n%%\r\nfiletext = fileread('totalLength.m');\r\nillegal = contains(filetext, 'assignin') || contains(filetext, 'assert') || contains(filetext, 'regexp'); \r\nassert(~illegal)","published":true,"deleted":false,"likes_count":0,"comments_count":7,"created_by":46909,"edited_by":46909,"edited_at":"2023-12-03T18:16:16.000Z","deleted_by":null,"deleted_at":null,"solvers_count":8,"test_suite_updated_at":"2023-12-03T18:16:16.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2023-12-02T17:23:24.000Z","updated_at":"2026-01-04T09:44:09.000Z","published_at":"2023-12-02T17:29:06.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a function to compute the total length of between all vertices of a regular polygon inscribed in a unit circle. For example, a square in a unit circle would have side length of \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"sqrt(2)\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\sqrt{2}\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and each of the two diagonals would have a length of 2. Therefore, for \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"n = 4\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en=4\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e the total length is \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"4(1+sqrt(2))\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e4(1+\\\\sqrt{2})\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. In the hexagon below, there are 6 lines of length 1 connecting adjacent points, 3 lines of length 2 connecting opposite points, and 6 lines of length \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"sqrt(3)\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\sqrt{3}\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e connecting points two away; therefore, for \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"n = 6\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en = 6\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, the total length is \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"6(2+sqrt(3))\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e6(2+\\\\sqrt{3})\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"328\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"438\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"middle\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"hexagon\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId1\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/image\",\"target\":\"/media/image1.png\",\"relationshipId\":\"rId1\"}]},{\"partUri\":\"/media/image1.png\",\"contentType\":\"image/png\",\"content\":\"data:image/png;base64,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\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":44492,"title":"Approximate the cosine function ","description":"Without using MATLAB trigonometric functions, calculate the cosine of an argument x to a precision of 0.0001\r\nHint: You may wish to consider the cosine Maclaurin series.","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 51.5px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 25.75px; transform-origin: 407px 25.75px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21.5px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.75px; text-align: left; transform-origin: 384px 10.75px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 262px 8px; transform-origin: 262px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWithout using MATLAB trigonometric functions, calculate the cosine of an argument\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 2px 8px; transform-origin: 2px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 4px 8px; transform-origin: 4px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; perspective-origin: 4px 8.5px; transform-origin: 4px 8.5px; \"\u003ex\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 52.5px 8px; transform-origin: 52.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e to a precision of\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 2px 8px; transform-origin: 2px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 24px 8px; transform-origin: 24px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; perspective-origin: 24px 8.5px; transform-origin: 24px 8.5px; \"\u003e0.0001\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 16px 8px; transform-origin: 16px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eHint:\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 93.5px 8px; transform-origin: 93.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e You may wish to consider the\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 2px 8px; transform-origin: 2px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://en.wikipedia.org/wiki/Taylor_series#Trigonometric_functions\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003ecosine Maclaurin series\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 2px 8px; transform-origin: 2px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = myCos(x)\r\n    y = 1 - 0.5*x^2;\r\nend","test_suite":"%%\r\nfiletext = fileread('myCos.m');\r\nassert(isempty(strfind(filetext, 'regexp')),'regexp hacks are forbidden')\r\n\r\n\r\n%%\r\nfiletext = fileread('myCos.m');\r\ntrigUsed = any(strfind(filetext, 'cos')) || any(strfind(filetext, 'sin')) ||...\r\n     any(strfind(filetext, 'sec')) || any(strfind(filetext, 'tan')) || any(strfind(filetext, 'cot'));\r\nassert(~trigUsed, 'Cannot use MATLAB trigonometric functions')\r\n\r\n%%\r\nx = 0;\r\nassert(abs(myCos(x)-cos(x)) \u003c 0.0001)\r\n\r\n%%\r\nx = pi;\r\nassert(abs(myCos(x)-cos(x)) \u003c 0.0001)\r\n\r\n%%\r\nx = pi/2;\r\nassert(abs(myCos(x)-cos(x)) \u003c 0.0001)\r\n\r\n%%\r\nx = 5*pi/3;\r\nassert(abs(myCos(x)-cos(x)) \u003c 0.0001)\r\n","published":true,"deleted":false,"likes_count":1,"comments_count":3,"created_by":140356,"edited_by":223089,"edited_at":"2022-10-17T13:07:34.000Z","deleted_by":null,"deleted_at":null,"solvers_count":343,"test_suite_updated_at":"2022-10-17T13:07:34.000Z","rescore_all_solutions":false,"group_id":61,"created_at":"2018-01-07T23:20:12.000Z","updated_at":"2026-02-11T20:08:56.000Z","published_at":"2018-01-07T23:20:12.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWithout using MATLAB trigonometric functions, calculate the cosine of an argument\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ex\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e to a precision of\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e0.0001\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eHint:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e You may wish to consider the\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://en.wikipedia.org/wiki/Taylor_series#Trigonometric_functions\\\"\u003e\u003cw:r\u003e\u003cw:t\u003ecosine Maclaurin series\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":60301,"title":"Compute the area of a lune","description":"Write a function to compute the area of the shaded moon-shaped region in the figure below—that is, the area of a smaller circle that does not overlap with a larger circle. The input will be the radius  of the smaller circle, the radius  of the larger circle, and the separation  between centers of the circles. \r\n","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 405.7px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 202.85px; transform-origin: 407px 202.85px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 31.5px; text-align: left; transform-origin: 384px 31.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 377.175px 8px; transform-origin: 377.175px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function to compute the area of the shaded moon-shaped region in the figure below—that is, the area of a smaller circle that does not overlap with a larger circle. The input will be the radius \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003ea\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 98.7917px 8px; transform-origin: 98.7917px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e of the smaller circle, the radius \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eb\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 41.225px 8px; transform-origin: 41.225px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e of the larger circle, and the separation \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003ec\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 98.4px 8px; transform-origin: 98.4px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e between centers of the circles. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 333.7px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 166.85px; text-align: left; transform-origin: 384px 166.85px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cimg class=\"imageNode\" width=\"438\" height=\"328\" style=\"vertical-align: baseline;width: 438px;height: 328px\" src=\"data:image/png;base64,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\" data-image-state=\"image-loaded\"\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = luneArea(a,b,c)\r\n%  a = radius of smaller circle\r\n%  b = radius of larger circle\r\n%  c = distance between the centers of the circles\r\n   y = (b-a)*(b+c)/2;\r\nend","test_suite":"%%\r\na = 1; \r\nb = 1.2;\r\nc = 0.9; \r\nA = luneArea(a,b,c);\r\nA_correct = 1.285341014608472;\r\nassert(abs(A-A_correct)/A_correct\u003c1e-13)\r\n\r\n%%\r\na = 4; \r\nb = 5;\r\nc = 3; \r\nA = luneArea(a,b,c);\r\nA_correct = 13.950360778678039;\r\nassert(abs(A-A_correct)/A_correct\u003c1e-13)\r\n\r\n%%\r\na = exp(1); \r\nb = pi;\r\nc = -psi(1); \r\nA = luneArea(a,b,c);\r\nA_correct = 0.443456401155954;\r\nassert(abs(A-A_correct)/A_correct\u003c1e-13)\r\n\r\n%%\r\na = 3; \r\nb = 4;\r\nc = 1.01; \r\nA = luneArea(a,b,c);\r\nA_correct = 0.0065019633283;\r\nassert(abs(A-A_correct)/A_correct\u003c8e-12)\r\n\r\n%%\r\na = 1/sqrt(2); \r\nb = 1;\r\nc = a; \r\nA = luneArea(a,b,c);\r\nA_correct = 1/2;\r\nassert(abs(A-A_correct)/A_correct\u003c1e-13)\r\n\r\n%% \r\na = 5*rand;\r\nb = a*sqrt(2);\r\nc = a; \r\nA = luneArea(a,b,c);\r\nA_correct = b^2/2;\r\nassert(abs(A-A_correct)/A_correct\u003c1e-13)","published":true,"deleted":false,"likes_count":1,"comments_count":2,"created_by":46909,"edited_by":46909,"edited_at":"2024-06-01T23:28:36.000Z","deleted_by":null,"deleted_at":null,"solvers_count":8,"test_suite_updated_at":"2024-06-01T23:28:36.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2024-05-13T12:25:08.000Z","updated_at":"2026-01-04T10:52:42.000Z","published_at":"2024-05-13T12:25:26.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a function to compute the area of the shaded moon-shaped region in the figure below—that is, the area of a smaller circle that does not overlap with a larger circle. The input will be the radius \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ea\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e of the smaller circle, the radius \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eb\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e of the larger circle, and the separation \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ec\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e between centers of the circles. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"328\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"438\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"baseline\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId1\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/image\",\"target\":\"/media/image1.png\",\"relationshipId\":\"rId1\"}]},{\"partUri\":\"/media/image1.png\",\"contentType\":\"image/png\",\"content\":\"data:image/png;base64,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\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":1257,"title":"PONG 001: Player  vs Wall, 4 Lives, Interactive download","description":"Variation of the Original Classic PONG game brought to Cody.\r\n\r\nAttempt to keep the ball alive against a Wall. The ball speeds up on every hit. When it is missed it restarts at a new location. The start locations and sequences are purely deterministic. Movement of the paddle are max up/down steps of -1 to 1 (effective delta 50) or no move. Partial paddle moves allowed.\r\n\r\nPaddle center is provided and paddle covers +/- 50 units.\r\nThe field is square at 1000 by 1000 with 3 walls and the lower left corner being (0,0)\r\n\r\nTo aid in development of your routine, a PONG_Interactive_001a.m file that creates a solver script and video has been posted at \u003chttps://sites.google.com/site/razapor/matlab_cody/PONG_Interactive_001a.m PONG_Interactive_001a.m\u003e. (Right click, 'save link as'). The routine creates a PONG_001_solver.m script from the interactive play. The script demonstrates Interactivity, figure/KeyPressFcn, listdlg, and VideoWriter.\r\n\r\n\r\n\u003chttps://sites.google.com/site/razapor/matlab_cody/PONG_001_video_63_185.mp4 PONG Interactive 63 Returns\u003e (MP4)\r\n\r\n\r\n\r\n*Inputs:* (paddle,ball)  \r\n \r\n   paddle = 500 ; Paddle Center on the Y-axis, Paddle is +/- 50 from center\r\n   ball=[500 500 40 60]; % x y vx vy  Posiiton and Velocity, Treated as a Point\r\n\r\n*Output:* Direction\r\n\r\n   1 Up, -1 is Down, 0-No move\r\n   Paddle moves 50*direction, half paddle step. abs(direction)\u003c=1 is allowed\r\n\r\n*Pass Criteria:* 10 hits, a score of 450 or better\r\n\r\n*Scoring:* 100 - 5 * Hits + 100 * Lives,  (500 - 5 * hits  for \u003c 100 hits)\r\n\r\n*Game Theory:* Position Paddle to minimize travel to next location. Vx=1.1*Vx and Vy=1.05*Vy after every return.\r\n\r\n*Near Future:* Paddle vs Paddle (Mirror). Followed by Angle varation based on Paddle/Ball Position","description_html":"\u003cp\u003eVariation of the Original Classic PONG game brought to Cody.\u003c/p\u003e\u003cp\u003eAttempt to keep the ball alive against a Wall. The ball speeds up on every hit. When it is missed it restarts at a new location. The start locations and sequences are purely deterministic. Movement of the paddle are max up/down steps of -1 to 1 (effective delta 50) or no move. Partial paddle moves allowed.\u003c/p\u003e\u003cp\u003ePaddle center is provided and paddle covers +/- 50 units.\r\nThe field is square at 1000 by 1000 with 3 walls and the lower left corner being (0,0)\u003c/p\u003e\u003cp\u003eTo aid in development of your routine, a PONG_Interactive_001a.m file that creates a solver script and video has been posted at \u003ca href=\"https://sites.google.com/site/razapor/matlab_cody/PONG_Interactive_001a.m\"\u003ePONG_Interactive_001a.m\u003c/a\u003e. (Right click, 'save link as'). The routine creates a PONG_001_solver.m script from the interactive play. The script demonstrates Interactivity, figure/KeyPressFcn, listdlg, and VideoWriter.\u003c/p\u003e\u003cp\u003e\u003ca href=\"https://sites.google.com/site/razapor/matlab_cody/PONG_001_video_63_185.mp4\"\u003ePONG Interactive 63 Returns\u003c/a\u003e (MP4)\u003c/p\u003e\u003cp\u003e\u003cb\u003eInputs:\u003c/b\u003e (paddle,ball)\u003c/p\u003e\u003cpre\u003e   paddle = 500 ; Paddle Center on the Y-axis, Paddle is +/- 50 from center\r\n   ball=[500 500 40 60]; % x y vx vy  Posiiton and Velocity, Treated as a Point\u003c/pre\u003e\u003cp\u003e\u003cb\u003eOutput:\u003c/b\u003e Direction\u003c/p\u003e\u003cpre\u003e   1 Up, -1 is Down, 0-No move\r\n   Paddle moves 50*direction, half paddle step. abs(direction)\u0026lt;=1 is allowed\u003c/pre\u003e\u003cp\u003e\u003cb\u003ePass Criteria:\u003c/b\u003e 10 hits, a score of 450 or better\u003c/p\u003e\u003cp\u003e\u003cb\u003eScoring:\u003c/b\u003e 100 - 5 * Hits + 100 * Lives,  (500 - 5 * hits  for \u0026lt; 100 hits)\u003c/p\u003e\u003cp\u003e\u003cb\u003eGame Theory:\u003c/b\u003e Position Paddle to minimize travel to next location. Vx=1.1*Vx and Vy=1.05*Vy after every return.\u003c/p\u003e\u003cp\u003e\u003cb\u003eNear Future:\u003c/b\u003e Paddle vs Paddle (Mirror). Followed by Angle varation based on Paddle/Ball Position\u003c/p\u003e","function_template":"function pdir = PONG_001_solver(paddle,ball)\r\n %  paddle=500; % position y % min max paddle [50 950]\r\n %  ball=[500 500 40 60]; % x y vx vy  Treated as a Point\r\n %\r\n % Output Paddle movement : pdir range [-1 1]\r\n %\r\n % Paddle Size is +/- 50 from paddle value\r\n % Predict ball location and move to within +/- 50\r\n % or Load PONG_001_solver.m from Interactive Play with file create\r\n \r\npdir = randi([-1 1]);\r\n \r\n \r\n","test_suite":"%%\r\nfeval(@assignin,'caller','score',500);\r\n\r\n pwidth=50; % Total size +/- 50 for 101 Paddle\r\n bwidth=10; % Radius of ball\r\n\r\n vup=10; % Sub-sampling ball movements for Interactive\r\n spfx=1.10; % Speed increase factor\r\n spfy=1.05; % to Avoid fixed Paddle solution\r\n negVmax=-200;\r\n posVmax=210;\r\n mov_step=50; % Paddle Quantized Movement  (1/2 Paddle)\r\n maxLives=4;\r\n maxHits=100;\r\n\r\n% Initial Start\r\n paddle=500; % position y % min max paddle [50 950]\r\n ball=[500 500 40 60]; % x y vx vy  Treated as a Point\r\n\r\nlives=0; % Lives\r\nhits=0;\r\nentry=0;\r\n\r\nwhile lives\u003cmaxLives \u0026\u0026 hits\u003cmaxHits\r\n\r\n [curdir]=PONG_001_solver(paddle,ball); % FUNCTION CALL\r\n\r\n if abs(curdir)\u003e1,curdir=0;end % Max 1 / -1 allowed\r\n curmov=mov_step*curdir;\r\n\r\n if entry==0\r\n  curdirvec=curdir;\r\n  entry=1;\r\n else\r\n  curdirvec=[curdirvec curdir]; % Saving moves for file create\r\n end\r\n\r\n% Paddle Move\r\n paddle=max(pwidth,min(1000-pwidth,paddle+curmov)); % [50 : 950] limits\r\n\r\n% Ball Move : Hopefully I got the Mirror solutions right\r\n\r\n  for j=1:vup\r\n    % ball=[500 500 1 1]; % x y vx vy  Treated as a Point\r\n\r\n    if ball(1)+ball(3)/vup\u003c=0 % Check if Point is Over\r\n\r\n    % Find x=0 crossing and check if paddle is within\r\n    % [paddle-pwidth-bwidth,paddle+pwidth+bwidth] pwidth=50; \r\n    % set speed scalar\r\n    \r\n      xc=ball(2)-ball(1)*ball(4)/ball(3);\r\n      if xc\u003e=1000\r\n       xc=1000-(xc-1000);\r\n      else\r\n       xc=abs(xc);\r\n      end\r\n      \r\n      paddlemax= paddle+pwidth+bwidth;\r\n      paddlemin= paddle-pwidth-bwidth;\r\n      \r\n      if xc\u003epaddlemax || xc\u003cpaddlemin % Swing and a Miss\r\n       lives=lives+1;\r\n       fprintf('Oops %i\\n',lives);\r\n       \r\n       if lives\u003e=maxLives,break;end\r\n       % draw ball\r\n       %paddle=500; % position y % min max paddle [50 950]\r\n\r\n       % Reset Ball Keep deterministic but different\r\n       ball=[500-100*lives 500 40+11*lives 35-3*lives];\r\n\r\n       break;\r\n      end\r\n      \r\n      \r\n      % Ball returned\r\n      hits=hits+1;\r\n      ball(1:2)=ball(1:2)+ball(3:4)/vup;\r\n      \r\n      ball(1)=-ball(1);\r\n      ball(3)=-spfx*ball(3);\r\n      \r\n      if ball(2)\u003c0\r\n       ball(2)=-ball(2);\r\n       ball(4)=-spfy*ball(4);\r\n      elseif ball(2)\u003e1000\r\n       ball(2)=2000-ball(2);\r\n       ball(4)=-spfy*ball(4);\r\n      else\r\n       ball(4)=spfy*ball(4);\r\n      end\r\n      \r\n      ball(3)=max(negVmax,min(posVmax,ball(3)));\r\n      ball(4)=max(negVmax,min(posVmax,ball(4)));\r\n      \r\n    else % Wall bounces\r\n     ball(1:2)=ball(1:2)+ball(3:4)/vup;\r\n     \r\n     if ball(1)\u003e=1000 % To the right\r\n      ball(1)=1000-(ball(1)-1000);\r\n      ball(3)=-ball(3);\r\n      if ball(2)\u003e=1000 % TR\r\n       ball(2)=1000-(ball(2)-1000);\r\n       ball(4)=-ball(4);\r\n      elseif ball(2)\u003c=0 % BR\r\n       ball(2)=-ball(2); % abs\r\n       ball(4)=-ball(4);\r\n      end\r\n     else % Middle\r\n      if ball(2)\u003e=1000 % TM\r\n       ball(2)=1000-(ball(2)-1000);\r\n       ball(4)=-ball(4);\r\n      elseif ball(2)\u003c=0 % BM\r\n       ball(2)=-ball(2); % abs\r\n       ball(4)=-ball(4);\r\n      end\r\n     end\r\n    \r\n     \r\n    end % Ball Pass / New Position\r\n\r\n  end % j vup\r\n\r\n\r\nend % while Alive and Hits \u003c Total Success\r\n\r\n%fprintf('%i ',curdirvec);fprintf('\\n'); % Moves\r\nfprintf('Hits %i\\n',hits)\r\nfprintf('Lives %i\\n',lives)\r\nscore= max(0,maxHits-5*hits+100*lives); % \r\n \r\nfprintf('Score %i\\n',score)\r\n% Passing Score is 10 hits to Score 450 or Less\r\n\r\nassert(score\u003c=450,sprintf('Score %i\\n',score))\r\n\r\n\r\nfeval( @assignin,'caller','score',floor(min( 500,score )) );","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":3097,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":16,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":33,"created_at":"2013-02-10T05:51:19.000Z","updated_at":"2026-02-07T15:54:36.000Z","published_at":"2013-02-10T06:57:18.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eVariation of the Original Classic PONG game brought to Cody.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eAttempt to keep the ball alive against a Wall. The ball speeds up on every hit. When it is missed it restarts at a new location. The start locations and sequences are purely deterministic. Movement of the paddle are max up/down steps of -1 to 1 (effective delta 50) or no move. Partial paddle moves allowed.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ePaddle center is provided and paddle covers +/- 50 units. The field is square at 1000 by 1000 with 3 walls and the lower left corner being (0,0)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eTo aid in development of your routine, a PONG_Interactive_001a.m file that creates a solver script and video has been posted at\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://sites.google.com/site/razapor/matlab_cody/PONG_Interactive_001a.m\\\"\u003e\u003cw:r\u003e\u003cw:t\u003ePONG_Interactive_001a.m\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e. (Right click, 'save link as'). The routine creates a PONG_001_solver.m script from the interactive play. The script demonstrates Interactivity, figure/KeyPressFcn, listdlg, and VideoWriter.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:hyperlink w:docLocation=\\\"https://sites.google.com/site/razapor/matlab_cody/PONG_001_video_63_185.mp4\\\"\u003e\u003cw:r\u003e\u003cw:t\u003ePONG Interactive 63 Returns\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e (MP4)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eInputs:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e (paddle,ball)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[   paddle = 500 ; Paddle Center on the Y-axis, Paddle is +/- 50 from center\\n   ball=[500 500 40 60]; % x y vx vy  Posiiton and Velocity, Treated as a Point]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eOutput:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e Direction\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[   1 Up, -1 is Down, 0-No move\\n   Paddle moves 50*direction, half paddle step. abs(direction)\u003c=1 is allowed]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ePass Criteria:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e 10 hits, a score of 450 or better\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eScoring:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e 100 - 5 * Hits + 100 * Lives, (500 - 5 * hits for \u0026lt; 100 hits)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eGame Theory:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e Position Paddle to minimize travel to next location. Vx=1.1*Vx and Vy=1.05*Vy after every return.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eNear Future:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e Paddle vs Paddle (Mirror). Followed by Angle varation based on Paddle/Ball Position\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":59501,"title":"Compute the sum of distances from a point to the sides of an equilateral triangle","description":"Write a function to compute the sum of the (shortest) distances from a point inside an equilateral triangle to the sides of the triangle. That is, for the triangle below, compute the sum . Input will consist of the point (x0,y0) and vectors x and y with the coordinates of the vertices of the triangle. \r\n","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 565.7px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 282.85px; transform-origin: 407px 282.85px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 31.5px; text-align: left; transform-origin: 384px 31.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 381.433px 8px; transform-origin: 381.433px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function to compute the sum of the (shortest) distances from a point inside an equilateral triangle to the sides of the triangle. That is, for the triangle below, compute the sum \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAHUAAAAkCAYAAAC31nXuAAAEcElEQVR4Xu1aOYtUQRDe/QHiGYmRR7AYKKgIooGCBwqiKKix4JmJeGceoGAisiporIKiCIoHaKAmXigiBh6RGHniD9Dvk66lXk/3m377uvftvO2Gj5md11NdVV9VdVfP9vfl0ToP9LfOomxQXya1hUGQSc2kttADLTQpZ2omtWc9MBmaDwCzgXfAk561JEDxtmfqYvjgCLBS+WJJJjUgMnpgyl1FbNsDecy0NM9B6nzgHrCqB4KwloqjKWr/Gkvm4vVNLauKX56OPz+Zj3bg9UJE2VoUS/1j4CcwKdEaQWLHAqmb4YnLiQImk9olzFJl6hWsu2kEMqhnM3UOnDMOeA98NyTRmK/A56Da4J+UitQfWHIicA7YZZaXFod/alvqmDCSpHJLmQr8ATq2qpDySwdsBQ4A94FXwDLgJXAoYllLQSqD8LXRcQteHwBHgZ2KPe6BB4G6e21qUknkXmAFcBX4bTh5ZoJ1KKm6kUqnXAdmAPoAQ6K/GcfEOhikIHUfdDxp9KQNdAYPTWeBacAgwCzmqHtAS0mq2EH9dwNSJT8abnQVKm1pSOgjY7TLYCGhIFBlQNW3KUjVrQwD8SKgM1Ifovbj2amqSqv5qUhl4LGykFDqK0Of6gvPfJmqCWXZ4mFDD52prucu38h+7PMb2wEOyvtS4tzQKz67mjD4DltyhQh+fMLx3FaD832DV5DnAVautSXznPugZ75kKGXOAiRDZfp2vBkPXNLPfKRKhL/A5AWOBVfjs9vm8ymOxVw66ludEptLH1Up9ToLWXJndrEjpIeVajJc/fk9O+N8sobdX7tI1c5YgxXvOFaVkuAj3aXocXw4r8Qbcj9LmXZEytd+4Y0uQWXOFR05x2cHdapy2GNg+gYrA2+tOHhz5RsP8SCkzGv9u519Cmu5Jsvm64tuHUEhJSs0qmPvqdLK+OygXmJrjOvD2Huq6F8lcf772iZVtwA+wnQExfzFIyap2g5fWdUVKYYdMUkN4cGbLDap3Hi52ftKlj5YcE7ofhqSrTFJ1XawlbEvRlgqPwBsZ+qeesW2mKRWPcCVll/d19n7kJyIeQHBazcpC4x4nsDqNu8xSZVDma/0yvPQQ0tIUMYkVW9xvpaRgbkRuAYUziB2pupTrS6/VPgWsBSQywg+fwscAxbagkO8YM2JRapuZez9iM/kRilWf50iUylTn21s/5J0BuRpwG43nZcPIoyC6RQOljASyntGcT7bC27mMQjlGrFIpcHUm6WVr/z9lJHMgD0D8Gcx9pGh/a4Ve94/Y2YqF9ElmATyFoxjEbAN2GD46FDIdfplNO8B2H6whbgJ6GjgfrUeuAF0pH6oBxzzYpFK0bRhObAOmGDW4l31U8DVotVQe+irsUmlYAYo792lFRQ+eIfta/tG1X8+cD/nYKDU/cUnBklVZZAA7nEcIX1oVfnB8ys1tcFS88RGPZBJbdT9aRbPpKbxa6NSM6mNuj/N4pnUNH5tVGomtVH3p1k8k5rGr41KzaQ26v40i/8DCd4INNEnsWsAAAAASUVORK5CYII=\" width=\"58.5\" height=\"18\" alt=\"a+b+c\" style=\"width: 58.5px; height: 18px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 95.675px 8px; transform-origin: 95.675px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. Input will consist of the point (\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 7.7px 8px; transform-origin: 7.7px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003ex0\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.94167px 8px; transform-origin: 1.94167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e,\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 7.7px 8px; transform-origin: 7.7px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003ey0\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 42.3917px 8px; transform-origin: 42.3917px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e) and vectors \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.85px 8px; transform-origin: 3.85px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003ex\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 15.5583px 8px; transform-origin: 15.5583px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.85px 8px; transform-origin: 3.85px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003ey\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0.241667px 8px; transform-origin: 0.241667px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e with the coordinates of the vertices of the triangle. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 493.7px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 246.85px; text-align: left; transform-origin: 384px 246.85px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cimg class=\"imageNode\" width=\"495\" height=\"488\" style=\"vertical-align: baseline;width: 495px;height: 488px\" src=\"data:image/png;base64,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\" alt=\"equilateral triangle with distances from a point\" data-image-state=\"image-loaded\"\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function d = sumdist(x,y,x0,y0)\r\n%  x,y = coordinates of the triangle's vertices\r\n%  x0,y0 = coordinates of the point in the interior of the triangle\r\n  d = sum(hypot(x-x0,y-y0));\r\nend","test_suite":"%%\r\nx = [1 6.215999461960969 2.397622843553612];\r\ny = [2 3.397622843553612 7.215999461960969];\r\nx0 = 2.1;\r\ny0 = 3.2;\r\nd = sumdist(x,y,x0,y0);\r\nd_correct = 4.676537180435970;\r\nassert(abs(d-d_correct)/d_correct \u003c 1e-8)\r\n\r\n%%\r\nx = [1   4.284147809382832  3.404163056034262];\r\ny = [-2 -2.879984753348571  0.404163056034262];\r\nx0 = 3;\r\ny0 = -1;\r\nd = sumdist(x,y,x0,y0);\r\nd_correct = 2.944486372867091;\r\nassert(abs(d-d_correct)/d_correct \u003c 1e-8)\r\n\r\n%%\r\nx = [1   1.292541480647668  0.910019578262454];\r\ny = [-2 -1.727200655975001 -1.610251974085906];\r\nx0 = 1.1;\r\ny0 = -1.8;\r\nd = sumdist(x,y,x0,y0);\r\nd_correct = 0.346410161513776;\r\nassert(abs(d-d_correct)/d_correct \u003c 1e-8)\r\n\r\n%%\r\nx = [-4  0.854101966249685 -4.627170779605921];\r\ny = [-8 -4.473288486245162 -2.032868627790361];\r\nx0 = -2;\r\ny0 = -4;\r\nd = sumdist(x,y,x0,y0);\r\nd_correct = 5.196152422706631;\r\nassert(abs(d-d_correct)/d_correct \u003c 1e-8)\r\n\r\n%%\r\nxr = 100*rand; yr = 100*rand; s  = 100*rand;\r\nx = xr+s*[-4  0.854101966249685 -4.627170779605921];\r\ny = yr+s*[-8 -4.473288486245162 -2.032868627790361];\r\nx0 = mean(x);\r\ny0 = mean(y);\r\nd = sumdist(x,y,x0,y0);\r\nd_correct = 5.196152422706631*s;\r\nassert(abs(d-d_correct)/d_correct \u003c 1e-8)\r\n\r\n%%\r\nx = [0 0.819152044288992 -0.087155742747658];\r\ny = [0 0.573576436351046  0.996194698091746];\r\nx0 = 0.2;\r\ny0 = 0.4;\r\nd = sumdist(x,y,x0,y0);\r\nd_correct = 0.866025403784439;\r\nassert(abs(d-d_correct)/d_correct \u003c 1e-8)\r\n\r\n%%\r\nfiletext = fileread('sumdist.m');\r\nillegal = contains(filetext, 'assignin') || contains(filetext, 'assert') || contains(filetext,'regexp'); \r\nassert(~illegal)","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":46909,"edited_by":46909,"edited_at":"2023-12-28T05:22:29.000Z","deleted_by":null,"deleted_at":null,"solvers_count":6,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2023-12-28T05:22:00.000Z","updated_at":"2023-12-28T05:22:29.000Z","published_at":"2023-12-28T05:22:07.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a function to compute the sum of the (shortest) distances from a point inside an equilateral triangle to the sides of the triangle. That is, for the triangle below, compute the sum \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"a+b+c\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ea+b+c\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. Input will consist of the point (\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ex0\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e,\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ey0\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e) and vectors \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ex\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ey\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e with the coordinates of the vertices of the triangle. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"488\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"495\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"baseline\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"equilateral triangle with distances from a point\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId1\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/image\",\"target\":\"/media/image1.png\",\"relationshipId\":\"rId1\"}]},{\"partUri\":\"/media/image1.png\",\"contentType\":\"image/png\",\"content\":\"data:image/png;base64,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\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":57512,"title":"Easy Sequences 89: Double Summation of a Trigonometric Product","description":"Given and angle  in radians and a positive integer , evaluate the following product summation:\r\n                    \r\nwhich 'directly' translates to Matlab as:\r\n    \u003e\u003e PS = @(A,x) sum(arrayfun(@(n) sum(arrayfun(@(m) prod(arrayfun(@(k) 2*sin(k*pi/m+A),0:m-1)),1:n)),1:x));\r\nFor example  and :\r\n    \u003e\u003e x = 3; A = 1;\r\n    \u003e\u003e PS(A,x)\r\n    ans =\r\n        8.9683\r\nPlease present your answer rounded-off to nearest 4 decimal places.","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.440001px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none; white-space: normal; \"\u003e\u003cdiv style=\"block-size: 288px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 492.078125px 144px; transform-origin: 492.078125px 144px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eGiven and angle \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eA\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e in radians and a positive integer \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003ex\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e, evaluate the following product summation:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 46px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 23px; text-align: left; transform-origin: 384px 23px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e                    \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-17px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"236\" height=\"46\" style=\"width: 236px; height: 46px;\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003ewhich 'directly' translates to Matlab as:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgb(247, 247, 247); block-size: 20px; border-bottom-left-radius: 4px; border-bottom-right-radius: 4px; border-end-end-radius: 4px; border-end-start-radius: 4px; border-start-end-radius: 4px; border-start-start-radius: 4px; border-top-left-radius: 4px; border-top-right-radius: 4px; margin-block-end: 10px; margin-block-start: 10px; margin-bottom: 10px; margin-inline-end: 3px; margin-inline-start: 3px; margin-left: 3px; margin-right: 3px; margin-top: 10px; perspective-origin: 489.078125px 10px; transform-origin: 489.078125px 10px; margin-left: 3px; margin-top: 10px; margin-bottom: 10px; margin-right: 3px; \"\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e    \u0026gt;\u0026gt; PS = @(A,x) sum(arrayfun(@(n) sum(arrayfun(@(m) prod(arrayfun(@(k) 2*sin(k*pi/m+A),0:m-1)),1:n)),1:x));\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 10px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 10px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 10px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eFor example \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAEkAAAAkCAYAAADFGRdYAAAAAXNSR0IArs4c6QAAAERlWElmTU0AKgAAAAgAAYdpAAQAAAABAAAAGgAAAAAAA6ABAAMAAAABAAEAAKACAAQAAAABAAAASaADAAQAAAABAAAAJAAAAABLVRfgAAADDUlEQVRoBe2YW4hNURjHDyGkQe5GaVxTSjyQogmTS7yM24M3vHhyefAipXhAIVLyIJQ8KUqSEi/EvLgWHlzKPcnInXL7/af9TWuOtffsfY7pzJ6zvvqd9e21vrXOWv+9bucUCsGCAkGBoEBQIFcKdMtVb8vv7CyamA4T4SVchyb4BFVvtShwDv54kFiToaqtL6O/BRLoBpyKUlewZvIGQNXafkb+DVYWKVDH8z0wsZYWlVfNYw0j1X7TGDPiFeSbSHtiYgrd4wq6SP4YxqGZdCZmPG+c/KeOH1xHga34mkm/YJKT38bt0ebp34c+ZDXAVFBDB+AzmC3AUfkVOGuZOUl70k/bh3bgPyil37uppPUscXzrdq+TL+F0iuTF1NfzoHFtK6fTE6jcD0aBRFCDpvamKO8o6RO4CGnsNEHv/gPz0nyZJ0Z78CK4CfbiP+Kvh7JNG581Oh//O2ipZTWJae2Uky7M+sXEa/Y8Tvj+DXFtpv1Zopmzz2lEx+Vm5zmtqxkwNm1wQpxe2tuE8riiERTo0jgONsJcMPuAMx5KabeljRl82pvXUZmn/adlAJ4PTZB1oH3XxrbKE5c6qxeRurWqMe0rXcl2MRgTabtvYNrI0piuCnb0z0xTIUcxF5y+DnT8VleDT2PagwZHgcNJtaYfRc9ZEs3C+iwVYmL1O+xSTFnW7GtU+A2aMA+zVrb4JTi6Kx0Cm5arrTBjWsnTLa6rQ51xzfEFafNKsmEU3oXjoLWrO47qHIM1oFvrQdgCzdCeVfp08/VPL1z3vdswDTQREk3LbzHoKOwNV0H/3tmyvIOvRl5HeYdJL0N7YhNSERvEtx6BE6ATutiGkPECfkJDcWHc81oKbEnpaNSdYbQTvNMpf4WvmeWWO6GdwnXHo33nJEyBkbAcnoEuxssgtbn/r2j5FJ9kdeT9AAn5HmZDZ7YaOvcc7MVbKsF0+9Y+q59dieZbJpqW/UFL7auntjY6xTRBybdTT7sdlaVtox5qQQfQ/YgvpMGCAkGBoEBQICgQFAgKBAWCAh2rwF+zttwFf+Tt/AAAAABJRU5ErkJggg==\" width=\"36.5\" height=\"18\" style=\"width: 36.5px; height: 18px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"40\" height=\"18\" style=\"width: 40px; height: 18px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgb(247, 247, 247); block-size: 80px; border-bottom-left-radius: 4px; border-bottom-right-radius: 4px; border-end-end-radius: 4px; border-end-start-radius: 4px; border-start-end-radius: 4px; border-start-start-radius: 4px; border-top-left-radius: 4px; border-top-right-radius: 4px; margin-block-end: 10px; margin-block-start: 10px; margin-bottom: 10px; margin-inline-end: 3px; margin-inline-start: 3px; margin-left: 3px; margin-right: 3px; margin-top: 10px; perspective-origin: 489.078125px 40px; transform-origin: 489.078125px 40px; margin-left: 3px; margin-top: 10px; margin-bottom: 10px; margin-right: 3px; \"\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 489.078125px 10px; transform-origin: 489.078125px 10px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e    \u0026gt;\u0026gt; x = 3; A = 1;\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 489.078125px 10px; transform-origin: 489.078125px 10px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e    \u0026gt;\u0026gt; PS(A,x)\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 489.078125px 10px; transform-origin: 489.078125px 10px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e    ans =\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 489.078125px 10px; transform-origin: 489.078125px 10px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e        8.9683\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 10px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 10px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 10px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003ePlease present your answer rounded-off to nearest 4 decimal places.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function p = PS(A,x)\r\n    p = sum(arrayfun(@(n) sum(arrayfun(@(m) prod(arrayfun(@(k) 2*sin(k*pi/m+A),0:m-1)),1:n)),1:x));\r\nend","test_suite":"%%\r\nA = 1; x = 3;\r\np_correct = 8.9683;\r\nassert(isequal(PS(A,x),p_correct))\r\n%%\r\nA = 2:2:20; x = 3:3:30;\r\np_correct = [1.8697 -3.3674 -62.4997 11.5088 -4.8523 -71.5196 25.1022 -3.2420 -64.7730 49.3233];\r\nassert(isequal(arrayfun(@(i) PS(A(i),x(i)),1:10),p_correct))\r\n%%\r\np_correct = 4166.0746;\r\nassert(isequal(sum(arrayfun(@(i) PS(i,i),1:100)),p_correct))\r\n%%\r\nA = 100; x = 200;\r\np_correct = -739.8950;\r\nassert(isequal(PS(A,x),p_correct))\r\n%%\r\nA = 2000; x = 3000;\r\np_correct = 2041.1906;\r\nassert(isequal(PS(A,x),p_correct))\r\n%%\r\nA = 10000; x = 20000;\r\np_correct = -3131.6478;\r\nassert(isequal(PS(A,x),p_correct))\r\n%%\r\nA = 200000; x = 300000;\r\np_correct = -8386548.7261;\r\nassert(isequal(PS(A,x),p_correct))\r\n%%\r\nA = 1000000; x = 2000000;\r\np_correct = -11067350.2876;\r\nassert(isequal(PS(A,x),p_correct))\r\n%%\r\nA = 123456; xs = 200001:200100;\r\nps = arrayfun(@(x) PS(A,x),xs);\r\nss_correct = [-88558 -88558 -88580 12]; \r\nassert(isequal(floor([mean(ps) median(ps) mode(ps) std(ps)]),ss_correct))\r\n%%\r\nfiletext = fileread('PS.m');\r\nnot_allowed = contains(filetext, 'persistent') || contains(filetext, 'global') || contains(filetext, 'java') || contains(filetext, 'py') || contains(filetext, 'regexp') || contains(filetext, 'eval') || contains(filetext, 'assignin');\r\nassert(~not_allowed)","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":255988,"edited_by":255988,"edited_at":"2023-01-07T06:37:48.000Z","deleted_by":null,"deleted_at":null,"solvers_count":2,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2023-01-06T09:42:25.000Z","updated_at":"2025-11-22T20:00:54.000Z","published_at":"2023-01-07T06:37:48.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eGiven and angle \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eA\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e in radians and a positive integer \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ex\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e, evaluate the following product summation:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e                    \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ePS(A,x) = \\\\sum_{n=1}^{x} \\\\sum_{m=1}^{n} \\\\prod_{k=0}^{m-1} 2 \\\\sin \\\\left( \\\\frac_{k\\\\pi}^{m} +A \\\\right).\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ewhich 'directly' translates to Matlab as:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[    \u003e\u003e PS = @(A,x) sum(arrayfun(@(n) sum(arrayfun(@(m) prod(arrayfun(@(k) 2*sin(k*pi/m+A),0:m-1)),1:n)),1:x));]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFor example \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ex = 3\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eA = 1\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[    \u003e\u003e x = 3; A = 1;\\n    \u003e\u003e PS(A,x)\\n    ans =\\n        8.9683]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ePlease present your answer rounded-off to nearest 4 decimal places.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":57969,"title":"Compute flow in a partially full pipe","description":"Problem statement\r\nWhen does the maximum flow occur in a pipe? Intuition might suggest that it occurs when the pipe is flowing full—i.e., when the depth of flow  equals the diameter  of the pipe. \r\nWrite a function that takes the ratio  and produces the flow rate as a fraction of the value for a full pipe. For example, when the input is 1/2, the output should be 1/2, and when the input is 1, the output should be 1. Assume that Manning’s equation applies and Manning’s roughness coefficient is constant. \r\nSee Test 13 for the answer to the initial question.\r\nBackground\r\nSteady uniform flow in a channel is often computed with Manning’s equation, which results from a balance between the component of the fluid’s weight in the flow direction and friction on the walls of the channel. The shear stress on the channel walls is computed with an empirical relation. Manning’s equation for the flow  is\r\n\r\nwhere  is Manning’s roughness coefficient,  is the hydraulic radius,  is the slope of the channel,  is the cross-sectional area of the flow, and  is the wetted perimeter (i.e., the perimeter of the solid wall of the channel that is touching the water.) The coefficient  is 1 for SI units and 1.5 (or 1.49) for U.S. customary units. ","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 392.8px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 196.4px; transform-origin: 407px 196.4px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 63.0083px 8px; transform-origin: 63.0083px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eProblem statement\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 384px 8px; transform-origin: 384px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWhen does the maximum flow occur in a pipe? Intuition might suggest that it occurs when the pipe is flowing full—i.e., when the depth of flow \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eh\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 65.35px 8px; transform-origin: 65.35px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e equals the diameter \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eD\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 38.5px 8px; transform-origin: 38.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e of the pipe. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 31.5px; text-align: left; transform-origin: 384px 31.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 109.933px 8px; transform-origin: 109.933px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function that takes the ratio \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"h/D\" style=\"width: 29.5px; height: 18.5px;\" width=\"29.5\" height=\"18.5\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 251.258px 8px; transform-origin: 251.258px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and produces the flow rate as a fraction of the value for a full pipe. For example, when the input is 1/2, the output should be 1/2, and when the input is 1, the output should be 1. Assume that Manning’s equation applies and Manning’s roughness coefficient is constant. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 150.917px 8px; transform-origin: 150.917px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eSee Test 13 for the answer to the initial question.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 40.8333px 8px; transform-origin: 40.8333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eBackground\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 31.5px; text-align: left; transform-origin: 384px 31.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 369.8px 8px; transform-origin: 369.8px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eSteady uniform flow in a channel is often computed with Manning’s equation, which results from a balance between the component of the fluid’s weight in the flow direction and friction on the walls of the channel. The shear stress on the channel walls is computed with an empirical relation. Manning’s equation for the flow \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eQ\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 7px 8px; transform-origin: 7px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 34.8px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 17.4px; text-align: left; transform-origin: 384px 17.4px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"vertical-align:-15px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"Q = (C/n)R^(2/3)S0^(1/2)A\" style=\"width: 105.5px; height: 35px;\" width=\"105.5\" height=\"35\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 64px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 32px; text-align: left; transform-origin: 384px 32px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 21.0083px 8px; transform-origin: 21.0083px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003ewhere \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003en\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 112.55px 8px; transform-origin: 112.55px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is Manning’s roughness coefficient, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"R = A/P\" style=\"width: 59px; height: 18.5px;\" width=\"59\" height=\"18.5\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 73.5167px 8px; transform-origin: 73.5167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is the hydraulic radius, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"S0\" style=\"width: 15.5px; height: 20px;\" width=\"15.5\" height=\"20\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 87.125px 8px; transform-origin: 87.125px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is the slope of the channel, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eA\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 39.6667px 8px; transform-origin: 39.6667px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is the cross-sectional area of the flow, and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eP\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 278.1px 8px; transform-origin: 278.1px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is the wetted perimeter (i.e., the perimeter of the solid wall of the channel that is touching the water.) The coefficient \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eC\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 182.383px 8px; transform-origin: 182.383px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is 1 for SI units and 1.5 (or 1.49) for U.S. customary units. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function f = pipeFlow(hoverD)\r\n  f = hoverD.^2;\r\nend","test_suite":"%%\r\nhoverD = 1;\r\nf_correct = 1;\r\nassert(abs(pipeFlow(hoverD)-f_correct)\u003c1e-4)\r\n\r\n%%\r\nhoverD = 0.9;\r\nf_correct = 1.06580;\r\nassert(abs(pipeFlow(hoverD)-f_correct)\u003c1e-4)\r\n\r\n%%\r\nhoverD = 0.8;\r\nf_correct = 0.97747;\r\nassert(abs(pipeFlow(hoverD)-f_correct)\u003c1e-4)\r\n\r\n%%\r\nhoverD = 0.75;\r\nf_correct = 0.91188;\r\nassert(abs(pipeFlow(hoverD)-f_correct)\u003c1e-4)\r\n\r\n%%\r\nhoverD = 0.6;\r\nf_correct = 0.67184;\r\nassert(abs(pipeFlow(hoverD)-f_correct)\u003c1e-4)\r\n\r\n%%\r\nhoverD = 0.5;\r\nf_correct = 0.5;\r\nassert(abs(pipeFlow(hoverD)-f_correct)\u003c1e-4)\r\n\r\n%%\r\nhoverD = 0.4;\r\nf_correct = 0.33699;\r\nassert(abs(pipeFlow(hoverD)-f_correct)\u003c1e-4)\r\n\r\n%%\r\nhoverD = 0.3;\r\nf_correct = 0.19583;\r\nassert(abs(pipeFlow(hoverD)-f_correct)\u003c1e-4)\r\n\r\n%%\r\nhoverD = 0.2;\r\nf_correct = 0.08757;\r\nassert(abs(pipeFlow(hoverD)-f_correct)\u003c1e-4)\r\n\r\n%%\r\nhoverD = 0.1;\r\nf_correct = 0.02088;\r\nassert(abs(pipeFlow(hoverD)-f_correct)\u003c1e-4)\r\n\r\n%%\r\nhoverD = 0;\r\nf_correct = 0;\r\nassert(abs(pipeFlow(hoverD)-f_correct)\u003c1e-4)\r\n\r\n%%\r\nhoverD = (1:6)/7;\r\nf_correct = [0.04395 0.17812 0.38187 0.62268 0.85931 1.03672];\r\nassert(all(abs(pipeFlow(hoverD)-f_correct)\u003c1e-4))\r\n\r\n%%\r\ng = @(x) -pipeFlow(x); \r\nhoverD_max = fminsearch(g,0.9);\r\nhoverD_max_correct = 0.93817;\r\nassert(abs(hoverD_max-hoverD_max_correct)\u003c1e-4)\r\n\r\n%%\r\nfiletext = fileread('pipeFlow.m');\r\nillegal = contains(filetext, 'assignin') || contains(filetext, 'assert'); \r\nassert(~illegal)","published":true,"deleted":false,"likes_count":1,"comments_count":9,"created_by":46909,"edited_by":46909,"edited_at":"2023-04-08T16:02:01.000Z","deleted_by":null,"deleted_at":null,"solvers_count":5,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2023-04-08T12:50:01.000Z","updated_at":"2023-04-08T16:02:01.000Z","published_at":"2023-04-08T12:50:08.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eProblem statement\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWhen does the maximum flow occur in a pipe? Intuition might suggest that it occurs when the pipe is flowing full—i.e., when the depth of flow \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"h\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eh\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e equals the diameter \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"D\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eD\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e of the pipe. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a function that takes the ratio \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"h/D\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eh/D\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and produces the flow rate as a fraction of the value for a full pipe. For example, when the input is 1/2, the output should be 1/2, and when the input is 1, the output should be 1. Assume that Manning’s equation applies and Manning’s roughness coefficient is constant. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eSee Test 13 for the answer to the initial question.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eBackground\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eSteady uniform flow in a channel is often computed with Manning’s equation, which results from a balance between the component of the fluid’s weight in the flow direction and friction on the walls of the channel. The shear stress on the channel walls is computed with an empirical relation. Manning’s equation for the flow \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"Q\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eQ\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"Q = (C/n)R^(2/3)S0^(1/2)A\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eQ = \\\\frac{C}{n}R^{2/3}S_0^{1/2}A\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ewhere \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is Manning’s roughness coefficient, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"R = A/P\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eR=A/P\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is the hydraulic radius, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"S0\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eS_0\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is the slope of the channel, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"A\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eA\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is the cross-sectional area of the flow, and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"P\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eP\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is the wetted perimeter (i.e., the perimeter of the solid wall of the channel that is touching the water.) The coefficient \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"C\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eC\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is 1 for SI units and 1.5 (or 1.49) for U.S. customary units. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":60336,"title":"Determine whether a property description closes","description":"The arrival of summer makes me think back to the summers I spent working for my father’s engineering firm. For the first several summers I worked on land surveying crews, and a common job was to measure properties. The measurements would then be used in a metes and bounds description of the property, as in this example:\r\n…Commencing from the point of beginning; thence N0°0ʹ0ʺE 35 m; thence N60°0ʹ0ʺE 34.64 m; thence S0°0ʹ0ʺE 52.32 m; thence S90°0ʹ0ʺW 30 m to the point of beginning. \r\nThis text describes a polygon by giving orientations and lengths of the sides.* The orientations are specified as bearings, in which angles are given as degrees, minutes, and seconds. For example, N60°0ʹ0ʺE is 60° to the east of north. The direction WSW would be written as S67°30ʹ0ʺW.\r\nAn important element of measuring and describing a property is to verify that the property, as described, closes—that is, the last side ends at the point of beginning. States in the U.S. will specify the tolerance for the closure. \r\nWrite a function to determine whether a property description closes. The input will be a character string with the bearings and distances between the points. The function should return a logical variable tf with the result as well as the distance d of the end point from the point of beginning. Take the property to close when the distance between the beginning and end points is less than 0.01 m. \r\n*The description would also specify the location of the point of beginning and describe the property and boundaries, among other things.  ","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 382.35px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 191.175px; transform-origin: 407px 191.175px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 31.5px; text-align: left; transform-origin: 384px 31.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 374.658px 7.79167px; transform-origin: 374.658px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe arrival of summer makes me think back to the summers I spent working for my father’s engineering firm. For the first several summers I worked on land surveying crews, and a common job was to measure properties. The measurements would then be used in a metes and bounds description of the property, as in this example:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42.9px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21.45px; text-align: left; transform-origin: 384px 21.45px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 369.6px 7.79167px; transform-origin: 369.6px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; perspective-origin: 369.6px 8.25px; transform-origin: 369.6px 8.25px; \"\u003e…Commencing from the point of beginning; thence N0°0ʹ0ʺE 35 m; thence N60°0ʹ0ʺE 34.64 m; thence S0°0ʹ0ʺE 52.32 m; thence S90°0ʹ0ʺW 30 m to the point of beginning. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 31.5px; text-align: left; transform-origin: 384px 31.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 381.992px 7.79167px; transform-origin: 381.992px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThis text describes a polygon by giving orientations and lengths of the sides.* The orientations are specified as bearings, in which angles are given as degrees, minutes, and seconds. For example, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 157.608px 7.79167px; transform-origin: 157.608px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eN60°0ʹ0ʺE is 60° to the east of north. The direction WSW would be written as S67°30ʹ0ʺW.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 384px 7.79167px; transform-origin: 384px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eAn important element of measuring and describing a property is to verify that the property, as described, closes—that is, the last side ends at the point of beginning. States in the U.S. will specify the tolerance for the closure. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 84.45px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 42.225px; text-align: left; transform-origin: 384px 42.225px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 374.458px 7.79167px; transform-origin: 374.458px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function to determine whether a property description closes. The input will be a character string with the bearings and distances between the points. The function should return a logical variable \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 7.7px 7.79167px; transform-origin: 7.7px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; perspective-origin: 7.7px 8.25px; transform-origin: 7.7px 8.25px; \"\u003etf\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 119.408px 7.79167px; transform-origin: 119.408px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e with the result as well as the distance \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.85px 7.79167px; transform-origin: 3.85px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; perspective-origin: 3.85px 8.25px; transform-origin: 3.85px 8.25px; \"\u003ed\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 7.96667px 7.79167px; transform-origin: 7.96667px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e of the end point from the point of beginning. Take the property to close when the distance between the beginning and end points is less than 0.01 m. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 382.4px 7.79167px; transform-origin: 382.4px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e*The description would also specify the location of the point of beginning and describe the property and boundaries, among other things. \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.94167px 7.79167px; transform-origin: 1.94167px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function [tf,d] = isPropertyClosed(s)\r\n  tf = sum(str2num(s))==0;\r\nend","test_suite":"%%\r\nc = {'N0°0ʹ0ʺE 35 m' 'N60°0ʹ0ʺE 34.64 m' 'S0°0ʹ0ʺE 52.32 m' 'S90°0ʹ0ʺW 30 m'};\r\ns = strjoin(c,char(13));\r\n[tf,d] = isPropertyClosed(s);\r\nd_correct = 8.800129070465346e-04;\r\nassert(tf)\r\nassert(abs(d-d_correct)\u003c1e-6)\r\n\r\n%%\r\nc = {'N0°0ʹ0ʺE 35 m' 'N60°0ʹ0ʺE 34.64 m' 'S0°0ʹ0ʺE 52.1 m' 'S90°0ʹ0ʺW 30 m'};\r\ns = strjoin(c,char(13));\r\n[tf,d] = isPropertyClosed(s);\r\nd_correct = 0.220001760044587;\r\nassert(~tf)\r\nassert(abs(d-d_correct)\u003c1e-6)\r\n\r\n%%\r\nc = {'N52°17ʹ31ʺE 46.13 m' 'S52°17ʹ31ʺE 23.67 m' 'S52°17ʹ31ʺW 46.13 m' 'N52°17ʹ31ʺW 23.67 m'};\r\ns = strjoin(c,char(13));\r\n[tf,d] = isPropertyClosed(s);\r\nd_correct = 1.913194867290181e-14;\r\nassert(tf)\r\nassert(abs(d-d_correct)\u003c1e-6)\r\n    \r\n%%\r\nc = {'N52°17ʹ31ʺE 46.14 m' 'S52°17ʹ31ʺE 23.66 m' 'S52°17ʹ31ʺW 46.12 m' 'N52°17ʹ31ʺW 23.68 m'};\r\ns = strjoin(c,char(13));\r\n[tf,d] = isPropertyClosed(s);\r\nd_correct = 0.024465531079178;\r\nassert(~tf)\r\nassert(abs(d-d_correct)\u003c1e-6)\r\n\r\n%%\r\nc = {'N4°23ʹ55ʺW 52.15 m','N33°10ʹ42ʺE 31.06 m','N52°52ʹ34ʺE 41.40 m','S60°15ʹ18ʺE 24.19 m','S37°28ʹ34ʺE 37.80 m','S55°53ʹ7ʺE 37.44 m','S16°15ʹ36ʺE 50.00 m','S84°44ʹ15ʺW 76.32 m','N75°44ʹ7ʺW 60.88'};\r\ns = strjoin(c,char(13));\r\n[tf,d] = isPropertyClosed(s);\r\nd_correct = 0.018626452840054;\r\nassert(~tf)\r\nassert(abs(d-d_correct)\u003c1e-6)\r\n\r\n%%\r\nc = {'N4°23ʹ55ʺW 52.15 m','N33°10ʹ42ʺE 31.06 m','N52°51ʹ11ʺE 41.40 m','S60°15ʹ18ʺE 24.19 m','S37°28ʹ34ʺE 37.80 m','S55°53ʹ7ʺE 37.44 m','S16°15ʹ36ʺE 50.00 m','S84°44ʹ15ʺW 76.32 m','N75°44ʹ7ʺW 60.88'};\r\ns = strjoin(c,char(13));\r\n[tf,d] = isPropertyClosed(s);\r\nd_correct = 0.007209083851337;\r\nassert(tf)\r\nassert(abs(d-d_correct)\u003c1e-6)\r\n\r\n%%\r\nc = {'N4°32ʹ55ʺW 52.15 m','N33°10ʹ42ʺE 31.06 m','N52°51ʹ11ʺE 41.40 m','S60°15ʹ18ʺE 24.19 m','S37°28ʹ34ʺE 37.80 m','S55°53ʹ7ʺE 37.44 m','S16°15ʹ36ʺE 50.00 m','S84°44ʹ15ʺW 76.32 m','N75°44ʹ7ʺW 60.88'};\r\ns = strjoin(c,char(13));\r\n[tf,d] = isPropertyClosed(s);\r\nd_correct = 0.142364438065814;\r\nassert(~tf)\r\nassert(abs(d-d_correct)\u003c1e-6)\r\n\r\n%%\r\nc = {'N69°26ʹ38ʺW 42.72 m','N19°34ʹ23ʺW\t47.76 m','N47°51ʹ44ʺE 56.64 m','N47°2ʹ43ʺE 39.62 m','S80°32ʹ15ʺE 42.58 m','S25°16ʹ39ʺE 39.81 m','S28°23ʹ34ʺW 42.06 m','S24°40ʹ36ʺW 40.72 m','S77°47ʹ58ʺW 37.85 m'};\r\ns = strjoin(c,char(13));\r\n[tf,d] = isPropertyClosed(s);\r\nd_correct = 0.002087577619808;\r\nassert(tf)\r\nassert(abs(d-d_correct)\u003c1e-6)\r\n\r\n%%\r\nc = {'N69°26ʹ38ʺW 42.72 m','N19°34ʹ23ʺW\t47.76 m','N47°51ʹ44ʺE 56.4 m','N47°2ʹ43ʺE 39.62 m','S80°32ʹ15ʺE 42.58 m','S25°16ʹ39ʺE 39.81 m','S28°23ʹ34ʺW 42.06 m','S24°40ʹ36ʺW 40.72 m','S77°47ʹ58ʺW 37.85 m'};\r\ns = strjoin(c,char(13));\r\n[tf,d] = isPropertyClosed(s);\r\nd_correct = 0.238926560421110;\r\nassert(~tf)\r\nassert(abs(d-d_correct)\u003c1e-6)\r\n\r\n%%\r\nn = randi(10);\r\nm = n+randi(10);\r\nA = m^2-n^2; B = 2*m*n; C = m^2+n^2;\r\nth = acosd(A/C);\r\ndeg = floor(th);\r\nmnt = floor(60*(th-deg));\r\nscd = floor(3600*(th-deg-mnt/60));\r\nc = {['N0°0ʹ0ʺW ' num2str(A,5) ' m'],['S' num2str(deg,2) '°' num2str(mnt,2) 'ʹ' num2str(scd,2) 'ʺE ' num2str(C,5)\t' m'],['N90°0ʹ0ʺW ' num2str(B,5) ' m']};\r\ns = strjoin(c,char(13));\r\n[tf,d] = isPropertyClosed(s);\r\nassert(tf)\r\n\r\n%%\r\nfiletext = fileread('isPropertyClosed.m');\r\nillegal = contains(filetext, 'assignin') || contains(filetext, 'assert'); \r\nassert(~illegal)","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":46909,"edited_by":46909,"edited_at":"2024-06-04T15:37:54.000Z","deleted_by":null,"deleted_at":null,"solvers_count":5,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2024-05-19T01:52:51.000Z","updated_at":"2024-06-04T15:37:54.000Z","published_at":"2024-05-19T01:53:17.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe arrival of summer makes me think back to the summers I spent working for my father’s engineering firm. For the first several summers I worked on land surveying crews, and a common job was to measure properties. The measurements would then be used in a metes and bounds description of the property, as in this example:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e…Commencing from the point of beginning; thence N0°0ʹ0ʺE 35 m; thence N60°0ʹ0ʺE 34.64 m; thence S0°0ʹ0ʺE 52.32 m; thence S90°0ʹ0ʺW 30 m to the point of beginning. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThis text describes a polygon by giving orientations and lengths of the sides.* The orientations are specified as bearings, in which angles are given as degrees, minutes, and seconds. For example, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003eN60°0ʹ0ʺE is 60° to the east of north. The direction WSW would be written as S67°30ʹ0ʺW.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eAn important element of measuring and describing a property is to verify that the property, as described, closes—that is, the last side ends at the point of beginning. States in the U.S. will specify the tolerance for the closure. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a function to determine whether a property description closes. The input will be a character string with the bearings and distances between the points. The function should return a logical variable \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003etf\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e with the result as well as the distance \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ed\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e of the end point from the point of beginning. Take the property to close when the distance between the beginning and end points is less than 0.01 m. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e*The description would also specify the location of the point of beginning and describe the property and boundaries, among other things. \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":57785,"title":"Inscribe a circle in a triangle with a side of length equal to the circle’s circumference","description":"A circle of radius  is inscribed in a triangle with a side that has a length equal to the circle’s circumference. The center of the circle is at , and the special side is along the -axis. \r\nWrite a function to determine the coordinates of the third vertex. If the circle cannot be inscribed, return (NaN, NaN).\r\n         ","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 344.7px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 172.35px; transform-origin: 407px 172.35px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 43px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21.5px; text-align: left; transform-origin: 384px 21.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 53.675px 8px; transform-origin: 53.675px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eA circle of radius \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003er\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 318.433px 8px; transform-origin: 318.433px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is inscribed in a triangle with a side that has a length equal to the circle’s circumference. The center of the circle is at \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"(xc,r)\" style=\"width: 38.5px; height: 20px;\" width=\"38.5\" height=\"20\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 105.417px 8px; transform-origin: 105.417px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, and the special side is along the \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003ex\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 18.6667px 8px; transform-origin: 18.6667px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e-axis. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 321.917px 8px; transform-origin: 321.917px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function to determine the coordinates of the third vertex. If the circle cannot be inscribed, return (\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 11.55px 8px; transform-origin: 11.55px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003eNaN\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.88333px 8px; transform-origin: 3.88333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 11.55px 8px; transform-origin: 11.55px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003eNaN\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 4.275px 8px; transform-origin: 4.275px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e).\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 262.7px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 131.35px; text-align: left; transform-origin: 384px 131.35px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cimg class=\"imageNode\" style=\"vertical-align: baseline;width: 510px;height: 257px\" src=\"data:image/png;base64,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\" data-image-state=\"image-loaded\" width=\"510\" height=\"257\"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 17.475px 8px; transform-origin: 17.475px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e         \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function [x,y] = Barker_circle(xc,r)\r\n  x = xc+r; y = hypot(xc,r);\r\nend","test_suite":"%%\r\nxc = 4;\r\nr = 15;\r\n[x,y] = Barker_circle(xc,r);\r\nx_correct = 4.909246587607476;\r\ny_correct = 33.409674703528040;\r\nassert(abs(x-x_correct)\u003c1e-10)\r\nassert(abs(y-y_correct)\u003c1e-10)\r\n\r\n%%\r\nxc = -8*tand(71);\r\nr = 8;\r\n[x,y] = Barker_circle(xc,r);\r\nx_correct = -130.0150820572266;\r\ny_correct = 52.767782896424826;\r\nassert(abs(x-x_correct)\u003c1e-10)\r\nassert(abs(y-y_correct)\u003c1e-10)\r\n\r\n%%\r\nxc = 1.5;\r\nr = 1;\r\n[x,y] = Barker_circle(xc,r);\r\nx_correct = 1.953199287786186;\r\ny_correct = 2.302132858524124;\r\nassert(abs(x-x_correct)\u003c1e-10)\r\nassert(abs(y-y_correct)\u003c1e-10)\r\n\r\n%%\r\nxc = -6;\r\nr = 3;\r\n[x,y] = Barker_circle(xc,r);\r\nx_correct = -8.464265885195013;\r\ny_correct = 7.232132942597507;\r\nassert(abs(x-x_correct)\u003c1e-10)\r\nassert(abs(y-y_correct)\u003c1e-10)\r\n\r\n%%\r\nxc = -3;\r\nr = 1;\r\n[x,y] = Barker_circle(xc,r);\r\nassert(isnan(x) \u0026 isnan(y))\r\n\r\n%%\r\nxc = sqrt(2)/2+sqrt(3)/3+sqrt(5)/5+sqrt(7)/7+sqrt(11)/11+sqrt(13)/13+sqrt(17)/17;\r\nr = 1;\r\n[x,y] = Barker_circle(xc,r);\r\nx_correct = 23.968050071481240;\r\ny_correct = 9.177341136326962;\r\nassert(abs(x-x_correct)\u003c1e-10)\r\nassert(abs(y-y_correct)\u003c1e-10)\r\n\r\n%%\r\np = primes(20);\r\nxc = -sum(sqrt(p)./p);\r\nr = 1;\r\n[x,y] = Barker_circle(xc,r);\r\nassert(isnan(x) \u0026 isnan(y))\r\n\r\n%%\r\nxc = 0;\r\nr = 30*rand;\r\n[x,y] = Barker_circle(xc,r);\r\nx_correct = 0;\r\ny_correct = 2.225489199919036*r;\r\nassert(abs(x-x_correct)\u003c1e-10)\r\nassert(abs(y-y_correct)\u003c1e-10)\r\n\r\n%%\r\nxc = 10*rand;\r\nr = 7;\r\n[x1,y1] = Barker_circle(xc,r);\r\n[x2,y2] = Barker_circle(-xc,r);\r\nassert(abs(x1+x2)\u003c1e-10)\r\nassert(abs(y2-y1)\u003c1e-10)\r\n\r\n%%\r\np = primes(4e6);\r\nxc = sum(1./p(1:264833));\r\nr = 1;\r\n[x,y] = Barker_circle(xc,r);\r\nassert(~isnan(x) \u0026 ~isnan(y))\r\n\r\n%%\r\np = primes(4e6);\r\nxc = sum(1./p(1:264834));\r\nr = 1;\r\n[x,y] = Barker_circle(xc,r);\r\nassert(isnan(x) \u0026 isnan(y))\r\n\r\n%%\r\nfiletext = fileread('Barker_circle.m');\r\nillegal = contains(filetext, 'assignin') || contains(filetext, 'assert'); \r\nassert(~illegal)\r\n","published":true,"deleted":false,"likes_count":2,"comments_count":1,"created_by":46909,"edited_by":46909,"edited_at":"2023-03-14T02:42:07.000Z","deleted_by":null,"deleted_at":null,"solvers_count":6,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2023-03-14T02:41:59.000Z","updated_at":"2023-03-14T02:42:08.000Z","published_at":"2023-03-14T02:42:08.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eA circle of radius \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"r\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003er\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is inscribed in a triangle with a side that has a length equal to the circle’s circumference. The center of the circle is at \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"(xc,r)\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e(x_c,r)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, and the special side is along the \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"x\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ex\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e-axis. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a function to determine the coordinates of the third vertex. If the circle cannot be inscribed, return (\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eNaN\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eNaN\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e).\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"257\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"510\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"baseline\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId1\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e         \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/image\",\"target\":\"/media/image1.png\",\"relationshipId\":\"rId1\"}]},{\"partUri\":\"/media/image1.png\",\"contentType\":\"image/png\",\"content\":\"data:image/png;base64,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\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":61082,"title":"Slicing the area of a circle","description":"Given the area, A, of a square, consider a circle having the area, πA, and the radius, r.\r\nFor a given slicing number n\u003e1, find the (n+1)×2 matrix, M = [A1/π a1; A2/π a2; ...; An/π an; A_r L], where\r\nin the first row (i=1), A1 stands for the area of one slice (like a pizza slice), and a1 stands for the logical 1 if A1 is smaller than or reaches the square's area A or a1 stands for the logical 0 if A1 surpasses A;\r\nin the second row (i=2), A2 stands for the area of two slices and a2 has the same previous false-true meaning relative to the areas A2 and A;\r\nand so on, until last slice of the circle;\r\nin the last row (i=n+1), A_r is the area of the rectangle, with dimensions L×r, which contains the maximum possible number of slices, such that have the true meaning of their sum has the area smaller or equal than the square's area, in their adjacent arrangement.\r\nHint: Compare with Problem 61081.\r\ninput: (A,n)\r\noutput:  M = [A1/π a1; A2/π a2; ...; An/π an; A_r L]","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(33, 33, 33); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none; white-space: normal; \"\u003e\u003cdiv style=\"block-size: 325.5px; display: block; min-width: 0px; padding-block-start: 0px; padding-inline-start: 2px; padding-left: 2px; padding-top: 0px; perspective-origin: 408px 162.75px; transform-origin: 408px 162.75px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eGiven the area, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eA\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, of a square, consider a circle having the area, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eπA,\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and the radius, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003er\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eFor a given slicing number \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003en\u0026gt;1\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, find the \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e(n+1)\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e×\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e2\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e matrix, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eM = [A1/π a1; A2/π a2; ...; An/π an; A_r L]\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, where\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cul style=\"block-size: 163.5px; font-family: Helvetica, Arial, sans-serif; list-style-type: square; margin-block-end: 20px; margin-block-start: 10px; margin-bottom: 20px; margin-top: 10px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 391px 81.75px; transform-origin: 391px 81.75px; margin-top: 10px; margin-bottom: 20px; \"\u003e\u003cli style=\"block-size: 40.875px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 20.4375px; text-align: left; transform-origin: 363px 20.4375px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003ein the first row \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e(i=1)\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eA1\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e stands for the area of one slice (like a pizza slice), and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003ea1\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e stands for the logical \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e1\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e if \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eA1\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is smaller than or reaches the square's area \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eA\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e or \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003ea1\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e stands for the logical \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e0\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e if \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eA1\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e surpasses \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eA\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e;\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 40.875px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 20.4375px; text-align: left; transform-origin: 363px 20.4375px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003ein the second row \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e(i=2)\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eA2\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e stands for the area of two slices and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003ea2\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e has the same previous false-true meaning relative to the areas \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eA2\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eA\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e;\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4375px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 10.2125px; text-align: left; transform-origin: 363px 10.2188px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eand so on, until last slice of the circle;\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 61.3125px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 30.65px; text-align: left; transform-origin: 363px 30.6562px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003ein the last row \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e(i=n+1),\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eA_r\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is the area of the rectangle, with dimensions \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eL\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e×\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003er\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, which contains the maximum possible number of slices, such that have the true meaning of their sum has the area smaller or equal than the square's area, in their adjacent arrangement.\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ul\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eHint: Compare with \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/61081-slicing-the-area-of-a-regular-polygon\"\u003e\u003cspan style=\"border-block-end-color: rgb(0, 91, 130); border-block-start-color: rgb(0, 91, 130); border-bottom-color: rgb(0, 91, 130); border-inline-end-color: rgb(0, 91, 130); border-inline-start-color: rgb(0, 91, 130); border-left-color: rgb(0, 91, 130); border-right-color: rgb(0, 91, 130); border-top-color: rgb(0, 91, 130); caret-color: rgb(0, 91, 130); color: rgb(0, 91, 130); column-rule-color: rgb(0, 91, 130); outline-color: rgb(0, 91, 130); text-decoration-color: rgb(0, 91, 130); text-emphasis-color: rgb(0, 91, 130); \"\u003e\u003cspan style=\"\"\u003eProblem 61081\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003einput:\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e(A,n)\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003eoutput: \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eM = [A1/π a1; A2/π a2; ...; An/π an; A_r L]\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function M = slicing_circle(A,n)\r\n  M = x;\r\nend","test_suite":"%%\r\nA = 8;\r\nn = 4;\r\ny_correct = [2 1; 4 0; 6 0; 8 0; 8*sqrt(2) 4];\r\nY = slicing_circle(A,n);\r\ntolerance = 1e-13;\r\nassert(all(Y(1:n) == y_correct(1:n)) \u0026 ...\r\n    abs(Y(end)-y_correct(end)) \u003c tolerance \u0026 all(Y(1:end,2) == y_correct(1:end,2)))\r\n\r\n%%\r\nA = 36;\r\nn = 6;\r\ny_correct = [6 1; 12 0; 18 0; 24 0; 30 0; 36 0; 36 6];\r\ntolerance = 1e-13;\r\nY = slicing_circle(A,n);\r\nassert(all(Y(1:n) == y_correct(1:n)) \u0026 all(Y(1:n,2) == y_correct(1:n,2)) \u0026 ...\r\n    all(abs(Y(end,:)-y_correct(end,:)) \u003c tolerance))\r\n\r\n\r\n%%\r\nA = 36;\r\nn = 12;\r\ny_correct = [3 1; 6 1; 9 1; 12 0; 15 0; 18 0; 21 0; 24 0; 27 0; 30 0; 33 0; 36 0; ...\r\n    37.92731310242232  6.32121885040372];\r\ntolerance = 1e-13;\r\nY = slicing_circle(A,n);\r\nassert(all(Y(1:n) == y_correct(1:n)) \u0026 all(Y(1:n,2) == y_correct(1:n,2)) \u0026 ...\r\n    all(abs(Y(end,:)-y_correct(end,:)) \u003c tolerance))\r\n\r\n%%\r\nfiletext = fileread('slicing_circle.m');\r\nillegal = contains(filetext, 'assignin') || contains(filetext, 'regexp') || ...\r\n          contains(filetext, 'str2num'); \r\nassert(~illegal)\r\n\r\n%%\r\nA = 70;\r\nn = 7;\r\ny_correct = [10 1; 20 1; 30 0; 40 0; 50 0; 60 0; 70 0; ...\r\n    94.4539467929851 11.28940594715244];\r\ntolerance = 1e-13;\r\nY = slicing_circle(A,n);\r\nassert(all(Y(1:n) == y_correct(1:n)) \u0026 all(Y(1:n,2) == y_correct(1:n,2)) \u0026 ...\r\n    all(abs(Y(end,:)-y_correct(end,:)) \u003c tolerance))\r\n\r\n%%\r\nA = 70;\r\nn = 10;\r\ny_correct = [7 1; 14 1; 21 1; 28 0; 35 0; 42 0; 49 0; 56 0; 63 0; 70 0; ...\r\n    88.7511366850995 10.6077897676978];\r\ntolerance = 1e-13;\r\nY = slicing_circle(A,n);\r\nassert(all(Y(1:n) == y_correct(1:n)) \u0026  all(Y(1:n,2) == y_correct(1:n,2))  \u0026  ...\r\n    all(abs(Y(end,:)-y_correct(end,:)) \u003c tolerance))","published":true,"deleted":false,"likes_count":0,"comments_count":10,"created_by":4993982,"edited_by":4993982,"edited_at":"2025-11-27T14:44:37.000Z","deleted_by":null,"deleted_at":null,"solvers_count":5,"test_suite_updated_at":"2025-11-27T14:44:37.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2025-11-20T14:17:04.000Z","updated_at":"2025-12-17T10:09:27.000Z","published_at":"2025-11-21T15:27:17.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGiven the area, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eA\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, of a square, consider a circle having the area, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eπA,\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e and the radius, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003er\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFor a given slicing number \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003en\u0026gt;1\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, find the \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e(n+1)\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e×\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e2\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e matrix, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eM = [A1/π a1; A2/π a2; ...; An/π an; A_r L]\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, where\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ein the first row \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e(i=1)\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eA1\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e stands for the area of one slice (like a pizza slice), and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ea1\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e stands for the logical \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e1\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e if \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eA1\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e is smaller than or reaches the square's area \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eA\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e or \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ea1\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e stands for the logical \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e0\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e if \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eA1\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e surpasses \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eA\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e;\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ein the second row \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e(i=2)\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eA2\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e stands for the area of two slices and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ea2\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e has the same previous false-true meaning relative to the areas \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eA2\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eA\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e;\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eand so on, until last slice of the circle;\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ein the last row \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e(i=n+1),\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eA_r\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e is the area of the rectangle, with dimensions \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eL\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e×\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003er\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, which contains the maximum possible number of slices, such that have the true meaning of their sum has the area smaller or equal than the square's area, in their adjacent arrangement.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eHint: Compare with \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/61081-slicing-the-area-of-a-regular-polygon\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eProblem 61081\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003einput:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e(A,n)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eoutput: \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eM = [A1/π a1; A2/π a2; ...; An/π an; A_r L]\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":45374,"title":" Hanging cable - 02","description":"previous problem -\r\n\r\n\u003chttps://www.mathworks.com/matlabcentral/cody/problems/45373-hanging-cable-01\u003e\r\n\r\n The height of the poles is h\r\n the length of the cable is l\r\n \r\n\r\nbut in this case, the two poles are of different heights.\r\n\r\n\u003chttps://ibb.co/2P4P14Q\u003e\r\n\r\nThe image is collected from Wikipedia.","description_html":"\u003cp\u003eprevious problem -\u003c/p\u003e\u003cp\u003e\u003ca href = \"https://www.mathworks.com/matlabcentral/cody/problems/45373-hanging-cable-01\"\u003ehttps://www.mathworks.com/matlabcentral/cody/problems/45373-hanging-cable-01\u003c/a\u003e\u003c/p\u003e\u003cpre\u003e The height of the poles is h\r\n the length of the cable is l\u003c/pre\u003e\u003cp\u003ebut in this case, the two poles are of different heights.\u003c/p\u003e\u003cp\u003e\u003ca href = \"https://ibb.co/2P4P14Q\"\u003ehttps://ibb.co/2P4P14Q\u003c/a\u003e\u003c/p\u003e\u003cp\u003eThe image is collected from Wikipedia.\u003c/p\u003e","function_template":"function d = cable_03(h,l)","test_suite":"%%\r\nassert(abs(cable_03([50,70],140)-55.4172)\u003c0.0001)\r\n%%\r\nassert(abs(cable_03([80,70],160)-35.4678)\u003c0.0001)\r\n%%\r\nassert(isequal(cable_03([80,70],150),0))\r\n%%\r\nassert(abs(cable_03([50 100],1000)-984.5341)\u003c0.0001)\r\n%%\r\nassert(abs(cable_03([500 100],1000)-721.5116)\u003c0.0001)\r\n","published":true,"deleted":false,"likes_count":1,"comments_count":2,"created_by":363598,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":9,"test_suite_updated_at":"2020-03-22T18:22:00.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2020-03-22T10:15:37.000Z","updated_at":"2020-03-22T18:22:00.000Z","published_at":"2020-03-22T11:05:56.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eprevious problem -\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/45373-hanging-cable-01\\\"\u003e\u003cw:r\u003e\u003cw:t\u003e\u0026lt;https://www.mathworks.com/matlabcentral/cody/problems/45373-hanging-cable-01\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e\u0026gt;\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[ The height of the poles is h\\n the length of the cable is l]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ebut in this case, the two poles are of different heights.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:hyperlink w:docLocation=\\\"https://ibb.co/2P4P14Q\\\"\u003e\u003cw:r\u003e\u003cw:t\u003e\u0026lt;https://ibb.co/2P4P14Q\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e\u0026gt;\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe image is collected from Wikipedia.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"}],"problem_search":{"errors":[],"problems":[{"id":44880,"title":"Angle between two vectors","description":"Given 2 pairs of _cartesian co-ordinates_, determine the angle between the 2 vectors formed by the _points_ and the _origin_. Angle must be in [0,180] and in degrees.\r\n\r\ne.g. \r\n\r\n* Input (3 separate inputs)\r\n\r\n  [0 1;2 0]\r\n  [1 1;-2 0]\r\n  [1 1;2 2]\r\n\r\n* Output (3 separate outputs):\r\n\r\n  90\r\n  135\r\n  0","description_html":"\u003cp\u003eGiven 2 pairs of \u003ci\u003ecartesian co-ordinates\u003c/i\u003e, determine the angle between the 2 vectors formed by the \u003ci\u003epoints\u003c/i\u003e and the \u003ci\u003eorigin\u003c/i\u003e. Angle must be in [0,180] and in degrees.\u003c/p\u003e\u003cp\u003ee.g.\u003c/p\u003e\u003cul\u003e\u003cli\u003eInput (3 separate inputs)\u003c/li\u003e\u003c/ul\u003e\u003cpre class=\"language-matlab\"\u003e[0 1;2 0]\r\n[1 1;-2 0]\r\n[1 1;2 2]\r\n\u003c/pre\u003e\u003cul\u003e\u003cli\u003eOutput (3 separate outputs):\u003c/li\u003e\u003c/ul\u003e\u003cpre class=\"language-matlab\"\u003e90\r\n135\r\n0\r\n\u003c/pre\u003e","function_template":"function y = angle(x)\r\n  y = x;\r\nend","test_suite":"%%\r\nx = [1 1;-1 -1];\r\ny_correct = 180;\r\nassert(isequal(angle(x),y_correct))\r\n\r\n%%\r\nx = [-1 1;-1 -1];\r\ny_correct = 90;\r\nassert(isequal(angle(x),y_correct))\r\n\r\n%%\r\nx = [0.5 sqrt(3)/2;0.2 0];\r\ny_correct = 60;\r\nassert(isequal(angle(x),y_correct))\r\n\r\n%%\r\nx = [-1 1;0.5 sqrt(3)/2];\r\ny_correct = 75;\r\nassert(isequal(angle(x),y_correct))\r\n\r\n%%\r\nx = [0 1;0 5];\r\ny_correct = 0;\r\nassert(isequal(angle(x),y_correct))","published":true,"deleted":false,"likes_count":1,"comments_count":1,"created_by":290843,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":34,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2019-04-02T11:16:36.000Z","updated_at":"2026-02-28T08:22:03.000Z","published_at":"2019-04-02T11:17:50.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGiven 2 pairs of\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ecartesian co-ordinates\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, determine the angle between the 2 vectors formed by the\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003epoints\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e and the\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eorigin\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e. Angle must be in [0,180] and in degrees.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ee.g.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eInput (3 separate inputs)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[[0 1;2 0]\\n[1 1;-2 0]\\n[1 1;2 2]]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eOutput (3 separate outputs):\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[90\\n135\\n0]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":2772,"title":"Find out phase angle of second order system. ","description":"Find out the phase angle of a second order system. \r\n\r\nIn a control system, the phase angle is given by the inverse of cos. ","description_html":"\u003cp\u003eFind out the phase angle of a second order system.\u003c/p\u003e\u003cp\u003eIn a control system, the phase angle is given by the inverse of cos.\u003c/p\u003e","function_template":"function y = phase_angle(x)\r\n  \r\nend","test_suite":"%%\r\nx = 1;\r\ny_correct = 0;\r\nassert(isequal(phase_angle(x),y_correct))\r\n%%\r\nx = 0.5;\r\ny_correct = 1.0472;\r\nassert(abs(phase_angle(x)-y_correct)\u003c0.0001)\r\n%%\r\nx = 0.25;\r\ny_correct =  1.3181;\r\nassert(abs(phase_angle(x)-y_correct)\u003c0.0001)\r\n%%\r\nx = 0.7;\r\ny_correct =   0.7954;\r\nassert(abs(phase_angle(x)-y_correct)\u003c0.0001)","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":27760,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":73,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2014-12-13T10:41:27.000Z","updated_at":"2026-03-02T14:05:34.000Z","published_at":"2014-12-13T10:41:27.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFind out the phase angle of a second order system.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eIn a control system, the phase angle is given by the inverse of cos.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":44271,"title":"0\u003c=x\u003c=pi?","description":"Check whether the given angle is between zero and pi.\r\nReturn logical true or false.","description_html":"\u003cp\u003eCheck whether the given angle is between zero and pi.\r\nReturn logical true or false.\u003c/p\u003e","function_template":"function y = ang(x)\r\n  y = (x==pi/2);\r\nend","test_suite":"%%\r\nx = rand*pi;\r\ny_correct = (200\u003e=100);\r\nassert(isequal(ang(x),y_correct))\r\n%%\r\nx = -rand*pi;\r\ny_correct = (100\u003e=200);\r\nassert(isequal(ang(x),y_correct))\r\n\r\n","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":166,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":140,"test_suite_updated_at":"2017-08-01T23:22:04.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2017-08-01T23:13:05.000Z","updated_at":"2026-02-16T12:15:51.000Z","published_at":"2017-08-01T23:13:38.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eCheck whether the given angle is between zero and pi. Return logical true or false.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":2518,"title":"Find out value of sine given by  degree. ","description":"Find out value of sine given by  degree. \r\nIf theta=30, it's value must be 0.5. ","description_html":"\u003cp\u003eFind out value of sine given by  degree. \r\nIf theta=30, it's value must be 0.5.\u003c/p\u003e","function_template":"function y = your_fcn_name(x)\r\n  y =  x;\r\nend","test_suite":"%%\r\nx = 30;\r\ny_correct =  0.5000;\r\nassert(abs(your_fcn_name(x)-y_correct)\u003c0.0001)\r\n%%\r\nx = 60;\r\ny_correct = 0.8660;\r\nassert(abs(your_fcn_name(x)-y_correct)\u003c0.0001)\r\n%%\r\nx = 90;\r\ny_correct = 1;\r\nassert(isequal(your_fcn_name(x),y_correct))","published":true,"deleted":false,"likes_count":2,"comments_count":0,"created_by":27760,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":356,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2014-08-20T07:02:02.000Z","updated_at":"2026-03-03T22:17:43.000Z","published_at":"2014-08-20T07:02:02.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFind out value of sine given by degree. If theta=30, it's value must be 0.5.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":43563,"title":"Calculate cosine without cos(x)","description":"Solve cos(x).\r\n\r\nThe use of the function cos() and sin() is not allowed.","description_html":"\u003cp\u003eSolve cos(x).\u003c/p\u003e\u003cp\u003eThe use of the function cos() and sin() is not allowed.\u003c/p\u003e","function_template":"function y = my_func(x)\r\n  y = cos(x);\r\nend","test_suite":"%%\r\nx = 0;\r\ny_correct = 1;\r\nassert(abs(my_func(x)-y_correct)\u003c0.0001)\r\n\r\n%%\r\nx = pi/2;\r\ny_correct = 0;\r\nassert(abs(my_func(x)-y_correct)\u003c0.0001)\r\n\r\n%%\r\nx = rand(1)*2*pi;\r\ny_correct = cos(x);\r\nassert(abs(my_func(x)-y_correct)\u003c0.0001)\r\n\r\n%%\r\nassessFunctionAbsence({'sin','cos'}, 'FileName', 'my_func.m')\r\n\r\n","published":true,"deleted":false,"likes_count":1,"comments_count":1,"created_by":14644,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":125,"test_suite_updated_at":"2016-12-01T18:38:29.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2016-10-16T10:35:20.000Z","updated_at":"2026-04-03T02:52:46.000Z","published_at":"2016-10-16T10:42:54.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eSolve cos(x).\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe use of the function cos() and sin() is not allowed.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":44282,"title":"Minimum possible M of the maximum side of a triangle of given area A.","description":"Suppose a triangle has area A.\r\nSuppose it has three sides S1, S2, and S3.\r\nSuppose M = max([S1 S2 S3]).\r\nWhat is the minimum possible value of M?\r\n","description_html":"\u003cp\u003eSuppose a triangle has area A.\r\nSuppose it has three sides S1, S2, and S3.\r\nSuppose M = max([S1 S2 S3]).\r\nWhat is the minimum possible value of M?\u003c/p\u003e","function_template":"function m = tri(a)\r\n  m = max(a/7);\r\nend","test_suite":"%%\r\na = 0.4331;\r\nm = 1.0001;\r\nassert(tri(a)\u003em*0.99)\r\n\r\n%%\r\na = 43.31;\r\nm = 10.001;\r\nassert(tri(a)\u003cm*1.01)\r\n\r\n%%\r\na = 4331;\r\nm = 100.01;\r\nassert(tri(a)\u003em*0.99)\r\n\r\n%%\r\na = 4331;\r\nm = 100.01;\r\nassert(tri(a)\u003cm*1.01)\r\n","published":true,"deleted":false,"likes_count":2,"comments_count":0,"created_by":166,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":62,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2017-08-10T11:39:30.000Z","updated_at":"2026-03-14T18:37:39.000Z","published_at":"2017-08-10T11:39:53.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eSuppose a triangle has area A. Suppose it has three sides S1, S2, and S3. Suppose M = max([S1 S2 S3]). What is the minimum possible value of M?\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":43564,"title":"Calculate sin(x) without sin(x)","description":"Calculate\r\ny = sin(x)\r\n\r\nx = 0 -\u003e y= 0\r\n\r\nwithout the use of sin(x) or cos(x)\r\n","description_html":"\u003cp\u003eCalculate\r\ny = sin(x)\u003c/p\u003e\u003cp\u003ex = 0 -\u0026gt; y= 0\u003c/p\u003e\u003cp\u003ewithout the use of sin(x) or cos(x)\u003c/p\u003e","function_template":"function y = my_func(x)\r\n  y = sin(x);\r\nend","test_suite":"x = 0;\r\ny_correct = 0;\r\nassert(abs(my_func(x)-y_correct)\u003c0.0001)\r\n\r\n%%\r\nx = -pi/2;\r\ny_correct = sin(x);\r\nassert(abs(my_func(x)-y_correct)\u003c0.0001)\r\n\r\n%%\r\nx = rand(1)*2*pi;\r\ny_correct = sin(x);\r\nassert(abs(my_func(x)-y_correct)\u003c0.0001)\r\n\r\n%%\r\nassessFunctionAbsence({'cos', 'sin'}, 'FileName', 'my_func.m');\r\n","published":true,"deleted":false,"likes_count":1,"comments_count":2,"created_by":14644,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":119,"test_suite_updated_at":"2016-12-01T18:41:33.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2016-10-16T10:50:54.000Z","updated_at":"2026-04-03T02:51:49.000Z","published_at":"2016-10-16T10:50:54.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eCalculate y = sin(x)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ex = 0 -\u0026gt; y= 0\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ewithout the use of sin(x) or cos(x)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":45345,"title":"Grazing-01","description":"A cow is tied to an outside corner of a rectangular barn of size (a,b) with a rope of length l. What is the maximum area the cow can graze outside the barn?\r\n\r\n\u003chttps://serving.photos.photobox.com/495639807b8e93bb90ab3c212fe921e51fefc77e0b8756d28871096f5482839b5e5d4bb8.jpg\u003e\r\n\r\nNb.the test cases are simpler for this problem. They'll be enhanced in the next case.","description_html":"\u003cp\u003eA cow is tied to an outside corner of a rectangular barn of size (a,b) with a rope of length l. What is the maximum area the cow can graze outside the barn?\u003c/p\u003e\u003cp\u003e\u003ca href = \"https://serving.photos.photobox.com/495639807b8e93bb90ab3c212fe921e51fefc77e0b8756d28871096f5482839b5e5d4bb8.jpg\"\u003ehttps://serving.photos.photobox.com/495639807b8e93bb90ab3c212fe921e51fefc77e0b8756d28871096f5482839b5e5d4bb8.jpg\u003c/a\u003e\u003c/p\u003e\u003cp\u003eNb.the test cases are simpler for this problem. They'll be enhanced in the next case.\u003c/p\u003e","function_template":"function y = grazing_01(a,b,l)\r\n  y = x;\r\nend","test_suite":"%%\r\nassert(abs(grazing_01(10,20,5)-58.9049)\u003c0.001)\r\n%%\r\nassert(abs(grazing_01(5,25,2)-9.4248)\u003c0.001)\r\n%%\r\nassert(abs(grazing_01(5,25,8)-157.8650)\u003c0.001)\r\n%%\r\nassert(abs(grazing_01(20,20,20)- 942.4778)\u003c0.001)\r\n%%\r\nassert(abs(grazing_01(10,20,0)-0)\u003c0.001)\r\n%%\r\nassert(abs(grazing_01(12,20,25)-1624.9888)\u003c0.001)\r\n\r\n","published":true,"deleted":false,"likes_count":2,"comments_count":3,"created_by":363598,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":19,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2020-02-20T10:45:47.000Z","updated_at":"2026-01-29T12:35:16.000Z","published_at":"2020-02-20T11:20:35.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eA cow is tied to an outside corner of a rectangular barn of size (a,b) with a rope of length l. What is the maximum area the cow can graze outside the barn?\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:hyperlink w:docLocation=\\\"https://serving.photos.photobox.com/495639807b8e93bb90ab3c212fe921e51fefc77e0b8756d28871096f5482839b5e5d4bb8.jpg\\\"\u003e\u003cw:r\u003e\u003cw:t\u003e\u0026lt;https://serving.photos.photobox.com/495639807b8e93bb90ab3c212fe921e51fefc77e0b8756d28871096f5482839b5e5d4bb8.jpg\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e\u0026gt;\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eNb.the test cases are simpler for this problem. They'll be enhanced in the next case.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":401,"title":"cos for boss?","description":"a programmer had too much coffee and his boss needs cos(alpha+beta) correctly, especially when alpha or beta are close to pi/2 and the coffee is close to ninety degrees. A hint: sin() may be appropriate for some input, without committing any sin!! ","description_html":"\u003cp\u003ea programmer had too much coffee and his boss needs cos(alpha+beta) correctly, especially when alpha or beta are close to pi/2 and the coffee is close to ninety degrees. A hint: sin() may be appropriate for some input, without committing any sin!!\u003c/p\u003e","function_template":"function coffee = cos_for_boss(alfa,bita)\r\n  coffee=cos(alfalfa+bitabita);\r\nend","test_suite":"%%\r\nalfa=pi/2;\r\nbita=-1/10^20;\r\ncos_correct = 1/10^20;\r\nassert(abs(cos_for_boss(alfa,bita)-cos_correct)\u003ceps/10)\r\n%%\r\nbita=pi/2;\r\nalfa=-1/11^20;\r\ncos_correct = 1/11^20;\r\nassert(abs(cos_for_boss(alfa,bita)-cos_correct)\u003ceps/10)\r\n%%\r\nbita=pi/6;\r\nalfa=pi/6;\r\ncos_correct = 1/2;\r\nassert(abs(cos_for_boss(alfa,bita)-cos_correct)\u003ceps*10)\r\n%%\r\nbita=pi/8;\r\nalfa=pi/8;\r\ncos_correct = 1/sqrt(2);\r\nassert(abs(cos_for_boss(alfa,bita)-cos_correct)\u003ceps*10)\r\n%%\r\nbita=pi/12;\r\nalfa=pi/4;\r\ncos_correct = 1/2;\r\nassert(abs(cos_for_boss(alfa,bita)-cos_correct)\u003ceps*10)\r\n","published":true,"deleted":false,"likes_count":2,"comments_count":2,"created_by":166,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":64,"test_suite_updated_at":"2012-02-26T08:30:12.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2012-02-24T22:49:02.000Z","updated_at":"2025-12-14T23:19:46.000Z","published_at":"2012-02-26T08:36:11.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ea programmer had too much coffee and his boss needs cos(alpha+beta) correctly, especially when alpha or beta are close to pi/2 and the coffee is close to ninety degrees. A hint: sin() may be appropriate for some input, without committing any sin!!\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":336,"title":"Similar Triangles - find the height of the tree","description":"Given the height, h1, of a power pole, shorter than a tree, a given distance, x2 away, please find h2, height of the tree. Please note that the angle, phi, is the acute angle measured from the ground to an observer's line of sight aimed to the sucessive peaks of the power pole and the tree, in that order. Also the distance from the observer to the power pole is x1, also a given. x2 is the distance between the tree and the power pole. In all tests x1 is always a multiple of x2.\r\n\r\n\r\nInputs: h1, x1, x2\r\n\r\nOutput: h2\r\n\r\nHINT: find phi, given h1 and x1. Phi may be measured in degrees or radians. Note that default trig functions in MATLAB operate in radians.\r\n\r\nEX:\r\nx1 = 4;\r\nx2 = 4;\r\nh1 = 3;\r\n\r\n\u003e\u003eh2=findHeight(x1,x2,h1)\r\n\r\nh2=6\r\n\r\n\u003e\u003e","description_html":"\u003cp\u003eGiven the height, h1, of a power pole, shorter than a tree, a given distance, x2 away, please find h2, height of the tree. Please note that the angle, phi, is the acute angle measured from the ground to an observer's line of sight aimed to the sucessive peaks of the power pole and the tree, in that order. Also the distance from the observer to the power pole is x1, also a given. x2 is the distance between the tree and the power pole. In all tests x1 is always a multiple of x2.\u003c/p\u003e\u003cp\u003eInputs: h1, x1, x2\u003c/p\u003e\u003cp\u003eOutput: h2\u003c/p\u003e\u003cp\u003eHINT: find phi, given h1 and x1. Phi may be measured in degrees or radians. Note that default trig functions in MATLAB operate in radians.\u003c/p\u003e\u003cp\u003eEX:\r\nx1 = 4;\r\nx2 = 4;\r\nh1 = 3;\u003c/p\u003e\u003cp\u003e\u003e\u003eh2=findHeight(x1,x2,h1)\u003c/p\u003e\u003cp\u003eh2=6\u003c/p\u003e\u003cp\u003e\u003e\u003e\u003c/p\u003e","function_template":"function h2 = findHeight(x1,x2,h1)\r\n  h2 = heightoftree\r\nend","test_suite":"%%\r\nx1 = 4;\r\nx2 = 4;\r\nh1 = 3;\r\ny_correct = 6;\r\nassert(isequal(findHeight(x1,x2,h1),y_correct))\r\n%%\r\nx1 = 4;\r\nx2 = 8;\r\nh1 = 3;\r\ny_correct = 9;\r\nassert(isequal(findHeight(x1,x2,h1),y_correct))\r\n%%\r\nx1 = 4;\r\nx2 = 12;\r\nh1 = 3;\r\ny_correct = 12;\r\nassert(isequal(findHeight(x1,x2,h1),y_correct))\r\n%%\r\nx1 = 4;\r\nx2 = 16;\r\nh1 = 3;\r\ny_correct = 15;\r\nassert(isequal(findHeight(x1,x2,h1),y_correct))\r\n%%\r\nx1 = 4;\r\nx2 = 20;\r\nh1 = 3;\r\ny_correct = 18;\r\nassert(isequal(findHeight(x1,x2,h1),y_correct))\r\n%%\r\nx1 = 4;\r\nx2 = 24;\r\nh1 = 3;\r\ny_correct = 21;\r\nassert(isequal(findHeight(x1,x2,h1),y_correct))\r\n%%\r\nx1 = 4;\r\nx2 = 12;\r\nh1 = 5;\r\ny_correct = 20;\r\nassert(isequal(findHeight(x1,x2,h1),y_correct))\r\n%%\r\nx1 = 4;\r\nx2 = 16;\r\nh1 = 10;\r\ny_correct = 50;\r\nassert(isequal(findHeight(x1,x2,h1),y_correct))\r\n%%\r\nx1 = 2;\r\nx2 = 4;\r\nh1 = 5;\r\ny_correct = 15;\r\nassert(isequal(findHeight(x1,x2,h1),y_correct))\r\n%%\r\nx1 = 3;\r\nx2 = 6;\r\nh1 = 4;\r\ny_correct = 12;\r\nassert(isequal(findHeight(x1,x2,h1),y_correct))\r\n\r\n\r\n","published":true,"deleted":false,"likes_count":4,"comments_count":6,"created_by":1103,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":469,"test_suite_updated_at":"2012-02-18T04:42:47.000Z","rescore_all_solutions":false,"group_id":17,"created_at":"2012-02-17T22:52:21.000Z","updated_at":"2026-03-13T05:26:44.000Z","published_at":"2012-02-18T04:42:47.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGiven the height, h1, of a power pole, shorter than a tree, a given distance, x2 away, please find h2, height of the tree. Please note that the angle, phi, is the acute angle measured from the ground to an observer's line of sight aimed to the sucessive peaks of the power pole and the tree, in that order. Also the distance from the observer to the power pole is x1, also a given. x2 is the distance between the tree and the power pole. In all tests x1 is always a multiple of x2.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eInputs: h1, x1, x2\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eOutput: h2\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eHINT: find phi, given h1 and x1. Phi may be measured in degrees or radians. Note that default trig functions in MATLAB operate in radians.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eEX: x1 = 4; x2 = 4; h1 = 3;\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003e\u003eh2=findHeight(x1,x2,h1)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eh2=6\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003e\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":837,"title":"Find all the zeros of sinus , cosinus and tangent in a given interval","description":"The aim is to find all the zeros of a function within an interval.\r\n\r\n*Input* : \r\n\r\n* fcn : an anonymous function (@sin, @cos...)\r\n* \r\n* lb : lower bound\r\n* \r\n* ub :upper bound\r\n\r\n\r\n*Output* :\r\n\r\n* output :  vector with unique values for which the input function return zero\r\nThe values must be sorted in ascending order. \r\n\r\n*Example* \r\n\r\n\r\n\r\n  output = find_zeros(@sin,0,2*pi) will return :\r\n\r\n  output = [0.0000    3.1416    6.2832]\r\n\r\nsince the sinus function between [0 2pi] is zero for [0 pi 2pi]\r\n","description_html":"\u003cdiv style = \"text-align: start; line-height: 20px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: normal; text-decoration: none; white-space: normal; \"\u003e\u003cdiv style=\"display: block; min-width: 0px; padding-top: 0px; transform-origin: 332px 197px; vertical-align: baseline; perspective-origin: 332px 197px; \"\u003e\u003cdiv style=\"font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-bottom: 9px; margin-left: 4px; margin-right: 10px; margin-top: 2px; text-align: left; transform-origin: 309px 10.5px; white-space: pre-wrap; perspective-origin: 309px 10.5px; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"display: inline; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; transform-origin: 0px 0px; perspective-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eThe aim is to find all the zeros of a function within an interval.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-bottom: 9px; margin-left: 4px; margin-right: 10px; margin-top: 2px; text-align: left; transform-origin: 309px 10.5px; white-space: pre-wrap; perspective-origin: 309px 10.5px; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"display: inline; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; transform-origin: 0px 0px; perspective-origin: 0px 0px; \"\u003e\u003cspan style=\"font-weight: bold; \"\u003eInput\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"display: inline; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; transform-origin: 0px 0px; perspective-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e :\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cul style=\"font-family: Helvetica, Arial, sans-serif; list-style-type: square; margin-bottom: 20px; margin-top: 10px; transform-origin: 316px 50px; perspective-origin: 316px 50px; margin-top: 10px; margin-bottom: 20px; \"\u003e\u003cli style=\"display: list-item; margin-bottom: 0px; margin-left: 56px; margin-top: 0px; text-align: left; transform-origin: 288px 10px; white-space: pre-wrap; perspective-origin: 288px 10px; margin-left: 56px; \"\u003e\u003cspan style=\"display: inline; margin-left: 0px; transform-origin: 0px 0px; perspective-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003efcn : an anonymous function (@sin, @cos...)\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"display: list-item; margin-bottom: 0px; margin-left: 56px; margin-top: 0px; text-align: left; transform-origin: 288px 10px; white-space: pre-wrap; perspective-origin: 288px 10px; margin-left: 56px; \"\u003e\u003c/li\u003e\u003cli style=\"display: list-item; margin-bottom: 0px; margin-left: 56px; margin-top: 0px; text-align: left; transform-origin: 288px 10px; white-space: pre-wrap; perspective-origin: 288px 10px; margin-left: 56px; \"\u003e\u003cspan style=\"display: inline; margin-left: 0px; transform-origin: 0px 0px; perspective-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003elb : lower bound\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"display: list-item; margin-bottom: 0px; margin-left: 56px; margin-top: 0px; text-align: left; transform-origin: 288px 10px; white-space: pre-wrap; perspective-origin: 288px 10px; margin-left: 56px; \"\u003e\u003c/li\u003e\u003cli style=\"display: list-item; margin-bottom: 0px; margin-left: 56px; margin-top: 0px; text-align: left; transform-origin: 288px 10px; white-space: pre-wrap; perspective-origin: 288px 10px; margin-left: 56px; \"\u003e\u003cspan style=\"display: inline; margin-left: 0px; transform-origin: 0px 0px; perspective-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eub :upper bound\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ul\u003e\u003cdiv style=\"font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-bottom: 9px; margin-left: 4px; margin-right: 10px; margin-top: 2px; text-align: left; transform-origin: 309px 10.5px; white-space: pre-wrap; perspective-origin: 309px 10.5px; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"display: inline; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; transform-origin: 0px 0px; perspective-origin: 0px 0px; \"\u003e\u003cspan style=\"font-weight: bold; \"\u003eOutput\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"display: inline; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; transform-origin: 0px 0px; perspective-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e :\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cul style=\"font-family: Helvetica, Arial, sans-serif; list-style-type: square; margin-bottom: 20px; margin-top: 10px; transform-origin: 316px 20px; perspective-origin: 316px 20px; margin-top: 10px; margin-bottom: 20px; \"\u003e\u003cli style=\"display: list-item; margin-bottom: 0px; margin-left: 56px; margin-top: 0px; text-align: left; transform-origin: 288px 20px; white-space: pre-wrap; perspective-origin: 288px 20px; margin-left: 56px; \"\u003e\u003cspan style=\"display: inline; margin-left: 0px; transform-origin: 0px 0px; perspective-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eoutput : vector with unique values for which the input function return zeroThe values must be sorted in ascending order.\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ul\u003e\u003cdiv style=\"font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-bottom: 9px; margin-left: 4px; margin-right: 10px; margin-top: 2px; text-align: left; transform-origin: 309px 10.5px; white-space: pre-wrap; perspective-origin: 309px 10.5px; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"display: inline; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; transform-origin: 0px 0px; perspective-origin: 0px 0px; \"\u003e\u003cspan style=\"font-weight: bold; \"\u003eExample\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgb(247, 247, 247); border-bottom-left-radius: 4px; border-bottom-right-radius: 4px; border-top-left-radius: 4px; border-top-right-radius: 4px; margin-bottom: 10px; margin-left: 3px; margin-right: 3px; margin-top: 10px; transform-origin: 329px 30px; perspective-origin: 329px 30px; margin-left: 3px; margin-top: 10px; margin-bottom: 10px; margin-right: 3px; \"\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-height: 18px; padding-left: 4px; transform-origin: 329px 10px; white-space: nowrap; perspective-origin: 329px 10px; \"\u003e\u003cspan style=\"border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-right: 45px; min-height: 0px; padding-left: 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; perspective-origin: 0px 0px; margin-right: 45px; \"\u003e\u003cspan style=\"margin-right: 0px; \"\u003eoutput = find_zeros(@sin,0,2*pi) will \u003c/span\u003e\u003cspan style=\"border-bottom-color: rgb(170, 4, 249); border-left-color: rgb(170, 4, 249); border-right-color: rgb(170, 4, 249); border-top-color: rgb(170, 4, 249); caret-color: rgb(170, 4, 249); color: rgb(170, 4, 249); margin-right: 0px; outline-color: rgb(170, 4, 249); text-decoration-color: rgb(170, 4, 249); column-rule-color: rgb(170, 4, 249); \"\u003ereturn :\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-height: 18px; padding-left: 4px; transform-origin: 329px 10px; white-space: nowrap; perspective-origin: 329px 10px; \"\u003e\u003cspan style=\"border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-right: 45px; min-height: 0px; padding-left: 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; perspective-origin: 0px 0px; margin-right: 45px; \"\u003e\u003cspan style=\"margin-right: 0px; \"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-height: 18px; padding-left: 4px; transform-origin: 329px 10px; white-space: nowrap; perspective-origin: 329px 10px; \"\u003e\u003cspan style=\"border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-right: 45px; min-height: 0px; padding-left: 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; perspective-origin: 0px 0px; margin-right: 45px; \"\u003e\u003cspan style=\"margin-right: 0px; \"\u003eoutput = [0.0000    3.1416    6.2832]\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003cdiv style=\"font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-bottom: 9px; margin-left: 4px; margin-right: 10px; margin-top: 10px; text-align: left; transform-origin: 309px 10.5px; white-space: pre-wrap; perspective-origin: 309px 10.5px; margin-left: 4px; margin-top: 10px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"display: inline; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; transform-origin: 0px 0px; perspective-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003esince the sinus function between [0 2pi] is zero for [0 pi 2pi]\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function output = find_zeros(fcn,lb,ub)\r\noutput = lb*up;","test_suite":"%% Test sinus between [0 2pi]\r\nassert(all(abs(find_zeros(@sin,0,2*pi) -[0 pi 2*pi])\u003c1e-9))\r\n\r\n%% [0 pi]\r\nassert(all(abs(find_zeros(@sin,0,pi) -[0 pi ])\u003c1e-9))\r\n\r\n%% [0 pi/3] \r\nassert(all(abs(find_zeros(@sin,0,pi/3) -0) \u003c1e-9))\r\n\r\n%% Test cos between [0 2pi]\r\nassert(all(abs(find_zeros(@cos,0,2*pi) -[pi/2 3*pi/2])\u003c1e-9))\r\n\r\n%% Test tan between [0 pi/4]\r\nassert(all(abs(find_zeros(@tan,0,pi/4) -0)\u003c1e-9))","published":true,"deleted":false,"likes_count":1,"comments_count":7,"created_by":639,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":24,"test_suite_updated_at":"2020-09-29T14:30:54.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2012-07-17T07:42:46.000Z","updated_at":"2026-01-03T12:33:06.000Z","published_at":"2012-07-17T08:10:10.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe aim is to find all the zeros of a function within an interval.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eInput\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e :\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003efcn : an anonymous function (@sin, @cos...)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003elb : lower bound\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eub :upper bound\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eOutput\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e :\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eoutput : vector with unique values for which the input function return zeroThe values must be sorted in ascending order.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eExample\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[output = find_zeros(@sin,0,2*pi) will return :\\n\\noutput = [0.0000    3.1416    6.2832]]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003esince the sinus function between [0 2pi] is zero for [0 pi 2pi]\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":44070,"title":"Under the sea: Snell's law \u0026 total internal reflection","description":"\u003chttps://en.wikipedia.org/wiki/Snell's_law\u003e\r\n\r\nWhen a light travels from one medium to another medium, depending on the refractive index, the light will bend with a certain angle. For certain combination of materials, it might be that light cannot escape one medium at all from a certain angle (greater than critical angle). It is called total internal reflection. If you point a flashlight from \"under the sea\" the light won't leave the water at all. \r\n\r\nFor given refractive indices, find critical angle where total internal reflection happens. If total internal reflection does not happen for any angle, then return \"-1\".\r\n\r\nExample1: n_in = 1.333, n_out = 1, theta_crit = 48.6 degrees;\r\nExample2: n_out = 1, n_in = 1.333, theta_crit = -1 (total internal reflection does not occur, if you are in the air, and beaming light at the water.)\r\n\r\nInput of function: n_in, n_out (refractive index, positive) \r\nOutput: critical angle (rounded to nearest integer), if total internal reflection occurs. Else return -1.","description_html":"\u003cp\u003e\u003ca href = \"https://en.wikipedia.org/wiki/Snell's_law\"\u003ehttps://en.wikipedia.org/wiki/Snell's_law\u003c/a\u003e\u003c/p\u003e\u003cp\u003eWhen a light travels from one medium to another medium, depending on the refractive index, the light will bend with a certain angle. For certain combination of materials, it might be that light cannot escape one medium at all from a certain angle (greater than critical angle). It is called total internal reflection. If you point a flashlight from \"under the sea\" the light won't leave the water at all.\u003c/p\u003e\u003cp\u003eFor given refractive indices, find critical angle where total internal reflection happens. If total internal reflection does not happen for any angle, then return \"-1\".\u003c/p\u003e\u003cp\u003eExample1: n_in = 1.333, n_out = 1, theta_crit = 48.6 degrees;\r\nExample2: n_out = 1, n_in = 1.333, theta_crit = -1 (total internal reflection does not occur, if you are in the air, and beaming light at the water.)\u003c/p\u003e\u003cp\u003eInput of function: n_in, n_out (refractive index, positive) \r\nOutput: critical angle (rounded to nearest integer), if total internal reflection occurs. Else return -1.\u003c/p\u003e","function_template":"function theta_crit = totalInternalReflection(n_in,n_out)\r\n  theta_crit = -1;\r\nend","test_suite":"%%\r\nn_in = 3; n_out = 3;\r\ntheta_crit_correct = -1;\r\nassert(isequal(totalInternalReflection(n_in,n_out),theta_crit_correct))\r\n\r\n%%\r\nn_in = 1; n_out = 1.333;\r\ntheta_crit_correct = -1;\r\nassert(isequal(totalInternalReflection(n_in,n_out),theta_crit_correct))\r\n\r\n%%\r\nn_in = 1.333; n_out = 1;\r\ntheta_crit_correct = 49;\r\nassert(isequal(totalInternalReflection(n_in,n_out),theta_crit_correct))\r\n\r\n%%\r\nn_in = 4; n_out = 3;\r\ntheta_crit_correct = 49;\r\nassert(isequal(totalInternalReflection(n_in,n_out),theta_crit_correct))\r\n\r\n%%\r\nn_in = 4; n_out = 2;\r\ntheta_crit_correct = 30;\r\nassert(isequal(totalInternalReflection(n_in,n_out),theta_crit_correct))","published":true,"deleted":false,"likes_count":2,"comments_count":6,"created_by":115733,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":58,"test_suite_updated_at":"2017-02-16T21:45:07.000Z","rescore_all_solutions":false,"group_id":37,"created_at":"2017-02-14T00:59:14.000Z","updated_at":"2026-02-08T13:00:17.000Z","published_at":"2017-02-14T00:59:14.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:hyperlink w:docLocation=\\\"https://en.wikipedia.org/wiki/Snell's_law\\\"\u003e\u003cw:r\u003e\u003cw:t\u003e\u0026lt;https://en.wikipedia.org/wiki/Snell's_law\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e\u0026gt;\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWhen a light travels from one medium to another medium, depending on the refractive index, the light will bend with a certain angle. For certain combination of materials, it might be that light cannot escape one medium at all from a certain angle (greater than critical angle). It is called total internal reflection. If you point a flashlight from \\\"under the sea\\\" the light won't leave the water at all.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFor given refractive indices, find critical angle where total internal reflection happens. If total internal reflection does not happen for any angle, then return \\\"-1\\\".\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eExample1: n_in = 1.333, n_out = 1, theta_crit = 48.6 degrees; Example2: n_out = 1, n_in = 1.333, theta_crit = -1 (total internal reflection does not occur, if you are in the air, and beaming light at the water.)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eInput of function: n_in, n_out (refractive index, positive) Output: critical angle (rounded to nearest integer), if total internal reflection occurs. Else return -1.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":44936,"title":"Float like a cannonball","description":"Given gravity on earth (g=9.81 [m/s/s]) find the distance s [m] by a cannonball propelled at a speed of u [m/s] from the origin at an angle theta [deg] measured from the horizontal. Assume no air resistance or bouncing. The altitude of the release of the cannon ball is 0 m and the travel should have the appropriate sign (i.e. behind the release point would be negative).\r\nHint: Consider logical reasoning when the orientation of the firing vector would be into the ground!!","description_html":"\u003cp\u003eGiven gravity on earth (g=9.81 [m/s/s]) find the distance s [m] by a cannonball propelled at a speed of u [m/s] from the origin at an angle theta [deg] measured from the horizontal. Assume no air resistance or bouncing. The altitude of the release of the cannon ball is 0 m and the travel should have the appropriate sign (i.e. behind the release point would be negative).\r\nHint: Consider logical reasoning when the orientation of the firing vector would be into the ground!!\u003c/p\u003e","function_template":"function s = CannonBall(u,theta)\r\n%Stones taught me to fly...\r\n  s = u*theta;\r\nend","test_suite":"%%\r\nu= 100;\r\ntheta=85;\r\ny_correct = 177;\r\nassert(isequal(round(CannonBall(u,theta)),y_correct))\r\n\r\n%%\r\nu= 31.42;\r\ntheta=45;\r\ny_correct = 101;\r\nassert(isequal(round(CannonBall(u,theta)),y_correct))\r\n\r\n%%\r\nu= 31.42;\r\ntheta=-41;\r\ny_correct = 0;\r\nassert(isequal(round(CannonBall(u,theta)),y_correct))\r\n\r\n%%\r\nu= 100;\r\ntheta=30;\r\ny_correct = 883;\r\nassert(isequal(round(CannonBall(u,theta)),y_correct))\r\n\r\n%%\r\nu= -100;\r\ntheta=30;\r\ny_correct = 0;\r\nassert(isequal(round(CannonBall(u,theta)),y_correct))\r\n\r\n\r\n%%\r\nu= -100;\r\ntheta=210;\r\ny_correct = 883;\r\nassert(isequal(round(CannonBall(u,theta)),y_correct))\r\n\r\n\r\n%%\r\nu= 100;\r\ntheta=210;\r\ny_correct = 0;\r\nassert(isequal(round(CannonBall(u,theta)),y_correct))\r\n\r\n%%\r\nu= 0;\r\ntheta=40;\r\ny_correct = 0;\r\nassert(isequal(round(CannonBall(u,theta)),y_correct))\r\n\r\n%%\r\nu= 100;\r\ntheta=90;\r\ny_correct = 0;\r\nassert(isequal(round(CannonBall(u,theta)),y_correct))\r\n\r\n%%\r\nu= 100;\r\ntheta=0;\r\ny_correct = 0;\r\nassert(isequal(round(CannonBall(u,theta)),y_correct))\r\n\r\n%%\r\nfiletext = fileread('CannonBall.m');\r\nassert(isempty(strfind(filetext, 'regexp'))); assert(isempty(strfind(filetext, 'eval'))) \r\n\r\n","published":true,"deleted":false,"likes_count":3,"comments_count":0,"created_by":170350,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":26,"test_suite_updated_at":"2019-08-02T09:56:25.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2019-08-02T09:45:02.000Z","updated_at":"2026-01-02T13:04:50.000Z","published_at":"2019-08-02T09:45:02.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGiven gravity on earth (g=9.81 [m/s/s]) find the distance s [m] by a cannonball propelled at a speed of u [m/s] from the origin at an angle theta [deg] measured from the horizontal. Assume no air resistance or bouncing. The altitude of the release of the cannon ball is 0 m and the travel should have the appropriate sign (i.e. behind the release point would be negative). Hint: Consider logical reasoning when the orientation of the firing vector would be into the ground!!\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":2495,"title":"Find the first N zeros of the 666 function","description":"Using the following definition of the 666 function for this problem: _f(n)=sin('nnn')-cos(n*n*n)_, write a function that returns the first N integer zeros of the 666 function, formatted as 'nnn'.\r\n\r\nFor example:\r\n\r\nsixsixsix(1) = should return 666\r\n\r\nsixsixsix(7) should return 666 151515 181818 272727 424242 636363 666666\r\n\r\nNote 1: Consider a 'zero' to occur when f(n)\u003c1e-8\r\n\r\nNote 2: The sin and cosine functions must be in degrees, not radians.","description_html":"\u003cp\u003eUsing the following definition of the 666 function for this problem: \u003ci\u003ef(n)=sin('nnn')-cos(n*n*n)\u003c/i\u003e, write a function that returns the first N integer zeros of the 666 function, formatted as 'nnn'.\u003c/p\u003e\u003cp\u003eFor example:\u003c/p\u003e\u003cp\u003esixsixsix(1) = should return 666\u003c/p\u003e\u003cp\u003esixsixsix(7) should return 666 151515 181818 272727 424242 636363 666666\u003c/p\u003e\u003cp\u003eNote 1: Consider a 'zero' to occur when f(n)\u0026lt;1e-8\u003c/p\u003e\u003cp\u003eNote 2: The sin and cosine functions must be in degrees, not radians.\u003c/p\u003e","function_template":"function M = sixsixsix(N)\r\n\r\nend","test_suite":"%%\r\nN = 1;\r\nM_correct = 666;\r\nassert(isequal(sixsixsix(N),M_correct))\r\n%%\r\nN = 7;\r\nM_correct = [666   151515   181818   272727   424242   636363   666666];\r\nassert(isequal(sixsixsix(N),M_correct))\r\n%%\r\nN = 25;\r\nM_correct=[666 151515 181818 272727 424242 636363 666666 757575 878787 909090 105105105 114114114 117117117 138138138 153153153 162162162 165165165 177177177 186186186 210210210 213213213 225225225 234234234 237237237 258258258];\r\nassert(isequal(sixsixsix(N),M_correct))\r\n%%\r\nN = 63;\r\nM_correct = [666 151515 181818 272727 424242 636363 666666 757575 878787 909090 105105105 114114114 117117117 138138138 153153153 162162162 165165165 177177177 186186186 210210210 213213213 225225225 234234234 237237237 258258258 273273273 282282282 285285285 297297297 306306306 330330330 333333333 345345345 354354354 357357357 378378378 393393393 402402402 405405405 417417417 426426426 450450450 453453453 465465465 474474474 477477477 498498498 513513513 522522522 525525525 537537537 546546546 570570570 573573573 585585585 594594594 597597597 618618618 633633633 642642642 645645645 657657657 666666666];\r\nassert(isequal(sixsixsix(N),M_correct))\r\n","published":true,"deleted":false,"likes_count":2,"comments_count":3,"created_by":379,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":24,"test_suite_updated_at":"2014-08-09T09:21:11.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2014-08-09T09:16:38.000Z","updated_at":"2026-01-03T12:55:27.000Z","published_at":"2014-08-09T09:21:11.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eUsing the following definition of the 666 function for this problem:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ef(n)=sin('nnn')-cos(n*n*n)\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, write a function that returns the first N integer zeros of the 666 function, formatted as 'nnn'.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFor example:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003esixsixsix(1) = should return 666\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003esixsixsix(7) should return 666 151515 181818 272727 424242 636363 666666\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eNote 1: Consider a 'zero' to occur when f(n)\u0026lt;1e-8\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eNote 2: The sin and cosine functions must be in degrees, not radians.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":61081,"title":"Slicing the area of a regular polygon","description":"Given the area, A, of a regular polygon with n sides, each of length s, consider its decomposition in congruent isosceles triangles of base s and heigth h. Find the rectangle, with dimensions L×h, which covers all n triangles in their adjacent positions (n\u003e3, cf. figure below). Complete the problem by determining the area, A_r, of the rectangle.\r\nHint: Consider that we are slicing the polygon into triangular slices and put them into the rectangle.\r\ninput: (A, n)\r\noutput: y = [L h A_r]\r\n","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none; white-space: normal; \"\u003e\u003cdiv style=\"block-size: 575.8px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 408px 287.9px; transform-origin: 408px 287.9px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 31.5px; text-align: left; transform-origin: 385px 31.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eGiven the area, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eA\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, of a regular polygon with \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003en\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e sides, each of length \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003es\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, consider its decomposition in congruent isosceles triangles of base \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003es\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and heigth \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eh\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. Find the rectangle, with dimensions \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eL\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e×\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eh\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, which covers all \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003en\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e triangles in their adjacent positions (\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003en\u0026gt;3,\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e cf. figure below). Complete the problem by determining the area, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eA_r\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, of the rectangle.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eHint: Consider that we are slicing the polygon into triangular slices and put them into the rectangle.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003einput:\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e(A, n)\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003eoutput:\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003ey = [L h A_r]\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 413.8px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 206.9px; text-align: left; transform-origin: 385px 206.9px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cimg class=\"imageNode\" width=\"501\" height=\"408\" style=\"vertical-align: baseline;width: 501px;height: 408px\" src=\"data:image/png;base64,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\" alt=\"Slicing square (n=4)\" data-image-state=\"image-loaded\"\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = slicing(A,n)\r\n  y = [L h A_r];\r\nend","test_suite":"%%\r\nA = 16;\r\nn = 4;\r\ny_correct = [10 2 20];\r\nassert(isequal(slicing(A,n),y_correct))\r\n\r\n%%\r\nA = 20;\r\nn = 5; \r\ny_correct = [10.22849568767431 2.34638608968871 24];\r\ntolerance = 1e-13;\r\nassert(all(abs(slicing(A,n)-y_correct)\u003ctolerance))\r\n\r\n%%\r\nfiletext = fileread('slicing.m');\r\nillegal = contains(filetext, 'assignin') || contains(filetext, 'regexp') || ...\r\n          contains(filetext, 'str2num'); \r\nassert(~illegal)\r\n\r\n%%\r\nA = 20;\r\nn = 6; \r\ny_correct = [7*sqrt(10*3^(-3/2)) sqrt(10*3^(-1/2)) 70/3];\r\ntolerance = 1e-13;\r\nassert(all(abs(slicing(A,n)-y_correct)\u003ctolerance))\r\n\r\n%%\r\nA = 32;\r\nn = 8; \r\ny_correct = [18*sqrt(sqrt(2)-1) 2/sqrt(sqrt(2)-1) 36];\r\ntolerance = 1e-13;\r\nassert(all(abs(slicing(A,n)-y_correct)\u003ctolerance))\r\n","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":4993982,"edited_by":4993982,"edited_at":"2025-11-19T14:59:52.000Z","deleted_by":null,"deleted_at":null,"solvers_count":8,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2025-11-18T11:18:12.000Z","updated_at":"2026-03-20T13:59:51.000Z","published_at":"2025-11-19T14:59:52.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGiven the area, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eA\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, of a regular polygon with \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e sides, each of length \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003es\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, consider its decomposition in congruent isosceles triangles of base \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003es\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e and heigth \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eh\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e. Find the rectangle, with dimensions \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eL\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e×\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eh\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, which covers all \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e triangles in their adjacent positions (\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003en\u0026gt;3,\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e cf. figure below). Complete the problem by determining the area, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eA_r\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, of the rectangle.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eHint: Consider that we are slicing the polygon into triangular slices and put them into the rectangle.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003einput:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e(A, n)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eoutput:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ey = [L h A_r]\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"408\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"501\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"baseline\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"Slicing square (n=4)\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId1\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/image\",\"target\":\"/media/image1.png\",\"relationshipId\":\"rId1\"}]},{\"partUri\":\"/media/image1.png\",\"contentType\":\"image/png\",\"content\":\"data:image/png;base64,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\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":60311,"title":"Travel a path","description":"In Cody Problem 60251, minnolina asks us to determine the end point given a string indicating unit movements forward, backward, left, and right. For example, ‘fflff’ brings the marker to the point (-1,4). \r\nThis problem extends that one by specifying a heading (H)—i.e., an angle in degrees measured clockwise from north, or the positive y-direction—and a distance (D) to move. The movement string corresponding to the example above would be ‘H0 D1 H0 D1 H270 D1 H0 D1 H0 D1’.\r\nWrite a function that determines the points, starting at an initial point with coordinates in x0y0, resulting from a movement string. The output should be an nx2 matrix with the x and y coordinates of the points in the columns.","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 165px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 82.5px; transform-origin: 407px 82.5px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 7.775px 8px; transform-origin: 7.775px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eIn \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/60251\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"text-decoration-line: underline; \"\u003eCody Problem 60251\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 298.35px 8px; transform-origin: 298.35px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, minnolina asks us to determine the end point given a string indicating unit movements forward, backward, left, and right. For example, ‘fflff’ brings the marker to the point (-1,4). \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 31.5px; text-align: left; transform-origin: 384px 31.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 384px 8px; transform-origin: 384px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThis problem extends that one by specifying a heading (H)—i.e., an angle in degrees measured clockwise from north, or the positive y-direction—and a distance (D) to move. The movement string corresponding to the example above would be ‘H0 D1 H0 D1 H270 D1 H0 D1 H0 D1’.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 272.15px 8px; transform-origin: 272.15px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function that determines the points, starting at an initial point with coordinates in \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 15.4px 8px; transform-origin: 15.4px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003ex0y0\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 88.675px 8px; transform-origin: 88.675px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, resulting from a movement string. The output should be an nx2 matrix with the x and y coordinates of the points in the columns.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function xy = travelPath(s,x0y0)\r\n% s = movement string of the form 'Hx Dy...', which moves y units with heading x degrees\r\n% x0y0 = [x0 y0], starting point\r\n  xy = x0y0+[cos(s) sin(s)];\r\nend","test_suite":"%% \r\ns = 'H0 D1 H0 D1 H270 D1 H0 D1 H0 D1';\r\nx0y0 = [0,0];\r\nxy = travelPath(s,x0y0);\r\nxy_correct = [0 0; 0 1; 0 2; -1 2; -1 3; -1 4];\r\nassert(all(abs(xy-xy_correct)\u003c1e-12,'all'))\r\n\r\n%% \r\ns = 'H0 D1 H0 D1 H90 D1 H0 D1 H0 D1';\r\nx0y0 = [0,0];\r\nxy = travelPath(s,x0y0);\r\nxy_correct = [0 0; 0 1; 0 2; 1 2; 1 3; 1 4];\r\nassert(all(abs(xy-xy_correct)\u003c1e-12,'all'))\r\n\r\n%% \r\ns = 'H0 D1 H180 D1 H270 D1 H90 D1';\r\nx0y0 = [0,0];\r\nxy = travelPath(s,x0y0);\r\nxy_correct = [0 0; 0 1; 0 0; -1 0; 0 0];\r\nassert(all(abs(xy-xy_correct)\u003c1e-12,'all'))\r\n\r\n%% \r\ns = 'H45 D3 H315 D3 H225 D3 H135 D3';\r\nx0y0 = [1,5];\r\nxy = travelPath(s,x0y0);\r\nxy_correct = [1 5; 3.121320343559643 7.121320343559643; 1 9.242640687119286; -1.121320343559643 7.121320343559643; 1 5];\r\nassert(all(abs(xy-xy_correct)\u003c1e-12,'all'))\r\n\r\n%% \r\ns = 'H10 D5 H20 D4 H30 D3 H40 D2 H50 D1';\r\nx0y0 = [-1 -4];\r\nxy = travelPath(s,x0y0);\r\nxy_correct = [-1 -4; -0.131759111665348 0.924038765061040; 1.236321461637326 4.682809248204673; 2.736321461637326 7.280885459557989; 4.021896681010405 8.812974345795945; 4.787941124129383 9.455761955482485];\r\nassert(all(abs(xy-xy_correct)\u003c1e-12,'all'))\r\n\r\n%% \r\ns = 'H27 D5 H153 D5 H27 D4 H153 D4 H27 D3 H153 D3 H27 D2 H153 D2 H27 D1 H153 D1';\r\nx0y0 = [0 0];\r\nxy = travelPath(s,x0y0);\r\nxy_correct = [0 0; 2.269952498697734 4.455032620941839; 4.539904997395468 0; 6.355866996353655 3.564026096753472; 8.171828995311843 0; 9.533800494530484 2.673019572565104; 10.895771993749124 0; 11.803752993228217 1.782013048376736; 12.711733992707311 0; 13.165724492446857 0.891006524188368; 13.619714992186404 0];\r\nassert(all(abs(xy-xy_correct)\u003c1e-12,'all'))\r\n\r\n%%\r\nx0y0 = 6*rand(1,2);\r\nr = round(8*rand,2);\r\nn = 2+2*randi(5); \r\nth = 360/n;\r\ntheta = th*(0:n-1);\r\ns = '';\r\nfor k = 1:n\r\n    s = [s 'H' num2str(theta(k)) ' D' num2str(r) ' '];\r\nend\r\ns = s(1:end-1);\r\nxy = travelPath(s,x0y0);\r\nassert(all(abs(xy(1,:)-xy(end,:))\u003c1e-12))\r\naxis equal\r\nk = randi(n/2);\r\n[x1,y1,x2,y2] = deal(xy(k,1),xy(k,2),xy(k+n/2,1),xy(k+n/2,2));\r\nassert(abs(hypot(x1-x2,y1-y2)-r/cosd(90*(n-2)/n))\u003c1e-12)\r\n\r\n%%\r\nfiletext = fileread('travelPath.m');\r\nillegal = contains(filetext, 'assignin') || contains(filetext, 'assert'); \r\nassert(~illegal)\r\n","published":true,"deleted":false,"likes_count":0,"comments_count":1,"created_by":46909,"edited_by":46909,"edited_at":"2024-05-15T02:50:53.000Z","deleted_by":null,"deleted_at":null,"solvers_count":4,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2024-05-15T02:48:52.000Z","updated_at":"2024-05-15T02:50:53.000Z","published_at":"2024-05-15T02:50:53.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eIn \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/60251\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eCody Problem 60251\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e, minnolina asks us to determine the end point given a string indicating unit movements forward, backward, left, and right. For example, ‘fflff’ brings the marker to the point (-1,4). \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThis problem extends that one by specifying a heading (H)—i.e., an angle in degrees measured clockwise from north, or the positive y-direction—and a distance (D) to move. The movement string corresponding to the example above would be ‘H0 D1 H0 D1 H270 D1 H0 D1 H0 D1’.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a function that determines the points, starting at an initial point with coordinates in \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ex0y0\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, resulting from a movement string. The output should be an nx2 matrix with the x and y coordinates of the points in the columns.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":1460,"title":"Cosine frequency doubler","description":"Given an input vector containing a cosine wave of unknown frequency, produce an output vector of the same length containing a cosine wave of twice the input frequency.  The output should have the same mean and amplitude as the input.  ","description_html":"\u003cp\u003eGiven an input vector containing a cosine wave of unknown frequency, produce an output vector of the same length containing a cosine wave of twice the input frequency.  The output should have the same mean and amplitude as the input.\u003c/p\u003e","function_template":"function y = SineDublr(x)\r\n  y = x;\r\nend","test_suite":"%%\r\nt = 0:0.001:1;\r\nx = cos(2*pi*5*t);\r\ny_correct = cos(2*pi*10*t);\r\n%assert(isequal(SineDublr(x),y_correct));\r\nassert(sqrt(sum((y_correct-SineDublr(x)).^2))\u003c0.1);\r\n\r\n%%\r\nt = 0:0.002:1;\r\nx = cos(2*pi*15*t)+2;\r\ny_correct = cos(2*pi*30*t)+2;\r\n%assert(isequal(SineDublr(x),y_correct));\r\nassert(sqrt(sum((y_correct-SineDublr(x)).^2))\u003c0.1);\r\n\r\n%%\r\nt = 0:0.001:1;\r\nx = 3*cos(2*pi*35*t)-2;\r\ny_correct = 3*cos(2*pi*70*t)-2;\r\n%assert(isequal(SineDublr(x),y_correct));\r\nassert(sqrt(sum((y_correct-SineDublr(x)).^2))\u003c0.1);\r\n\r\n%%\r\nt = 0:0.001:1;\r\nfreq = floor(rand*100);\r\noffset = floor(rand*10);\r\namp = floor(rand*10);\r\nx = amp*cos(2*pi*freq*t)-offset;\r\ny_correct = amp*cos(2*pi*2*freq*t)-offset;\r\n%assert(isequal(SineDublr(x),y_correct));\r\nassert(sqrt(sum((y_correct-SineDublr(x)).^2))\u003c0.1);","published":true,"deleted":false,"likes_count":2,"comments_count":0,"created_by":13007,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":21,"test_suite_updated_at":"2013-04-25T21:13:33.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2013-04-25T20:47:42.000Z","updated_at":"2026-01-20T14:22:54.000Z","published_at":"2013-04-25T20:47:47.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGiven an input vector containing a cosine wave of unknown frequency, produce an output vector of the same length containing a cosine wave of twice the input frequency. The output should have the same mean and amplitude as the input.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":42306,"title":"Esoteric Trigonometry","description":"From Wikipedia: \"All of the trigonometric functions of an angle θ can be constructed geometrically in terms of a unit circle centered at O. Many of these terms are no longer in common use.\"\r\n\r\n\u003c\u003chttps://i.imgur.com/vVIFB1x.png\u003e\u003e\r\n\r\nNonetheless, suppose you do need to use one of these esoteric trigonometric functions that is not built into Matlab. Write a function that takes an angle as the first input (radians) and the trigonometric function name as the second input (string, function name will be completely spelled out). Make sure your function covers both the esoteric and commonly used functions; then it's a more useful tool. In particular, include sine, cosine, tangent, cosecant, secant, cotangent, versine, vercosine, coversine, covercosine, haversine, havercosine, hacoversine, hacovercosine, exsecant, excosecant, and chord. Formulas for each function are available \u003chttp://en.wikipedia.org/wiki/List_of_trigonometric_identities here\u003e.","description_html":"\u003cp\u003eFrom Wikipedia: \"All of the trigonometric functions of an angle θ can be constructed geometrically in terms of a unit circle centered at O. Many of these terms are no longer in common use.\"\u003c/p\u003e\u003cimg src = \"https://i.imgur.com/vVIFB1x.png\"\u003e\u003cp\u003eNonetheless, suppose you do need to use one of these esoteric trigonometric functions that is not built into Matlab. Write a function that takes an angle as the first input (radians) and the trigonometric function name as the second input (string, function name will be completely spelled out). Make sure your function covers both the esoteric and commonly used functions; then it's a more useful tool. In particular, include sine, cosine, tangent, cosecant, secant, cotangent, versine, vercosine, coversine, covercosine, haversine, havercosine, hacoversine, hacovercosine, exsecant, excosecant, and chord. Formulas for each function are available \u003ca href = \"http://en.wikipedia.org/wiki/List_of_trigonometric_identities\"\u003ehere\u003c/a\u003e.\u003c/p\u003e","function_template":"function y = trig_func_tool(theta,f_name)\r\n \r\nend","test_suite":"%%\r\ntheta = pi/3;\r\nf_name = 'sine';\r\nassert(isequal(trig_func_tool(theta,f_name),sin(theta)))\r\n\r\n%%\r\ntheta = pi/3;\r\nf_name = 'cosine';\r\nassert(isequal(trig_func_tool(theta,f_name),cos(theta)))\r\n\r\n%%\r\ntheta = pi/3;\r\nf_name = 'tangent';\r\nassert(isequal(trig_func_tool(theta,f_name),tan(theta)))\r\n\r\n%%\r\ntheta = pi/3;\r\nf_name = 'cosecant';\r\nassert(isequal(trig_func_tool(theta,f_name),csc(theta)))\r\n\r\n%%\r\ntheta = pi/3;\r\nf_name = 'secant';\r\nassert(isequal(trig_func_tool(theta,f_name),sec(theta)))\r\n\r\n%%\r\ntheta = pi/3;\r\nf_name = 'cotangent';\r\nassert(isequal(trig_func_tool(theta,f_name),cot(theta)))\r\n\r\n%%\r\ntheta = pi/3;\r\nf_name = 'versine';\r\nassert(isequal(trig_func_tool(theta,f_name),1-cos(theta)))\r\n\r\n%%\r\ntheta = pi/3;\r\nf_name = 'vercosine';\r\nassert(isequal(trig_func_tool(theta,f_name),1+cos(theta)))\r\n\r\n%%\r\ntheta = pi/3;\r\nf_name = 'coversine';\r\nassert(isequal(trig_func_tool(theta,f_name),1-sin(theta)))\r\n\r\n%%\r\ntheta = pi/3;\r\nf_name = 'covercosine';\r\nassert(isequal(trig_func_tool(theta,f_name),1+sin(theta)))\r\n\r\n%%\r\ntheta = pi/3;\r\nf_name = 'haversine';\r\nassert(isequal(trig_func_tool(theta,f_name),(1-cos(theta))/2))\r\n\r\n%%\r\ntheta = pi/3;\r\nf_name = 'havercosine';\r\nassert(isequal(trig_func_tool(theta,f_name),(1+cos(theta))/2))\r\n\r\n%%\r\ntheta = pi/3;\r\nf_name = 'hacoversine';\r\nassert(isequal(trig_func_tool(theta,f_name),(1-sin(theta))/2))\r\n\r\n%%\r\ntheta = pi/3;\r\nf_name = 'hacovercosine';\r\nassert(isequal(trig_func_tool(theta,f_name),(1+sin(theta))/2))\r\n\r\n%%\r\ntheta = pi/3;\r\nf_name = 'exsecant';\r\nassert(isequal(trig_func_tool(theta,f_name),sec(theta)-1))\r\n\r\n%%\r\ntheta = pi/3;\r\nf_name = 'excosecant';\r\nassert(isequal(trig_func_tool(theta,f_name),csc(theta)-1))\r\n\r\n%%\r\ntheta = pi/3;\r\nf_name = 'chord';\r\nassert(isequal(trig_func_tool(theta,f_name),2*sin(theta/2)))\r\n\r\n%%\r\ntheta = pi/5;\r\nf_name = 'sine';\r\nassert(isequal(trig_func_tool(theta,f_name),sin(theta)))\r\n\r\n%%\r\ntheta = pi/10;\r\nf_name = 'cosine';\r\nassert(isequal(trig_func_tool(theta,f_name),cos(theta)))\r\n\r\n%%\r\ntheta = pi/2.5;\r\nf_name = 'tangent';\r\nassert(isequal(trig_func_tool(theta,f_name),tan(theta)))\r\n\r\n%%\r\ntheta = 2*pi/3;\r\nf_name = 'cosecant';\r\nassert(isequal(trig_func_tool(theta,f_name),csc(theta)))\r\n\r\n%%\r\ntheta = pi/7;\r\nf_name = 'secant';\r\nassert(isequal(trig_func_tool(theta,f_name),sec(theta)))\r\n\r\n%%\r\ntheta = pi/13;\r\nf_name = 'cotangent';\r\nassert(isequal(trig_func_tool(theta,f_name),cot(theta)))\r\n\r\n%%\r\ntheta = pi/31;\r\nf_name = 'versine';\r\nassert(isequal(trig_func_tool(theta,f_name),1-cos(theta)))\r\n\r\n%%\r\ntheta = pi/1.3;\r\nf_name = 'vercosine';\r\nassert(isequal(trig_func_tool(theta,f_name),1+cos(theta)))\r\n\r\n%%\r\ntheta = pi/3.3;\r\nf_name = 'coversine';\r\nassert(isequal(trig_func_tool(theta,f_name),1-sin(theta)))\r\n\r\n%%\r\ntheta = pi/33;\r\nf_name = 'covercosine';\r\nassert(isequal(trig_func_tool(theta,f_name),1+sin(theta)))\r\n\r\n%%\r\ntheta = pi/0.7;\r\nf_name = 'haversine';\r\nassert(isequal(trig_func_tool(theta,f_name),(1-cos(theta))/2))\r\n\r\n%%\r\ntheta = pi/0.3;\r\nf_name = 'havercosine';\r\nassert(isequal(trig_func_tool(theta,f_name),(1+cos(theta))/2))\r\n\r\n%%\r\ntheta = pi/13;\r\nf_name = 'hacoversine';\r\nassert(isequal(trig_func_tool(theta,f_name),(1-sin(theta))/2))\r\n\r\n%%\r\ntheta = pi/31;\r\nf_name = 'hacovercosine';\r\nassert(isequal(trig_func_tool(theta,f_name),(1+sin(theta))/2))\r\n\r\n%%\r\ntheta = pi/30;\r\nf_name = 'exsecant';\r\nassert(isequal(trig_func_tool(theta,f_name),sec(theta)-1))\r\n\r\n%%\r\ntheta = pi/1.3;\r\nf_name = 'excosecant';\r\nassert(isequal(trig_func_tool(theta,f_name),csc(theta)-1))\r\n\r\n%%\r\ntheta = pi/13;\r\nf_name = 'chord';\r\nassert(isequal(trig_func_tool(theta,f_name),2*sin(theta/2)))","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":26769,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":41,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":26,"created_at":"2015-05-12T17:53:15.000Z","updated_at":"2026-02-19T10:17:18.000Z","published_at":"2015-05-12T17:53:15.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/image\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/media/image1.JPEG\"}],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFrom Wikipedia: \\\"All of the trigonometric functions of an angle θ can be constructed geometrically in terms of a unit circle centered at O. Many of these terms are no longer in common use.\\\"\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"-1\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"-1\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId1\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eNonetheless, suppose you do need to use one of these esoteric trigonometric functions that is not built into Matlab. Write a function that takes an angle as the first input (radians) and the trigonometric function name as the second input (string, function name will be completely spelled out). Make sure your function covers both the esoteric and commonly used functions; then it's a more useful tool. In particular, include sine, cosine, tangent, cosecant, secant, cotangent, versine, vercosine, coversine, covercosine, haversine, havercosine, hacoversine, hacovercosine, exsecant, excosecant, and chord. Formulas for each function are available\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"http://en.wikipedia.org/wiki/List_of_trigonometric_identities\\\"\u003e\u003cw:r\u003e\u003cw:t\u003ehere\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"},{\"partUri\":\"/media/image1.JPEG\",\"contentType\":\"image/JPEG\",\"content\":\"data:image/JPEG;base64,/9j/4AAQSkZJRgABAgAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAMgBOIDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIhMUEGE1FhByJxFDKBkaEII0KxwRVS0fAkM2JyggkKFhcYGRolJicoKSo0NTY3ODk6Q0RFRkdISUpTVFVWV1hZWmNkZWZnaGlqc3R1dnd4eXqDhIWGh4iJipKTlJWWl5iZmqKjpKWmp6ipqrKztLW2t7i5usLDxMXGx8jJytLT1NXW19jZ2uHi4+Tl5ufo6erx8vP09fb3+Pn6/8QAHwEAAwEBAQEBAQEBAQAAAAAAAAECAwQFBgcICQoL/8QAtREAAgECBAQDBAcFBAQAAQJ3AAECAxEEBSExBhJBUQdhcRMiMoEIFEKRobHBCSMzUvAVYnLRChYkNOEl8RcYGRomJygpKjU2Nzg5OkNERUZHSElKU1RVVldYWVpjZGVmZ2hpanN0dXZ3eHl6goOEhYaHiImKkpOUlZaXmJmaoqOkpaanqKmqsrO0tba3uLm6wsPExcbHyMnK0tPU1dbX2Nna4uPk5ebn6Onq8vP09fb3+Pn6/9oADAMBAAIRAxEAPwD3+iiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACvmz4v8AjvxRoXxEvbDS9burW1SKJlijIABKAnqPXmvpOvkr47/8lVv/APrjB/6LFAGwsfxyZQytrJBGQQ8fP60vk/HT+9rP/fyP/Gvpa1/49Yf9xf5VNQBwPwpXxavhu7/4TH7V9v8AtjeV9oKlvK2LjGOMZ3frXfUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABXyV8d/8Akqt//wBcYP8A0WK+ta+Svjv/AMlVv/8ArjB/6LFAGunxg+JiIqrpiFQAAf7OfkDp3p3/AAuP4n/9AtP/AAXP/jX0ta/8esP+4v8AKpqAMXwpqF5qvhPStQ1GPZeXFskkyhCmGIBIwenPatqiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigArnvFPjHRvBtrbXOtXDQw3E3lIUQuQcEkkDnAxyQD1HrXQ18wfGC41Xxh8VLTw9DbTxJCy2tosqModmI3yjP8ACTgZHBCA0AfSOm6lZaxp8N/pt1FdWkw3RzRNlW5II+oOQR1BBB5FXqzdC0e28P6FZaTaDEFpCsS8YLYHLH3JyT7k1pUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAV8lfHf/kqt/8A9cYP/RYr61ryPx18E/8AhNfFVxrZ8QfYvNRE8n7F5mNqgdfMGc49KAPVrX/j1h/3F/lU1RxJ5cSJnO1QM+uBUlABRRRQAlFFZGuaumk2m/AaZ+ETpk+p9hxWVWrGlBzm9EVThKpJQitWa2cdTRkHoRXAW9hrHiIm4lnKxE8M5IX/AICo/Lt9c1ZbSNc0YefaXJlReqqc8f7vT+vpXmxzKpJc6pPl7/8AAO6WChF8jqLm/rqdvRWHoWuLqyFJE2XEf31HQ+4/wrcr0qNaNaCnDZnFUpypycJbi0UUVqQFFFFABRRRQAUUUUAFFFFABRRRQAVXltoZpYpZYY3khJaNmUEoSMEqexwSOOxrhp/i54etPHkvhWcXInWVIFuI03xtK2BsIHzAgkDOCM5zjFeg0AFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFACUVDdI727rH94jA5xzWT9iv8A1b/vv/69K5pTpqW7sbmaOKwmtL5QSxYDqfn/APr0yGC7nTfGzFen3/T8aLvsa+wja/MjoMiisP7Fferf99//AF6vWEU8MbibOScjLZ4oTM504xV1K5dorMvoLmWcNCfl2gcNjnJ96baW13Hco0hOznOWz2+tF9bAqcXHm5jWoo4xVK/imliUQHndzg47UzOKTdrl2isQWV+D1b/vv/69bQ6deaLl1IKGzuLRUNyrvA6x/eKnHPesn7Hferf99/8A16Tdgp01JauxuUVXtFaO2RZT84znnNWKZm97IKKxJLO9MjFS2CSR8+OPzq5p8U8KuJzyTxls0rmsqcYxvzGhSZ9aOtZd7bXUk+6LO3HZsc/nTuRCKk7N2NTNLWTZ211FcBpSdmD1fPP51qgj1ouE4qLsncKKo6hDNKiCHOQecNiua8Qat/wjNgt5fztEjuI4zy2XwSAQOg4JJ4HHXmonNQTky404tXckjs6K830vxdexxRyiYXds+WUsc5GTnDD0Ix3xgjHFddp/iTT9QAUS+VKf+WcnH5HpXDh8zoVny35X2ZtVwNWmuZK67o26KBRXonIJXA6vu1jxYLQH5FcRjHYDlj9ev5Cu+rgrpv7J8Z/aJuIzJvBP91gR/MmvHzfWEE/h5lc9HLdJza+KzsdxDEkESRxqFRAFUDsBxUuMimI6yIGUgqRkEHNPr1opWXLsee7313KkNnb29xLNFEqSS43kd8f/AK6zdU8S2mmuYeZpx1ROi+xP+TUniLUzpumM6HE0h2J7ep/KsHwzoKXa/b71PMRmPlo3RueWPr3GDXl4nEVFVWGwytLr5HdQowdN16702S7luDxtA8mJrWSNT/ErBv6CujtbuC8gE1vKJEbuDUdxpdlcw+VLaxlcYGFwR9PSuQ0p30TxO9hvJhd9hB755U/X/E0vbYnCziq75oydr+Y/ZUcRCTpLlktbd0d52oyBVa5uobS3aedwkafeY9q4/wARas19eW1rp8pYAhg0bYy54HP4/r7V14rGQw8bvV6aHPh8NOvKy27nc0tV7WN4baJJZC7qoDOerHHWp66ou6TOdqzsLRRRVAFFFFABWV4gvbvTdA1C8sLOS8u4YGeGCNdzSPg7RgckZxnHOM4ya1aKAPmr4IeFLvWPHF74i1eKUtpzsT56kM1y+ckg9wCSe4JU19K0wKAWIAyxyfc4/wAMU+gAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKAM/VZ/Ktdg+85x+Hf8Aw/Gqukz7ZWiPRhkfUf8A1v5VX1Cbz7tgD8q/KP6/rVeNjFIrr1U5FRfU9CFH9zbqzqSccmvHPEfjHXfFfiV/DfhN2ihRir3EbbWfBwzF+qqDwCOT6nIFel+IL1rbwpqd7A2Hjs5ZIz6EISP5V4N4C13V9BlvZ9J0OTU3lCI7JG7mMAk9VBxkn8dvHSsK87NRvueHiptSUGdePgvqEyefceJP9LPJ/cMwz/vFgfxxmqemeI/EXw78SQ6P4huHutNlIxI7Fwqk43ox5wD1U9AOByCdX/hZHjP/AKEq5/78Tf4Vy/jHUfE/jGO0Fz4UvbdrYsVZLaU53YBHI9hWUuSOtO9zCTpx96le57hqunQ61pU9lK7okyYEkTkMvowI7g4PoehyK8g8NeINT8A+MJ9C8QzySWczgea7FgpPCyqST8pHB9O/IIPrPhoT/wDCL6ULpHS4FnEJFkBDBtgzkHvnNc18T/DllrHhma/lkjt7qxQyRzMcAr3Q+oPb3xjqc71YtpTjudNaLcVUjujd8VeJrTwvocuozFWY/LBHnmVyOAP5k9gK87+HGlat4l1iXxPrN3ctbCUtFH5jBZZAeoGcbV6AdMjHQEVxPh+G88a67pGi6hqTC2gQpHvflUHJVQerEDAPOAB1AxX0hZWcFhZw2lrGsUEKhEReigVMG60uboiKcnXlzvRIzvEuv23hnQ59TuRuCDEcYODI56KP6nsAT2ryDT7bxl8Tbia5fUGtdNVypwzLEDwdqqD8xHqTx654rb+ONzItto1qG/du8sjD3UKAfwDn867/AMF2cVj4N0eCJQoFqjnHdmAZj+JJNEr1KnI9kOV6tVweyPPD8GdTsx52neJSLkcg+U0Qz/vKxI/I16F4RtNYsfDkFtrkxnvo2YNIX37l3Hac9Txjrz610FJW0aUYO8TaFGMHeJ4XNqfiL4meKLnT9Ovms9Ni3EKrlVEYIAZscsx4IB4Hbua1B8Ep0HmReJSJuoItSOfqHz+NZE+keJvhr4kudQ0uya60+QsoYIXRoychXxypGAMnAPbOSK6HTvjbYSEJqWlXFu2cboXEg+pztIH51yR5Lv2u5xx9ndqte50XgTQPEPh86hb61qBvYD5ZtW81nCgbtwG7kfw8dKu+NvFsPhDRDdbFlupW2W8ROAzYzk98AcnH04zkauja7p2v2f2vTLtLiLo2MgqfQg8g/WvHvjTPLP4s0+yLYjS0DKD0DM7An8lH5VvOSp0/dOirNUqN4MbpXhzxd8RIzqWo6vJb2Lk7N5O1uf4IwQMcYySM+/WtM/CDWtNHnaN4lxcDkfK8H6qzH9K9bs7WKxs4LWBQsUMaxovoAAB/KrFCw8bXe4RwsGry3M3QY76HQrGPU23Xywqs7bgcvjk5HB5rhfjb/wAinY/9fy/+i3r0wV5n8bf+RTsf+v5f/RclVWX7torEaUWjQ+Gtnb3vw202O4iWVd02Nw6fvW6e9Y3xDfTvBFjaai4nNvcXIgKKAxQlWbI5Bx8vr/hXQ/Cn/knWm/70v/o1q479o7/kStL/AOwiP/Rb1zywVDEQXPHX8TrwWKq0YRcH8jQ8P+Lp5LCK90+6+1WLkqu4ErkdQMgEEenGMjjmu10/xZY3mEnJtpTx8/3fwbp+dcP8BIY5/hi0csauhvZcqwyDwvWuw1HwdbT5eybyHP8AAeVJ/p/niuJ4bGYTWhLmj2e56Pt8NiNKseWXdHRmRfKMikMoUkYPXivGfDnxStviV4it9Bk8PmxkkSR0uhd+YU2qTjbsGc4x1rpW/trw+Sp3rCcg/wAUZ7fhn8DXn/gLwYPCXxCstW+2rJp6pKrb1IdNyEDpweSBnj6VcMxoV06WJXK+zJeCq0v3tF8y8j1FLDxHoxKWjieDPCgggD6HGPoPzro9Imv57MyahGscpPCKCMD35PfNXYpo54xJFIrow4KnI/OpO3WurDYSNGV4Tbj26HNXxDqq0opPv1OJ8bSsby1jP3QhYfif/rCuvs4Ut7KGFPuogA/KsbxPpEmpWiS243TQ5IX+8D1H14qhpPiqKC2W21FZEkiG3ftJzj17g/z61xRnHDY2cq2ilazOqUZV8LBU9XG90deeATXA27f2t4zE0fKCXfkeijAP44H51Z1nxSLqFrWwVxv+VpCMHHTAHXnpzWl4X0ZtPtjc3C7Z5RwpH3F/xPf8KmtVWOrwpUtYxd2yqVN4WjKpU0lJWSNHWltW0qc3aloUXcQDgk9uRXC6Vpt/d77qxwGgPBJ5z+PBOPX1FbfjG/LvFp0RJPDvjv6D69/yrodGsBpumQ25A343OfVj1qa1GONxnL0h18x0qssLhubrLo+xjaV4hvWvU0+/tGEzcBgNpHuQe3B5/IGupNMKIzBio3DoSKju7qCxsp7y5kWK3gjaSSRuAqqMkn6AGvWw1KpSjyzlzHnVqkKkuaEbFmisvRdf0rxDp632kX0N5bt/FG3Kn0YHlT7EA1qV0mQUUUUAZXiHWrbw54ev9Yuz+5tIWkIzgseiqPckgD3Irm/h58SbL4g21wbexuLS5tQvno+GQbs42uMZzg9QDx0rlPj+niC88OWdnpun3M+m7zNezQjdgr91SAc4ySSSMcD0rqfhN4T/AOES8C2kE0e2+u8XV1kYIZgMKf8AdUAEeoJ70Ad3RRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAJVa8nFvbO4xuxgfU1ZrF1affKIh0QZP1//AFfzpNmlGHPNIz+9FFFQeuXUgTVNFvdLlOFmheP6Kykf1ryL4a60vhHxXfaPq5+zCciJ3fhUlQnGSegIJ56dD0OR6tZzeRco5PHRvof85qh4v+Hul+LD9pLNaagFwLiNc7h2DLxuA+oPbOOKzqQcrSjujxMfQkqiqQOxyCMjFVr7ULPTbZri9uYreFeryuFA/E15Mnwy8bWCiDTfE4jtgeFW6miH/fKggfnU9t8Hb2+nWfxB4gluCOoj3OxHs7nj8jR7Sp/Kc3taj0UD108CvD/HPiC78ceJIfC+ht5lqku1nU/LK4zliR/CvPsTnrxXqnifT9T1XQ5bDSruO0lm+V5nBJCYOQuOhPAz2Gcc4IxvAfgODwhDPLLKlzqE3ytMq4CoP4R+IyfXj0p1VKbUVt1CtGdRqC26nDeM/hy3hrSbPWNCklMlkqm5YE7sg5Eo54weoHAGD2Jr0HwH4vi8WaKruVW/gAS5j6c9mHscH6EEdq6mSNJUaORQyMCCpGQR0Neb6f8ADa/8P+Lzq2h6lFFaF+baVWOYz95Ce49D2wOuOV7NwknDYXs3SmnDYT4zaNLfeHbXUokLtYyt5gHOEfAJ/Ahfzz2rT+GfiW11nwta2RlVb2xiEMkRPJVeFYeoIx+Oa7WWGOeF4pUWSNwVZWGQwPUEdxXlmsfB3F8bzw7qbWTbiyxSFsJ/uupyAOwwfrROMoz54hOE41PaQV/I9X3AdeKhjuIZo2kilR0UkFlYEAjrnFeSf8K08bXo8nUfFRNu3BH2qaX/AMdbAP516J4a8OR+HPDsOkrcNOqBsyFQuSxJOBzjrVxnJvVGkKk5PWNjVtL21v7dbizuYriFh8skThlP0I4rO1nw7oer28n9p2FtINp3SsoVlAHUOMEY+tebXPwk1LR2e50bxOLZf70paAge7KTn64Fc5qFjNg22vfEzSzb5+eIag9w34pxn6Goc5vRxM3Um1Zw1ND4Ru9v48vrW0laSyaGTJ7MquArEDjPPX3PrWj8a9Hl8/T9ajUmMIbaVh/CQSy/nlufUD1qHw74++GfgezkisdTub+6kx508dq+5yM4A3AADk4APfqabrPx78IahZTWb6JqV5byja6TLGit/48T6HPUHmlGi/Zcj3FHDv2PJLc9L8I+JbXxPodveQyqZ1QLcRZG6N8cgj0JBIPcV0DMFGSQB718cSeL7S11R7jRk1CxiP3CZ8yL7blA4/X3NJf8AjzUL6Ex3F/qN0n9ye5Zl/Ik01OolZxHGpVSs46n2LDLHPEssMiyIwyrKQQR7Eda84+Np/wCKTsf+v5f/AEW9eT6d8e/EGk6VbafaaXphitoljRpldmIAwM4YD8hU0nj/AMT/ABQQaTNp+nqtuftP+jBkbI+Xku5BHzHgDPvwa0qRlKDSWrHipKNCUpaaHtXwq/5J1pv+9L/6NauO/aO/5ErSx/1ER/6LeuIT4r+KPACDw3Fp2mMlrkqZ1dn+f5+SrgHluw6cVznjf4q6v480i307UbKxgSCcTq9urgkhSuDuY8YY06cXGKT3Lw7TpRa1Vj0H4P8AxH8J+FvA/wDZ2s6t9luvtUknl/Z5X+UhcHKqR2Nd/wD8Lt+Hn/Qw/wDklcf/ABuvlOwuNHiixqGn3lw+7O6C8WIY9MGNvzzWvb3vgVji50TXkHrHqkTfoYB/OrNj6Qn+M/w9lhkT+3wdykYNlcc/+Q68g+Fev6r4h8TwaBeXXmQyxyMssg3OpVSRz36d81i27/CeRcTxeLoXwcESW7r7ZwAf0qH4Sa1pvh/4hWWoardLbWiRyq0rKSAWQgdAT1NYVsNSrR5akbmtKtUpO8HY9/l0/WtAkMsJfyxzviJZSP8AaB/w/GtXTvGanCX8RX/ppGCR+I6/lmr1l458KalhbTxFpcjN0T7Ugb/vkkH9KlvfDum6mnmoojduRLCeD7+hry3gMRh3zYWenZncsXRrK2Ijr3W5p215b3kQkt5lkX1U1Dd6RY3x3XNsjtjG7GD+Y5rjbnQNW0iTz7VnkUdHh6491/wzVvT/ABlNHiO/i3gcGRBhh9R3/ChZjBv2WMhyv8AeCkl7TDT5l+J0tpounWL77e1RX7McsR9CelaB6VTstTs9QXdbTq5HVehH4GrtepRVJQ/dWt5HBUdTm/eXv5nA6aFvvGMklywBEjMFbuVOFH8j+Fd7XO6x4YS+mNzav5Fx1Pox9fY+4qbQYtWh86PUX3KmBGSQxPvnuPrzXn4KFTDVJUpx+J3v/mdmKlTrQVSMtklb/I3q8X/aA8X/ANmeH4PDdrLi51H95Pg8rAp4H/AmGPcKw717Bd3UFjZz3lzIsUEEbSSOx4VVBJJ+gBNfKulQXPxg+MLXFwriykl86Vc/6q1QgKvHQkbVyO7E+teueeZ1noHjzwPplj4t06K6tbW4hEomtzuCockeauCMEYI3Ajkd+B6x4J+P2naj5dl4oiXT7kgAXcYJhc/7Q5KdvUdTkV7MsaJGI1VQgG0KAMAen0ry7xt8D9C8R+ZeaRt0nUmyx8tf3Eh/2lH3T7rjuSDQB6fBPDdQJPbzJLC6hkkjYMrA9CCOCPpU9fJkF/8AED4NamIJVeOydsiKXMlrP6lT0BOOxDdMiu9uP2jrRbCwlt9Dka5ZyLyCSUBVXAwUcA5yT3Axgg9QaAPdqKzdF1Nda0Sy1RLea3S7hWZYpgA6hhkZwSOlN8Q6zB4e8Pahq9xjy7SBpSCcbiBwo9ycAe5oA8a+JHxp1nw74yudI0JLJ7e0RUlaeIsTKRlgCGGAMgYx1BrvfhV45m8deFnu70QrqFvO0U6QgquDyrAEkgEHHXqprw74VeEj8Q/FWtXur5khFvK8suM5nm3BTj2y7D0KirfwV1efwn8TLnw9fnylvC1nKhOAs8ZJX9Qyj3agD6iooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAjkbZGznsM1zkglkkZyjZY5PFdPSY+lJq5tSq+z6HLbHA+4w/CjY5HCt+Vb9+P9Cl+lVdHGUk+opW6HUsQ3BztsZXlv8A3G/Kt7T5DJagMMMvyn/P0q3ge1LimlY5qtf2is0FFFFMwCiiud8QeN/DXhgEavrFtbyDnyQ26X/vhct+OMUAdFRXg+v/ALR1pFvi8P6PJOecT3jbFz/uLkkfiK4pvFfxW+ITFNOOotbOSNunxGCIZ7GQY49mb+tAH0tq3ibQ9BXOravZ2fGQs0yqx+i5yfwFef6x8f8AwhYbksVvdSkHQwxeWmfcuQfyBrzzSv2fvEN6Dc69qdpp6n5nGTPIPXOCF/8AHjXT6f8ACfwJpRH2pb/V5B1Mkvlx59gmD+ZNXCnKfwo5cRjaGGV60rHP6p+0brVwWTStGsrRTwGndpm/DG0foayD4j+MHizBtTrZhf7rWlsbdB9HUD9TXuWiL4W0Yqun6Fa2JH/LSKBd34t94/jXU3uox2VoLkozoSPu4796cqM4uzW5FLMcLVg6kJ3S3PmiH4KfEPXZBNqkkULnnff3pkb/AMd3Guisf2bJ2UNqHiSJD3S3tS2f+BMw/lXu9jepf2onjBAPGD1FXKzaadmdVOpGpBTg7pnj1n+zr4Vh2m61DVbhu4EiIp/ALn9a3rX4JeAbYDdozzt/emupT+gYD9K62+1uGyuhbskjuQOEHqa0WkVY97HCgZJPpVOElZtbmcMTSqSlGMtY7+RzNv8ADPwTbD934Y00/wDXSESf+hZrRi8IeGbcfufDukR/7llGP5LUc/ie1jbbGjye4HFNj8VW7HDwyKPUYNafVqrV7HG85wKly+0Ropoulxf6vTLJP92BR/SsjxLa28FnCYYIoyXx8iAdj6CuggmS4hSWM5VgCD6g1ieK/wDjzh/66f0NPDK1ZJmedSUsuqNbWJdBs7WfSImmtoZGy3LoCep9RXl37Q1jZ2vg7TZILSCKRtQALJGFJHlvwSB9K9Y8O/8AIGi+rfzNeefHzSNT1nwjp8Ol6dd30qX4do7aFpWVdjjJCg4GSB+NTW/iS9Tpyv8A3Kl/hX5Gd8EPDWhax8OzPqei6deS/bJVElzapIwAC4AJBOOTXeXPwv8ABF1/rPDOnj/rlH5f/oOKwvgdpmoaT8PjbalY3NlP9slbyrmJo2wQuDhgDjg16XWR3Hm1/wDA/wABzQyNFpUtswUnMN1J1x6MxH6V85/D7wtD4z8XW+iz3MlskscjeZGoYjapPQ/SvtCYEwSAckqRj1OK+Zfgz4V8Q6V8SrG61DQtUtLdIpQ0txZvGgJQgZZgAOeKANa//Zrv0BOneIrab0W4t2j/AFUt/KsF/hB8TPDbmTSXLkc79Nv/ACz9RuKn9K+p6KAPlY+Nvi34R/5CJ1MQL1N/Z+Yh/wC2hXJ/BquQ/HR73A13w5azMePPspWhce+G3Z+mQK+nK5/VfBPhjWwx1HQdPndushhCv/30MN+tZ1KUKi5Zq6KhOUHzRdmeNWHxI8NXUymC9uLKTICi5j2EH2ZSVwPUkfSvRNJ8azrFG0rJeW7D5ZEYZx6gjIP+eaw9Y/Z68K3oZ9Oub7TZD91RIJYx+DfMf++q46X4OePfCsjT+HdTt76POfKR/LZ/qj/L/wCPGvLllbpPnwk3F9uh6McfGouXERuu/U970/XLHUQBDMBJjmNuGH4VpA183x+MNR0WdLbxbod3pcucC48pvLY+2QfzBNeiaH42la3WW3uo7+1PT58ke24ZIPselSsxq0Hy4uFvNbA8DCqubDSv5Pcxfj/4v/szw/B4btZcXOo/vLjB5WBTwP8AgTDH0Vh3rT+BnhD/AIR/wcNVuI9t9quJeRysI+4PxyW+jD0rz3UfB+r+Nvi2l7rBjGl3NwGZ1l4SBB8sYBwQxAAyB1JPrX0lGqRxqkahUUAKq8ADtivVpVqdVc1OVzgqUp03yzVmS0UUVqZlW9sLXU7SS0vraK5tpBh4pkDKw9weK+aY/hJq118VI7C50OSy0GS5aVXRjJELdSWC78khiMDBOctnGBX1BRQAxEVECqoCgYAAxivFf2ifEn2TQbHw7DJ+8vpPPnAPIjQ/KCPQsQf+AV7bXx7468QWfjD4qz3V5d+VpKXK2omClglujYLAAEnPzMBjq1AHvXwS8Of2B8O7WeRNtzqZ+2SZ67SAEH02gH6sa8n+OGjTeGviPbeILHMQvQtzG4H3Z4yA2PyRvqxr1mL40fDuCGOGLWSkUahVUWc2FAGAB8lcL8XPHfgfxn4NNvp+rGXU7WZZrZTayru/hZdxUAAqSeT1UUAe2eHNah8ReHNP1i3x5d3AsmAc7SR8yn3ByPqK1a8Q/Z18SfatDv8Aw7PJ+8sn+0QAnkxucMAPQNz9Xr2+gAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAq3/8Ax5S/Squj/cl+oq1f/wDHlL9Kq6P9yX6ip6nRH+DI1KKo6lqlhpFi95qN5DaWyfelmcKo9snv6Dqa8Z8W/tD2VqZLXwtZfa5BwLy6BWMH/ZThmH1K89iKo5z2y6ureyt3uLueKCCMZeSVwiqPUknAFeXeJ/j34Z0Yvb6SkmsXK8ZiOyEH/fI5/wCAgg+teT2nh74j/Fq4S7u5Lh7MnctxeMYrdc90UDB9Mqp9zXqnhb4BeHtICT63LJq9yOdjZjhU/wC6DlufU4PpQB5jd/EL4k/ES6e00dbuOBjgwaXGUCj/AGpOoGODlgD6Vt+H/wBnfWb9hceItUisgx3NDAPOlPqC2QoPuC1fQ9lY2mm2qWtjaw21ugwsUMYRVHsAABVmgDhfD/wj8GeHlVodIS7nXH7+9PnMSO+CNoP0ArtkRY0CooVVGAAMAYqSigDlPEl5JJcJZRk44LD+8T0H+fatTT9FtrSFdyLJKRlmYZ5rD1X5fEis3ALofw4/+vXYjoMeldlaThShGPU+ay6lDE46vWrK7i7K/RFKfTLO4UiSBOnUDBp13aLcWL2wAClcD2xVyjFcqnLue68NSaklFLmVmcp4ZuDFdTWcnBPIHoR1/wA+1dQ7hELNwACa5LVUOm66lygwrEOMfr/n3rW129WLSfkOTONqkeneuutT9pOMo/aPAy7F/U8NWo1XrSvb06GTpqnU9ea4YZRW3/4f59q1/EbOukts+6WAb6Zpnhu08mwMxHzTHPvgdK1p4Y7iBopFDIwwR61NWqlWXaJrl+BnPLpJu06t3f1MPw/b2T2SvhGnyd+7GRWvLYWk4+e3RvfFYk/hdkYvaXJU9gw5/OqskusaMQ0jlos9zuH59auUFVlzU569jno15YGiqWLw/ux05lZr1Z1UMKQRJFGNqKMAZ7VieK8/ZIfTzP6GtTT7xb+0SdVwTwV9DWD441C103TLea8l8tGmCg7ScnBPYH0Nc9JqnVTnpY9XHU3i8BKGFXM5LRLr8jV8O/8AIGh+rfzNatfP998ZtS0a8ew0u0sp7OPBSSZHDHIyc/MOhJ7Dp+NQf8L98Rj/AJhul/8AfMn/AMVXr/2FjK/72mk4vVao2wV6OGhSqLllFJNPofRFFfO3/C/fEf8A0DNL/wC+ZP8A4qj/AIX74j/6Bml/98yf/FU/9W8w/lX3o6vbRPomivnb/hfviP8A6Bml/wDfMn/xVH/C/fEf/QM0v/vmT/4qj/VvMP5V96D20T6Jor52/wCF++I/+gZpf/fMn/xVH/C/fEf/AEDNL/75k/8AiqP9W8w/lX3oPbRPomivnb/hfviP/oGaX/3zJ/8AFUf8L98R/wDQM0v/AL5k/wDiqP8AVvMP5V96D20T6Jor52/4X74j/wCgZpf/AHzJ/wDFUf8AC/fEf/QM0v8A75k/+Ko/1bzD+Vfeg9tE+hJoYrmFopo0kjYYZHUMpHuDXFah8KvDVzcNdafBLo14esunSeWD7GMgoR7bea8w/wCF++I/+gZpf/fMn/xVL/wv3xH/ANAzS/8AvmT/AOKqXwzj5KzivvQ44hRd07HbXHhHxJpfQwaxAOjwgQTj3KMdrY7kMD6LzT7DxFqGmymAPICoy1tcowZR0BwQGA9OgPXmuG/4X74j/wCgbpn/AHzJ/wDFVWvPjZq+oReXeaJo86g5AeNyVOOoO7IPuMEeteVV4GxvNz4f3JeTVj0KebXjyVlzL8T22w8X2NyQlyrWznAy3KZJ/vD+ZAHvXQLLHJEJFdWjIyHBBBHrmvmC2+JEv2n/AErT4xAf4YXbKjpxuJJ/E85612GneIbPW9PurPT9RljFzE0c0SNtfDDBwpyM4OAQDjsa8/FYbNMr/wB9pXj/ADR1No0MNidcPKz7M0fC/wAZrrxJ8R5vD9vpcdxp007ra3MTlXSNQSXbOQQQCe3UDk17FXzbpPhTxL8OtYbWvDDWupAxGOW2uEAcqSCQDkZ6A5BBOOhr0vwx8YtB1q4Gn6skmhaqCFa3vflUseyuQB+DAHnjNbRnGaumefKDi7M1fij4l/4Rf4fanexybLqVPs1tg4PmPxke4G5v+A14V8H/AIY2HjqHU73V2uks7dlihMDhS0hBLZJB6Db/AN9V6P8AGfwl4s8aXGmWmiWaS6dbK0sjNcIm6VjgcEjoo4P+0a7P4c+Fm8IeCLDS5kVbwAy3W0g5lY5IyODgYXI6hRVknK/8M8+C/wDnrqv/AIEL/wDEUf8ADPPgv/nrqv8A4EL/APEV6xRQB8k+Hp5Phh8afss7lbaC6a1mZjjdA+ArH2AKv+FfW1eIfGP4Wa14p8RWmr+H7WOZ5IPKulaVY+VPytliMkg446BR616l4RTVovCemQ65CItSigEU4Dh9xX5Q2QSCSACfc0AbtFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFec+Ovi/oHg0PaRMNS1VePssLjbGf+mjchfoMnpkAHNAHd6gQtjLkgcY/EnFeVfED4m3PgK3gtbCxjnvb1WZZZmOyIKQM7RgsfbIxjv0rhfC/iHxn8RfHtjql2sz6VYzGR0hUpbQDaQBzwW57ksc+nT2pPCei63qkGqanYx3dxZrtgWYbkTJyTt6E5x1zjAxg80up0R/gs8A0zwh4++LV+up6jPMLRj8t5e5WJQeoiQDkcH7oAyOSDXs/hD4MeGPC2yeeD+1b9cHz7tQVU/wCzHyB65OSOxr0cAAYHSlpnOJgAcdKWiigAooooAKKKKAOe8QaW90i3MIzKgwVHVh/j1qCw8SCOJYrtGDLxvAznHqOua6eqk2nWlw26W3Rm9SK6I1o8nJUV0eLiMtrRxDxOEnyylunszKm8T2yL+6jeQ47/ACj9a3InMsSORgsM4qtFptnBIHjto1Yd9vNXazqOm/gR2YSni4tvETT8kjF8R2nn6f5qj54ju/Dv+lc0sk2oPaWfZPkX6Hr+g/Su7kQSKVYAqQQQR1qvFp9pDIJIreNXHRgoBFbUcSoQ5WvQ8zMcllisR7WMrJ25l3syeGJYYUjUYCjA9qo6tqDabAkqoHy+CM44wa0qayhhggEHsRXOmua71Paq05Ok4Unyu2jMSLxPaOvzrIh+mf5VQ1fWo7+3+y26M25hkkfy9TxW8+kWEhy1tHn2UCpILC1tzmGBEPqBXRGpRi+ZJ3PHq4PMq8HRqVI8r0bS1K+iWj2mnIknDk7iPSuK+Mn/ACLlj/1+D/0B69I6V5v8ZP8AkXLH/r8H/oD1wYyTlCUn1PrOHqMaGKoUo7JpF74bWFlceBrGSa0gkctLlnjBP+sbuRXW/wBkab/z4Wv/AH5X/Cub+F//ACINh/vS/wDoxq7Gro1JqlHV7BmaX12r/if5lL+yNN/6B9r/AN+V/wAKP7I03/oH2v8A35X/AAq9RWvtJ92cNkfK/i+KKP8AaLjt0iRYf7UsV8sKNuCIsjHoea+mv7I03/oH2v8A35X/AAr5m8Zf8nKx/wDYVsf5RV9T0OrPu/vCyKP9kab/ANA+1/78r/hR/ZGm/wDQPtf+/K/4Veoo9pPuwsij/ZGm/wDQPtf+/K/4Uf2Rpv8A0D7X/vyv+FXqKPaT7sLIo/2Rpv8A0D7X/vyv+FH9kab/ANA+1/78r/hV6ij2k+7CyKP9kab/ANA+1/78r/hR/ZGm/wDQPtf+/K/4Veoo9pPuwsij/ZGm/wDQPtf+/K/4Uf2Rpv8A0D7X/vyv+FXqSl7SfdhYpf2Rpv8Az4Wv/flf8K+Z/F3iSHXviXenTxHHZWKG2t/KAUNtPzOMdctnB9AK9s+K3iz/AIRHwLeXEMm2+u82trzyGYHLD/dUEj3AHevn7wn4akj8G3XiWZSqyXKWlvnowwS7fmFAPs1Y4mcnSkmz08nS+vUl5o9a8LzXd14YSd2M043BPMYjdgkAE4JGSMZIJHXnFYw1bwj41LabqUEaX0bGNra7URzRsCQQrA9QQeFJJxyK7DwDY/bPh9CyDMscshXHf5uR/nuKytb+GegeNHkMpew1ZhlLuEZD47OhIDYx2IOBjOABWFKkpU09mPMp8mMqRS0TZn6baeK/BJA8N6kNT0xf+YVqL8qM9I5ONp5PBwB1Oa9B8OePtL1+ZbGdJtM1fBJsLwbHb1MbdJB15U5xyQK8P1KH4g/Cx8Xy/wBp6MCFSckyRgZwBu+9GcdAePTOK29M8e+FvFcKWmpJHbTkgiK7xtDdir9ARxgkg56CtOapDdXRw2hLbQ+g6K4LRtVvtKCxPcyX1ljCidt0qDjpIeWHs2SSfvYAFdlaX9vepugkDdyO4+oq41Iy2IlCUS3RRRWhIUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABWZrWuab4e02TUdWvI7W1j6ySHqewAHJJx0GSfSuS+IHxU0fwNE9uCL3VyuY7SNh8mehkP8I745J44wcjwyx0rxt8ateN3cyn7JG2GnkBW3tweSqKOpxjgcnjJ70AbPjX40a14tuf7E8JwXVpazN5atECbm49htyVB9BknucEitnwJ8AWcx6h4xc9Q66fE/X2kYfyU/j2r1HwT8OtC8D2m2xg82+ZcTXsoBkf1A/ur7D2ySRmuwoAzDY2unaMbSyt4re3iXCRRIFVRnoAOKbo/wB2T6ird/8A8eUv0qpo/wB2T6il1OiP8B+pq0UUUznCiiigAooooAKKKKACiiigAooooAKKKxfE/iKz8K+HbzWr4nybZMhBwZGPCqPckge3egCxq+t6ZoNi17qt9BZ269ZJXC5PXAHUn2HJrzjUP2hPBtpKY7aLUr7HSSGAKp/77YH9K8fsrXxR8a/GrtNcbY0+Z5GBMNnETwFXPU4wBnJOST1I9u0b4HeCtLgVbmxk1KcAbprqVgCfZVIUD8Cfc0AZNt+0X4UlcLPp+rQA/wAflxsB9cPn8ga7zw5478M+K8Lo+rwTzYJ8hiY5QB1OxgCQPUAj3rJvPg94DvYih0CKIkcNDI6MPybB/EV5d4t+A1/orrqnhO7mu0hYP9mcgTpg5yjAAMR1xgHjjJoA+jK82+Mv/IuWP/X4P/QGr0mvNvjL/wAi5Y/9fg/9AasMT/Ckenkv+/0vU1/hf/yINh/vS/8Aoxq7GuO+F/8AyINh/vS/+jGrsaqj/Dj6GWZ/77V/xP8AMWiiitThPljxn/ycrH/2FbH+UVfU9fLHjP8A5OVj/wCwrY/yir6noAKKKKACiiigAooooAKKKKACiiuT+IvipfB/gm+1RWAuivk2oOOZWyF4PXHLEeimgDwf4ua3c+OfiZB4e0w+bFZyCygUdGnYgOx9MHCk9gma9O8e6JbeG/hjpWj2g/c2kscYOMFjtYsxA7kkk+5rh/2ffCrahrV54qvFZ0tMw27NyWlYfM2fUKcf8D9q9M+MH/IpQ/8AX2n/AKC1Y4j+FL0PRyj/AH6l/iRa+FP/ACJEH/XWT/0KtDWLRrO7W6hyqs2QRxtYc/kev5is/wCFP/IkQf8AXWT/ANCrsbm3S6t3hccMOuOh9aKH8KPoLNf9+q/4mQWlxFqdhl0Vg4KSxsMj3BB7HPQ9jXlHjn4DaXq4lvfDLJpt6csbZs+RIfbHKH6ZHsOtdzYzyaVqTRTcISFf+jD25/ImurByM9q2PPPjaLWPGPw71I6Zdia3MZ5tbob42Hqpz0OOqkZ9a9E8OfFvSr5447/fpl1wA5bMZPThgAV/EYHqa9s8ReGNI8Vaa1jrNklzCfuEjDRn+8rDlT9OvQ8V82fED4M6t4S83UNN36lo4yS6rmWAf7ajqP8AaHHHIFZypRl6lxqSWh77p3il2iR2ZLqBgCsiMDkeoI4P+ea6O11K1vQPJlG4/wAB4YfhXxPovifV/D0u/Tb2SJc5aIncjfVTx+OM16j4f+MNlcFIdatzZy/894ctHn1I5ZfwzWdqkNtUV7k/I+k6K4vTPE0rW8U0c0d3bSDMbhgQwzjIYdR155ro7LWLS8wqybJDxsfgn6ev4VcasZeRMqckaVFFFakBRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUVWvr2102ymvLyeOC2hUtJLI2FUDqSaAJ2IVSSQAOpNeFfEr44JamXR/CUqyTjKzaiOVT1EY6E/wC0ePTPBHMfEL4rap47vv8AhHPC8Vwmmyv5QEanzrwnjBA5CnsvUjk+g774Z/Be18NmHV/EKR3WrjDRwfeitj1B9GcevQHpnANAHG/D34LX3iGca74vM8VpI3mLbOxE9wSclnJ5UH3+Y89OCfoexsbTTLKKysreO3toV2xxRLtVR6ACrdFABRRRQBVv/wDjyl+lVdH+5L9RVq//AOPKb6VV0f7kv1FT1OiP8GRqUUUVRzhRRRQAUUUUAFFFFABRRRQAUUUUAFeD/tJavJHY6JoyMdk0klzKPdQFX/0J/wAq94r5t/aSRh4m0Vz902bAfUOc/wAxQB6F8B9Di0z4cQXoQCfUpXmkYjnCsUUZ9MKSP9416hXGfCd1f4W+HynT7Nj8QzA/qDXZ0AFFeEeN/H/xH0jxlqdjo2mTS6dC6rA405pAQVBJ3AYPJNcje/Gr4jabKsd9FDauy7lSex2EjpkA4OOvNAH1LXm3xl/5Fyx/6/B/6A1dj4X1CfVvCWjajclTcXdjBPKVGAWZFY4HYZJrjvjL/wAi5Y/9fg/9AasMT/Cl6Hp5L/v9L1PHovhX4t8TxjVtKe2FnNwge5KnKnaeMccg0/8A4UV8QP8Anraf+Bh/wr3b4X/8iDYf70v/AKMauwqqP8OPoZZn/vtX/E/zPln/AIUV8QP+etp/4GH/AAo/4UV8QP8Anraf+Bh/wr6norU4T5n8PfBHxlp/inSdRuxZGK1vYZ5CLncxVXBOOOTgcV9MUUUAFFFFABRRRQAUUUUAFFFFABXzL8cvEc3iXxtaeGNO3TR2LCLYhz5lw+AQPUjKrz0JYV7z4z8SQ+EvCeoazKQXgjIhQ9HkPCL9CSM+2TXg/wACvDc3iLxnd+KNR3Sx2LGQO/PmXD5OSe5AJY+hKmgD3rwd4ch8J+FNP0WHBNvEPNcD78h5ZvxJOPQYHauc+MH/ACKUP/X0n/oLV6F2rz34wf8AIpQ/9fSf+gtWOI/hS9D0so/36l/iRa+FP/IkQf8AXWT/ANCrt64j4U/8iRB/11k/9Crt6KH8KPoTmv8Av1X/ABMx9csPPg+0Rr+8jHzcclf/AK3Wm6Ff+dD9mkb54/uknkr6fUdK2sZ4rlb+3fStRWaHhCSyeg9V+nOPoRWx551dFQWtyl3bpMnRh09D6VPQB418RvghZ6752qeGljstSOWe24WGc98dkb9CeoGSa+ctS0680i+lsdQtpba6hbbJFKpVlP0P5579a+8q47xz8PNH8dWHl3sfk30a4gvYwN6H0P8AeXPYnucYPNAHzD4K8e6j4Ou9qKLvTZGzPZSt8rdAWU8lW46j0GQcV9GaBd6P4z0n+0/Dt5vAwJbaXAkhY/wsOx44PIPOCa+Z/F3grWPBWqmy1WDCtkw3CAmOZfVT6+oPI7jkZq+G/E2q+FNXj1PSLloZ0+8OqSL3Vh0IP/1xggEROnGW5UZyWx9aRajqWkuI5lYqOAsgJBA9D/gT9K2rTX7S5wrnyZPRjx+B6VzfgP4haP8AELTCgVIdSiXNxZSHJA/vL/eX36jOD1BO3eeGopMtav5bH+FuV/xFZclSHwu6L5oS30ZvAhhwc0tcaJNU0ZgrBhGDwG+ZD9D2/MGtez8RW0wCXAMLnjJOVP49vxqo1k3Z6CdNrVam5RTEdXUMjBlIyCDkH8afWxmFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRWTr2v6d4Z0efVNVuFgtYh16szdlUd2PYf0FAEmta1p/h7SZ9T1S5S3tIFyzsevoAOpJPAHU18yeKvGHiT4weJYdG0e2lWwDk29mp4IHHmynpkZ78AHAySSYtY1rxN8a/GEdhYxMlmjZgtyx8u3ToZJCB155OCeQAOx+hfAvgPS/AukC0sU8y6kANzdso3zN/RQc4Xt7nJIBnfDr4Y6Z4DshKQt1rEq4muyOF9VjB6L+pxk44A76iigAooooAKKKKAKt//AMeU30qro/3JfqKtX/8Ax5TfSquj/cl+oqep0R/gyNSiiiqOcKKKKACiiigAooooAKKKKACiiigArxf9onQJL7wxp+tQoWOnTMk2B0jkwNx9gyqP+BV7RVTULG21OwuLG8hWa2njMcsbdGUjBFAHk37PniaG+8JzeH5JALvTpGdEzy0TndkeuGLA+mR617JXyv4p+Hvin4Ya/wD254ekuZrCJi0N5Au5olP8MqgEYxwSRtPsTgdNo37SDJAkeuaF5ko4aazl2hv+AMOP++vwFAH0FXzP+0j/AMjnpX/YPH/ox66m5/aS0dYibXQL6WTsssqRg/Ujdj8q811u98U/GfxNFc2Oh/6mPyEEIPlxpknLyNxnk+meMDNAH0x4E/5J54a/7BVr/wCilrl/jL/yLlj/ANfg/wDQGrsvDenTaP4W0nS7hkaaysobeRoySpZECkjIBxkHGQK434y/8i5Y/wDX4P8A0BqwxP8ACl6Hp5L/AL/S9TX+F/8AyINh/vS/+jGrsa474X/8iDYf70v/AKMauxqqP8OPoZZn/vtX/E/zFooorU4QooooAKKKKACiiigAooooAKKKyfEeuW/hrw7f6zdkeVaQl9ucF26KoPqSQB7mgDwX9oHxU+o67Z+FLNmdLQiWdV53TMPlXHchT/4/jtXs3w88Kp4O8FWOlFQLnb5t0wx80rctyOoHCg+iivBvhBodx43+JVx4i1QebHZyG8mYjhp2JKL7YOWHptAr6joAO1ee/GD/AJFKH/r6T/0Fq9C7V578YP8AkUof+vpP/QWrHEfwpeh6WUf79S/xItfCn/kSIP8ArrJ/6FXb1xHwp/5EiD/rrJ/6FXb0UP4UfQnNf9+q/wCJi1Vv7Rb21aJuD1U+h7GrVFbHnnL6RdtY3j2s/wAqs2CCeFbpn8en5V1FYGvWOR9sjHIGJAO46A/h/hVrR7/7ZbeXIf3seAT6jsf8aANWiiigDI8QeHtM8UaTLpmrWqz2snOD95G5wynqCPUfyJFfKvxE+GWpeBL0y/Nd6PKxEN2F+6eyyAdG/Q9R3A+wap31ja6nZTWV7bx3FtOpWSKUZVgexH+e1AHw1pup3ujalBqGnXMlvdwMGjljOCD/AFB6EHIIyDwa+qPhl8VLPxvbCxvPLttchT95DnCzgdWj/mV6j3HNeM/FH4T3Xgud9T0wPc6FI33jy1sScBX9RyMN+B5wT5vaXlxYXcN3aTPBcwsHjkjYhlYcggjpQB96OiupVlDKRggjNY954etp8tBmF+uAPlP4dvwrjPhZ8VLfxnarpmpOkOuxLyowFuVA5ZR69yv4jjIHp1RKEZbocZOOxxjQapozlkLBOpZfmU/UY/ng+laVn4ljfC3aeWT/ABrkj8R1H61v8YrLvNCtLrLKvkuf4kHB+o6fyrL2co6wZpzxl8SNGKaKeMPE6up6FTmpK4+XTdS0uTzIGZl/vR5P5j/9f1q3Z+JTwl5Hn/bQfzH+fpTjWW0lYHT6x1Omoqvb3cF0m6GVXHfB5FWK2TT1Rla24UUUUwCiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiqeo6haaXp9xfX1wkFrAhklkc4Cgf56dTQBBrmt6f4d0a41XU51htIFyzHqT2UDuSeAO5r5g1fV/Efxr8ax2VlC0dohPkQEny7aPIBkkI79Mnr0A7Av8VeJtc+MfjO30nSIJBYq5Fpbk4Cr3mkIyAcdeuBwMkkn6E8CeB9O8DaElhZgSXEmGurorhpnA6+yjkAdvckkgEngrwVpfgfRF0/T03Svhrm5YfPO47n0A5AHQA9yST09FFABRRRQAUUUUAFFFFAFW/wD+PKb6VV0f7kv1FWr/AP48pvpVXR/uS/UVPU6I/wAGRqUUUVRzhRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABXPaj4G8K6rI0t94e02aVjlpDbKGJ92ABP510NFAHLW3w48GWjh4vDGmbh/ft1fH/fQNdJDBFbwrFDEkcajCoihVA9gOBUtFABXm3xl/5Fyx/wCvwf8AoDV6TXm3xl/5Fyx/6/B/6A1YYn+FL0PTyX/f6Xqa/wAL/wDkQbD/AHpf/RjV2Ncd8L/+RBsP96X/ANGNXY1VH+HH0Msz/wB9q/4n+YtFFFanCFFFFABRRRQAUUUUAFFFFABXz7+0R4s3PZ+FLWThcXV4FPfoin8MsR7qa9z1fVLbRdIu9TvH221rE0sh74AzgepPQDuTivmP4eaZdfEv4tS6zqSb7eKU31yDyowR5cYJ6jIUYP8ACpoA9z+FXhP/AIRHwNZ2ssey+uR9pusjkOwHy/8AAVwMeoJ713FFFAB2rz34wf8AIpQ/9fSf+gtXoXavPfjB/wAilD/19J/6C1Y4j+FL0PSyj/fqX+JFr4U/8iRB/wBdZP8A0Ku3riPhT/yJEH/XWT/0Ku3oofwo+hOa/wC/Vf8AExaKKK2PPGOiuhVgCpGCD3rlZUl0bVAyZKZyuf4lJ5BP6fUA+ldbVDU7EXtqygDzF5Q+/p+NAFqGVJ4lljOUYZBqWub0K+MUps5cgMTtz2buPx/n9a6SgAooooAguLeG7tpLe4iSaGVSkkbrlWU8EEHqCOMV8vfFf4TzeEZ31jSI3l0ORvmXq1qxPCnuVJ4DdsgHnBP1RUFxbw3dvJBcRJNDKpSSN1BVlIwQQeoI4xQB8H2l3cWF3Fd2kzwXELB45IyQysDkEH1r6u+FnxPt/HGnCyvWSHXLdAZYxwJl6b1H8x2J9CK8Z+LHwtm8GXrappiPLoU74B6m2Y/wMe6nsfwPOCfPNM1K80jUrfUdPuHt7u3cPHKh5Uj+h6EHggkHgmgD7yorhvhv8QrTx5oYl+SHVLcBbu2B4B7OvcqcfgeDngnuaAErPvNItLzLPHskP8acH/6/41oUtTKKe6BNp3RyNxol9Yv5ts7SAZ+aMkN+I7/mfpUlp4jnhPl3cfmAHBYDDDHqOh/Supqnd6da3q/vogW/vDgj8axdJxd4M1VRP4kLaaja3q5hkBPUqeCPwq3XK3fh24t28y0k8wA5AJww/Hof0pltrt7Zv5V0hkA4IcEMPx/x/OhVWnaaB009Ys66is+z1a0vcCOXa/8Acfg/h6/hWhWykpbGTTW4UUUVQBRRRQAUUUUAFFFFABRRRQAUVm6vf/YLPehHmsQEBGee/wClP026lvLJJpkVGbOACf69KnnXNyj5Xa5foooqhBRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQBHI6xozuwVFBLMTgADrk18wfE/x7e/EPxDD4b8OrLNpqzCOJY85u5em4j+6O2fcnsB0fxw+JbM0vg7RJif4dQmjOST/wA8QR/49j6eorqPg58M18Kacut6tAP7buk+VHHNrGR93HZj3PUdPXIBvfDb4e2ngPRPLOybVbhQbu5A79Qi+ijP4nk9gO6pjOqDLMAPc4pi3ELnCyoT7MKAsyaiimsyoMsQAPU4oAdSVELmAnAlTP8AvCpQQRweKAaa3FpKWo3kRB8zqvuSBQFm9h9LUSTxucLIh+jA1LQFrblW/wD+PKb6VV0f7kv1FWr/AP48pvpVXR/uS/UVPU6I/wAGRqUUUVRzhRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFebfGX/kXLH/r8H/oDV6TXm3xl/5Fyx/6/B/6A1YYn+FL0PTyX/f6Xqa/wv8A+RBsP96X/wBGNXY1x3wv/wCRBsP96X/0Y1djVUf4cfQyzP8A32r/AIn+YtFFFanCFFFFABRRVW51GysiBdXlvAT0Esqrn6ZNAFqiq9vdW95F5ttPHNHkjdG4YZ9Mg9asUAFFFV7y7gsLKe8uZBHBBG0srnoqqMkn6AGgDxT9ofxb9m0y08L20v7y6P2i6A7RqfkU/VgT/wABHrXWfBjwl/wjHgWCeePbf6mRdTZHKqR+7U9+F5x2LGvFvDtrP8WvjE97eRsbJ5jczq3Oy3TAWM/X5VP1Jr6vAAGBwKAFooooAO1ee/GD/kUof+vpP/QWr0LtXnvxg/5FKH/r6T/0FqxxH8KXoellH+/Uv8SLXwp/5EiD/rrJ/wChV29cR8Kf+RIg/wCusn/oVdvRQ/hR9Cc1/wB+q/4mLRRRWx54UUUUAc3rtiYZReQggMfmx2bsfx/n9a1dMvhe2qsSPMX5XHv6/jVqaJJ4XicZVgQRXLxPLo2qFXyUzhsD7yk8ED9fqCPWgDraKYjq6hlIKsMgjvT6ACiiigCpf2NtqdjPY3sCz2s6FJInHDKeoNfJHxN+HV14E1ndGrzaPcsTazkcqevlt/tAdD0I59QPsKsnX9BsPE2i3Ok6nD5ltOuDjG5T2ZTzgg8g+3pQB8XeG/EeoeFddttW0yUxzwnofuyKeqsO4I4/UYIBH2N4O8Waf4z8PQ6rp78N8s0LHLQyDqp/mD3BB718jeNPB9/4J8RTaXfDeo+a3nAws0Z6MPQ9iOxHccm98OvHd14D8RpdJvk0+fCXtuD99P7wHTcucg/UcAmgD7Moqnp9/a6pYQX1lOs9tOgkjkXoykZB/wDrdquUAFFFFABVa5tILtNs0QcdiRgj6HqKs0Umk9GCbWxzF54aZcvaSbh1CP1/A/5+tVodU1HTHEU6syj+CX09j1+nWuwqGa3iuEKTRq6nswzWMqPWDsaKp0lqULPW7S6wpbypD/C56/jWpXPXnhpGy9pIUPXYxyD+PUfrWetzqmjsEcMEHRXGVPsCP6Y96XtJR0mh8kZfCzsqKxbPxDa3GFmzC545OV/Pt+OK2FYMoZTkHoa1jOMtmZyi1uOoooqxBRRRQAlRyqzxOqNsYggNjOD61LVDVbz7FYSSAgOflT6nv+HJ/Cpk7JtjSbZyFws3nm3MjTCIkDGSAB1wOw457cV0dhrlnLGkLDyCoAAY/L+f4d8VB4bs8RyXj9X+VPoDyfzH6Vo3Gk2dxKJHiAYEHK8Z5zg+tc9KEkuZdTWck/dZocGlrP1K5ubaFWtbczOTjAXOB+FZ0fiQo4S7tXjPcj/A4NbOoluZqDeqOhoqC3uYbqISwyB1PcGp6tO+xIUUUUwCiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigArzb4ufEQeCtC+yWUgOs3ykQDg+SnQyEfXgZ6nJ5AIrr/E3iGx8KeH7vWdQbENupIUH5pG6Koz3JwP16A180+FdD1X4yfES41LVWYWSuJbx1JAjj/hhT0yBgewJOT1AOn+CHw6bULpfGOtxF4UctYxyjPmyA8ynPYHp6nJ7DPv8Ae3ItoC3VjwB70+2tobS2itraJYoIkEccaDCqoGAAPTFZ+sk7oh2wf6UPRGlKKlNJkVvZyXx82aRgv+enoKsNpERX5ZHB98Gr1uAtvGAONoH6VLSSKlWnzaaIr28bQWwjY7iuefWsuJJNSuWZ3IVew7Dtj/Gtusd7O5tJi9vyp9Ov/wBehoqjJe90bLB0eHtJIPxH+FTWdqbUON+5WORx0qmuqTRnE0P6EfzrQt7qO5QmM8jqPSjQVT2qj72xBf3ZtogEx5jcDPaqlvp73C+bO7DI6d/xpNT+a+RT0wP5mthcY46UdRuXs6a5d2Zz6RHj5JWB7Z5q9ChjiRGOWAAJ9alpaexjKcpfEVb/AP48pfpVXR/uS/UVav8A/jym+lVdH+5L9RU9TaP8GRqUUUVRzhRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFebfGX/kXLH/AK/B/wCgNXpNebfGX/kXLH/r8H/oDVhif4UvQ9PJf9/pepr/AAv/AORBsP8Ael/9GNXY1x3wv/5EGw/3pf8A0Y1djVUf4cfQyzP/AH2r/if5i0UUVqcIUUUUAeFfFLSfiPrXjSS08Of2p/ZXkR8Q3PkQliDu5LKCfUEmvLfF/wANPEXhDR4dY1yW2xcXAg8tZjJIGKs2ScYxhT3Jr7Hrxz9pD/kRdM/7Ca/+ipKAL37Pn/JNP+36X+S16rXlX7Pn/JNP+36X+S16rQAV43+0B4t/svwzD4etpMXOpndNg8rCpz+G5gB7gMK9flkSCJ5ZXVI0UszE4AA5JzXyifP+MHxlwC5sZZuO3l2kf8iR/wCPPQB678CfCX9heDP7WuI9t5qxEvI5WEZEY/HJbI6hh6V6tUUUUcEKRRIqRooVVUYCgcAAfSpaACiiigA7V578YP8AkUof+vpP/QWr0LtXnvxg/wCRSh/6+k/9BascR/Cl6HpZR/v1L/Ei18Kf+RIg/wCusn/oVdvXEfCn/kSIP+usn/oVdvRQ/hR9Cc1/36r/AImLRRRWx54UUUUAFZWsWH2y28yMfvY8kD1Hcf4Vq0UAYGgX+V+xyHkcxk+nUj8Oo9s+lb9cvq9o1herdQfKrNkEdFbr+vX863rG7S9tEmXGejD0PpQBDqOpx2CAY3ysPlQfzJ7CsVf7V1QllZxGehyVX8h1/U0WUP8Aa2qySzHKA7yD3GcAfTGPyrqFUKoVRgAcADGKAOaaDVdMHmiQug5YBiwH1B7e4/MVs6ffJfwb14dThl9DV3AI56Vz9vG1h4hMMYPlSgnAB4ByR+RBGfSgCj8QvA9p468OSWMoSO9iy9ncMOY5PQnrtOACPocZAr481LTrrSNSuNOvoWgurdzHLG4wVYfzHoehH1r7yrx343/Doa9pbeJNMhzqdlH+/RBzPEOc+7KOR3IyOSAKAOH+B/xGOiaknhnVJv8AiW3b/wCjSOeIJT29lY/gDg8ZJr6ar4BBwc19VfBn4hf8JboX9lajNnWLBAGZmyZ4hgB+eSR0br2OecAA9UooooAKKKKACiiigApjosiFXUMpGCCMg0+ihoDCvPDtvNlrcmFzzjkqfw7Vk7dU0ViRuEeeo+ZD+HYn8DXZUhAI5rGVGL1Whoqj2ephWfiSGTCXSeU3TcvK/wCNbccqTIHjdXU9CpyKy7zQLS5y0Y8hz3Xp+XT8sVjSWOp6S/mRFtvXdHkg49R6fUfjU89SHxK6Hywl8LszsaK5uy8Sg4W8jwenmJyPqR2/DNbsFzDcx74ZFdfUGtI1Iy2IlBx3J65bXpHu9Uis0OApA9tzYPPtjH611FYOr6VNLci9tD+9GCV4GcdCM9+BU1k3HQdNpM2beFLeBIkGFRQo/CnySJEhd2CqBkknGKxtL1aa5uPslzbkSgElhxgD1B6dvz6CqviS5d5obNDgEbiAcZJOAPwxmh1EoXQKDcrM0v7e07ft8/8AHYcfnirDLZ6lCQfLmQ8ZznH+BqlF4eslgCyIzvjl9xHP0zVK40Say3XFjcsoUZIY4IHXr0P0IFK87XktB2g9nqRWYbS/EH2VXJicheT1BHH4g4H5+tdVXJaOJtQ1kXMx3GMbmPQZAwBgcZ7/AIGuqkkSKNpHICqCSfYUUH7rfQdRapdRwYEkA806uKt7+Z9Xa6VJJHYkiNCQSMYAOOw4zwenvWk+u31u2bmxKxnoeR/Q8+1ONaLWonTadjo6KqWV9Dfw+ZExOOGU8FT6EVbrVNNXRm01owooopgFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRXlPxu8ef8Iz4c/saxlxqmpIVypwYoejN6gnlR+JByKAPMfip4tu/iJ42t/DmhFriyt5vIt0Q5E8x4aT0wOQD0AycgE1774G8H2ngnwzb6Vb4eX/WXM2MebKQMt9OAAOwArzX4CeA/sFgfFuoQ/wCk3IKWSsPuRdC/sW5AP90ZGQ1e40AJWdqsBkgEijJTPT071pUhwRRYqEuSXMjP0+8SSERswDqAMHv71daRUXczAfU1Sm0uGRtyFoyew5H5VEujqOXmJHoFx/U0jWSpSfMnY0VlR4/MVgV55+lNjuYZR8kit7UsUEcMIiXO0cc1SfSIzykjL7daZEVB3u7FycxeUfOK7Mc7qy9JB+1OVzt29/8APtUqaOucvMxHoBitCG3jt02RjApdS3KMIOMXe5natCxKTr0HDe1W7S7S4jAJAcDlelWWUMu1hkEYxWfLpMTNlGKe3UUWEpxlBRn0L7yJGuXdVHucUqsrqGU5BGQazV0dB9+ZmHoBitGNFjjVF6KMflTInGC+F3Ib/wD48pvpVXR/uS/UVav/APjym+lVdH+5L9RU9TaP8GRqUUUVRzBRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFebfGX/AJFyx/6/B/6A1ek15t8Zf+Rcsf8Ar8H/AKA1YYn+FL0PTyX/AH+l6mv8L/8AkQbD/el/9GNXY1x3wv8A+RBsP96X/wBGNXY1VH+HH0Msz/32r/if5i0UUVqcIUUUUAFeOftIf8iLpn/YTX/0VJXsdeOftIf8iLpn/YTX/wBFSUAXv2fP+Saf9v0v8lr1WvKv2fP+Saf9v0v8lr1QnAz2oA8r+Oviz+wfBZ0u3kxeasTEMHlYRzIfxBC+4Y+lZ/7P/hP+zPDU/iK5jxc6kdsORysKnHHcbmBPuFU15p4lu7j4s/GFLKzkY2bTC1t2XkJAmSzj6jc34gV9T2VnBp9jBZWsYjt7eNYokHRVUYAH0AFAFmiiigAooooAO1ee/GD/AJFKH/r6T/0Fq9C7V578YP8AkUof+vpP/QWrHEfwpeh6WUf79S/xItfCn/kSIP8ArrJ/6FXb1xHwp/5EiD/rrJ/6FXb0UP4USc1/36r/AImLRRRWx54UUUZB70AFFFFAEF1bpd27wv0YdfQ+tc3YXD6VqLwzZCEhXHYeh+nOfoa6usXXbHz4ftMY+eP74A6r/iP5UAVLFhpmsSQSYEcnCsTgcnK8+mOPrXS1zNmkerWgt5G23MI+R/VfQ+uDx7cEe+zp0Fzb2/l3MokI+7jJwPTNAF2mbV3bsDdjGabNPFbxmSVwijua5681ie8cw2auqHj5Rlm/w+g59+1AG6t3C9y1ukimUDJUHpzg1ZxmuStobjTZBdTWUjBeQQ2AvYk4B/Wujs76G+i3xE5HDKeCPwoA+X/jR8Ph4U10atp8RXSNQY4VRxBL1KewPJHtkdq4Lw14hvfC3iC01iwfbPbuG2k8Ov8AEh9iCR/+oV9n+JfD9l4p0C70e/TdBcIRuA5jb+Fh7ggH8Pevi7xDoV54a1680e/TbPbOVJxww6qw9iCCPY0AfaXhzX7LxNoVnrFhJut7lN2CeUb+JT7g5B9xWvXzB8CvHX9g+ID4evptun6k48oseIp8YB9gwAU+4XpzX0/QAUUUUAFFFFABRRRQAUUUUAFFFFAGZeaLaXmWKeXIf404P49jWFPo+oafJ5tuzOB0aPIb8R/hmuvorKdKMtdmWqklocvaeJJUOy8j3jOCygBvy6fyrftb23vE3QSq2Oo7j6io7vTLW9BMsQ344deG/OsG50C6tW8y0cyBTkY+VhUfvIb6or3J+TOp2Lu3YG7GM47Via9pst0UubdSzoMMo6kdiPoc1Qttfu7VvLukMgHB3Daw/wAfyrfs9Ttb0YilAfH3G4b8qfPCouXYXLKDuZdt4kVY9l3E4kXglQMH69MH2qnqmtteRGGFGSJurNwWwenoB+Jz/PqJLeGU5khjc9tyg1mXeipdXkc5lIRSAYyOMDsPQHnP1pShU5bJjjKF7tEmh2X2XT1LDEkvzN9Ow/L+dVfEl55Vstqp+eQ5bHZR/if5GtxmVFLMQABnJrlLcHWdeMrAmJTuwR/CDgD8e4+tE/dioIIaycn0NnRbBbOzVmUedIMse49B+FaMkaSxsjqGVhgg9xUlZus3n2PT3KnEj/IuPU9T+Aya0soRIu5SMbw6SmrTJGSY9h+mARg/Xn9TXV1g+G7PyrVrlh80pwuf7v8A+v8AkK3qVFNQHUactAooorUgKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKAKOranaaLpV1qV9II7W2jMkjegHPHqewHcnHevlvQ7G++MnxUlu70OtmX864AJxDbqQFjB7EjCj6k44Ndj+0F40LPD4QspM42z3209T1RD9OGP1X0r0L4S+Cx4N8HQrcRbNSvsT3ZI5U/wAKH/dB/Mt60AdzBDHbwRwQoqRRqERFGAoAwAB6CpqKKACiiigAooooAKKKKACiiigAooooAKKKKAKt/wD8eU30qro/3JfqKtX/APx5TfSquj/cl+oqep0R/gyNSiiiqOcKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigArzb4y/8i5Y/wDX4P8A0Bq9Jrzb4y/8i5Y/9fg/9AasMT/Cl6Hp5L/v9L1Nf4X/APIg2H+9L/6Mauxrjvhf/wAiDYf70v8A6MauxqqP8OPoZZn/AL7V/wAT/MWiiitThCiiigDkfFfxG8O+DL2C01meaOaeMyII4Wf5ckdR06V458Y/iT4b8Z+F7Kw0e4mknivVmYSQsg2hHGcnvlhXsPi34b+HvGt7BeaxHcNNBH5SGKYqNuSeQB6k1z//AAoLwN/zwvv/AAKP+FAHD/CX4oeGPCPgv+zNWuJ47n7TJJiOBmG0hccj6Gtzxx8atCvvA2pw+HbqZr6fbbDfEU2K4bcwz6KrDI6Eitz/AIUF4G/54X3/AIFH/CvA9Z8PadqnxMbw54TicWxuRaRPI5cswOHcn+6CGPHYZoA9X/Z48JfZ9OvPFNymJLkm2tc9owcuw+rAD22H1r3WqGj6XbaJo9npdmu23tIlijHfAGMn3PUnuTmr9ABRRRQAUUUUAHavPfjB/wAinD/19J/6C1ehdq89+MH/ACKcP/X0n/oLVjiP4UvQ9LKP9+pf4kWvhV/yI8H/AF2k/wDQq7brXE/Cr/kR4P8ArtJ/6FWj4p8Y6d4VhU3O6W4kB8uCPGTjuewHuaVKSjRTl2KzCjOtmNSnTV25M6ajivJR8WNXuf3lr4dLRdiGZ/1C4rY8N/E0a1rUGlXWlyWs8xIUiTcAQCTkEAjpQsTTbSTHVyXGU4Oco7b6rT8Tr9d8/wDsDUPsvmfaPs8nleXndu2nGMc59K5D4YLrqxaj/bf9obiyeX9sLn1zt3f0rtNUvf7O0u7vfL8z7PC0uzON20ZxnBx+Rrn/AAV4yPi5Lx/sH2T7OVH+u37s5/2R0xTlb2iu7GVH2v1OpywTjpd9V6ep11IRmua8ZeKj4T0uG9Fn9qMkwi2eZsx8pOc4PpWJd/FKwtdFs7n7K0l9cpvFokmdgJ4y2B/In2pyrQi7NkUcuxNaCnThdN2+Z6DnIpCAc15KvxfvbedftuhbI26YkKtj2yMH9M16LoWuWXiDTI7+xcsjcMp4ZGHUEdj/APr70U68Ju0WVi8sxWEip1Y6Prv+RlX0D6TqSzQ8ISWQ/wA1Ptzj6EVuTaiBpn2yGMyAgcZ+6e+foetS6hZre2jRHG7qp9DWDpN2bS5ezuBiNztIbs3Tntg9D+FanAEVpe6zKJpmKxZ+8RgAeij+v5k10FpZQWUeyFMZ6seSfqasAADA4FNd1jQu7BVAySeMCgBxAIII4rLtNL+yahLOkm2I8LGB1B5OfYHpVK71yaaXybFTycBtuWY+w7D8CfpUYtNbYeZ5koPXBlwT+GcD6UAdNXjnx38C/wBt6EPElhFuv9OQicKOZIOST9VJJ+hb0Ar0jS9Tle4NpeAiXopIwSeuCPXHfvWu6LKjI4DKwIKkZBHQ5FAHwMrFGDKSCDkEdRX2D8KfGo8Z+DoZbiTdqdniC7GeWIHyv/wIc/UN6V85/E/wY/gzxhcWsUbDTrkmazbHGw9Uz6qePXGD3pfhd4zbwX4zt7mV8afdYgvB22E8N9VOD9MjvQB9j0U1WDqGUggjII5Bp1ABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFAFW6sbe8XbNErY6HuPxrBu/DcsZ32km/nIVuGH0PTP5V1FFZypRluVGco7HIQ6xqGnSeVcKzgfwycNj2PU/U5rcs9atLzC7/LkPG1zj8j0NXJ7aG5jKTRq6+hFYV54aHLWcmD18t+R+B7fjms7VIbaou8Jb6HQOiuhVwCpGCD3qC1sbeyMnkIE3kEge1czHfanpDiOUMUHAWTkEex/wOPatm01+0ucLIfJkPGH6H6H/HFONWDeujE6cltqjXrlNTkbVNaS0iJ2IdmR2P8AEfwxj8K6oEEAg5FVIdOtre6a4ijCyMCDjp69O1VUi52SJhLl3LMUaxRLGgAVQAB6AdKkoorRKxIUUUUwCiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACsbxPr9r4Y8N3+s3fMdrEWC5xvboqj3JIH41s186/tCeLGutTs/Cdo5ZbfE90F6tIwwi49lOffeO4oAxfhR4fuvH/wAR7jxDq/763tJftk7EfK8xOUT6AgnHTC46EV9SVxvwz8JDwb4JtNPkQC8lHn3ZHeVgMjP+yAF/DPeuyoAKKKKACiiigAooooAKKKKACiiigAooooAKKKKAKt//AMeU30qro/3JfqKtX/8Ax5TfSquj/cl+oqep0R/gyNSiiiqOcKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigArzb4y/8AIuWP/X4P/QGr0mvNvjL/AMi5Y/8AX4P/AEBqwxP8KXoenkv+/wBL1Nf4X/8AIg2H+9L/AOjGrsa474X/APIg2H+9L/6MauxqqP8ADj6GWZ/77V/xP8xaKKK1OEKKKKACiiigDiPip4t/4RDwNeXcUm2+uB9mtcHBEjD73/AVBOfUAd68z/Z38J+ZNeeK7qPITNraEjuQC7D6DCgj1YdqwPjFrtx41+JFv4d0zMsdnILOFAch52IDn2wcKfTaTX0X4b0O28M+HNP0a1x5VpCE3AY3N1ZiPUsST7mgDXooooAKKKKACiiigA7V578X/wDkU4f+vpP/AEFq9C7V578YP+RTh/6+k/8AQWrHEfwpeh6WUf79S/xItfCr/kR4P+u0n/oVcP8AELZb/Eq2n1JC9jiFiCMhowfmGO/fI9/eu4+FX/Ijwf8AXaT/ANCrf1zw7pniG2EGo24l25KOOGQn0PX/ABrH2bqUIpb6He8ZHCZrVnNXTck7b69ULpWr6RqUCf2fd2syBRhY2GV+o7VcksrWa4iuHt4nmiJMchUFkJGDg9uCR+Nea3/wciB36bq0sbDkLMm7n/eUjH5GsnSvEHiHwV4nh0fV7hri2dlVld94CscB0Y8gZ7Hjg8d6r20otKpG3mZ/2bRxClLBVuZpN8rVnb9T1TxR/wAirqv/AF6S/wDoBrgPgt/qNX/34v8A2au/8TnPhTVT/wBOcv8A6Aa4D4Lf6jV/9+L/ANmpVP48PmPCf8inEesfzND4yY/4Riz9ftq/+gPR8LvDlrbaFHrMsSveXJbazDJjQEgAfXGeKT4yf8izZ/8AX4v/AKA9dB8P/wDkRtK/65H/ANCNJJPE3fYuVWdPJIqLteev3Ghr2jW2t6RPY3EasrqdpI+63Yg9iK81+DV263upWRJ8tkSQA9iCQfzyM/SvX3+430rxf4O/8jFf/wDXsP8A0IU6qSrQa8ycvk55biYS1S5WvW57XXP6/Y8fbI154EgA/AH+Q/KugpjIroyMAVYEEHvXWeAZ+j3/ANstgjn97Hw3v6H+h96peILhzJFZx/xYZgO5JwB+lUpFk0bVAVyUzkejKTyPqOn1ANWtZBM1tqMPzR4HI7EEkZ+uf0oA1NP06OxhGADKR8zY7+3oKv1BbXUV3CJYmBB6jPIPoR2qG81O2slO99zjoinJ/H0/GgDO1hETU7J1IVyw3EkAAAggn2HP5e1Jf66dxhsgWJ48wjPPoB3+v/66z/LutZu2kC4GcEnO1QOgz+PQcnJNb9jpcFkAwG+UjlyOfwHagDz34g+B7vxJ4H1A7BJqEK/aLdGBLFl5IBz1K7gBzyRnHb5Sr7/r5G+Mng8eFPG80lvHt0/Ugbm3AGArE/Og+jHOB0DAUAez/A/xj/wkfg1dNupN1/pWIWycl4j/AKtvwAKn/dBPWvUq+M/hj4sPg7xvZX8jlbOU/Z7v08piASf90gN+HvX2UpDKCCCD0IoAdRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUARyRpKhSRFdT2YZBrEvPDcMmWtn8pjztPK/wCIrepaiUIy3Q4ycdjjN2qaKwB3LHnofmQ/j2J/A1rWfiK3mwtwDC54zyVP49q2yoZSrAEHqDWReeHrW4y0OYHP90fKfw/wxWXs5w1gzTnjL4kaqSLKgZGDKehB60+uOe11PR3LxlgmclkOVx7jH8x9K0LPxKj4S7TYem9OR+I6j8M041ltLQTpveOp0VFRQzxXEYeGRXQ91OalrZNPUzCiiimAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFAGbrur22gaFfatdnEFpC0rAHBbA4Ue5OAPcivmv4U6Rc+PvijPr+pjzIrWU39wSPlMpY+WvsM8geiEV2f7RXig22l2Phm3fD3Z+03IBx+7U4QEdwWBP1QV1/wAGvC3/AAjXgC1eVNt5qOLubjBAYfIv4Lg47EmgD0SiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAq3/APx5TfSquj/cl+oq1f8A/HlN9Kq6P9yX6ip6nRH+DI1KKKKo5wooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACvNvjL/yLlj/ANfg/wDQGr0mvNvjL/yLlj/1+D/0BqwxP8KXoenkv+/0vU1/hf8A8iDYf70v/oxq7GuO+F//ACINh/vS/wDoxq7Gqo/w4+hlmf8AvtX/ABP8xaKKK1OEKKKKACuV+IPilPB/gu/1UMPtIXyrVT/FK3C8HrjliPRTXVV8zfHbxLN4g8Y2nhfT90sdiQhROfMuHwMe5AIA9CWFAFn9n/ws+p6/e+K70F0syYoHbJ3zsPmbJ6kKefdwe1fSFc94L8NQ+EvCen6NFtLQRgzOOjynl2+hJOPQYHauhoAKKKKACiiigAooooAO1ee/GD/kUof+vpP/AEFq9C7V578YP+RTh/6+k/8AQWrHEfwpeh6WUf79S/xItfCr/kSIP+usn/oVZfiPx1rnhrxNdxyaZ9o0rK+UzKyfwrnDgY657E1qfCr/AJEeD/rtJ/6FXalAeoBHvUQi5Uo8rtob4qtTo5hWdWHOrvTbqeX/APC5rPy8/wBkT+Zjp5ox+dYVhYav8QvF8Or3NobawjZSXIOAinIVSQNxPPPufYV7J/Z1n5m/7LDv/veWM1aAA6AAe1L2M5Nc8roqOZ4egm8JR5ZNWu23b0MnxOMeFNVHpZy/+gGuA+C3/Hvq/wDvxfyavVu1IFA6ACtZU7zU77HFRx3s8JUw3L8dte1jzn4yf8ixZ/8AX6v/AKA9dB4AH/FDaV/1yP8A6Ea6YgEcgGjgcAUKnapz+QSxvNg44Xl2le/yEf7p+leMfB3/AJGK/wD+vYf+hCvaaTAB4AFE6XNOMuwYbG+ww9Why357a9rDqKKK1OEz9UsRe2hCj96mSn9R+NZWi3S5awuQCjkhQw4B7gg+vUf4mulrmtcsjBMLyIEKx+bb2brn8f5/WgCHVrOGzmRYI5QZBnO4FeuMAdSfx/PNT6foLSYku8ovURg8n6+g9v5VqaddpqFskrKplQ4bjkH1HpkVoUAMjiSJAkahUAwAB0p9FFABXn3xg8Jf8JV4EufIj3X+n5urfA5O0HcvryueO5C16DRQB8AV9cfBbxT/AMJJ4Bt4J5C17pp+yy5PJUDKN9CuBnuVNfPfxR8LHwn47v7KOPbaTn7TagDAEbknA9lIZfw962Pgj4oPh7x9BaSvttNUAtZATgBycxt9dx2+wY0AfWdFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFACEVl3miWd2SQnkyH+JBgfiK1KKmUU90NSaehyE2l6jpkhlt2Zl/vRk5x7j/8AXVmz8SMpCXke4dC68EfUf/q+ldNVC90m0vctJHiQ/wAacH/6/wCNY+ylHWDNPaJ6SRPb3lvdpuglV/UA8j6jtViuSudCvbJ/NtXMgXkFCQw/DPP4ZJ9Kfa+IbiBvLu4/MAOCcYYfh3/SmqrWk1qHs76xdzq6KpWmo2t6P3MoLY5U8N+VXa2TTWhk01uFFFFMAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACmswRSzEAAZJPAFOrgvi/4i/4Rz4c6hJG+25vB9jhPu+dxHoQoY57ECgDwuMP8V/jcScvYS3RJ64FrF0+m5QB9Wr6vUBQFUYA6ACvDP2c/Dfk6fqfiSZMPOwtLckc7FwzkexO0fVTXutABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAVb/8A48pvpVXR/uS/UVav/wDjym+lVdH+5L9RU9Toj/BkalFFFUc4UUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABXm3xl/wCRcsf+vwf+gNXpNebfGX/kXLH/AK/B/wCgNWGJ/hS9D08l/wB/pepr/C//AJEGw/3pf/RjV2Ncd8L/APkQbD/el/8ARjV2NVR/hx9DLM/99q/4n+YtFFFanCFFFFAGD4w8Rw+FPCt/rU2D9njzGhP35Dwq/iSM+gye1eBfA7w5N4m8c3XifUi0yWLGYyOM+ZcSZIPuRlmOOh2+tX/2g/FTX2sWXhSzYutsRPcqvO6VhhFx6hST77x6V6/8OfCq+D/BNjpjKBdMvnXZHeVsFhnvgYUH0UUAdbRRRQAUUUUAFFFFABRRRQAdq89+MH/IpQ/9fSf+gtXoXavPfjB/yKUP/X0n/oLVjiP4UvQ9LKP9+pf4kWvhT/yJEH/XWT/0Ku3riPhT/wAiRB/11k/9Crt6KH8KPoTmv+/Vf8TFooorY88KKKKACiiigAooooAKKKKACopokuIWicZVhg1LRQByUEkmjaoUfOzOGx0ZSeCPcdfzHrXVKwdQykFSMgis3WbD7VbeYi5ljyRjuO4/z7+tVtBv96m0kPzLyhPcdSPw/l9KAN6iiigAooooA8d/aC8M/wBp+EYNchTNxpkn7wjqYXIB+uG2/QE18zxSPDKksTFJEYMrDggjkY96+7NU0631fSrvTrpd1vdQvDIO+1gQce/PFfDus6XcaLrN7pdz/rrSZoXx0JUkZHscZFAH2h4K8Qp4q8H6ZrC7d9xCPNA6LIvyuMf7wOPbFdBXgf7OXiHdBqvhyV+UIvLcZ7HCyD2AOw49zXvlABRXjnizwD4+8YeKtQP/AAkjaboO8LbwiZvmXaMny0wCM55Y59qwZv2dNRt1NxY+Lg14OV32rRAntlw7Ec98GgD6BorwL4eeOPE3hnx0PA3jGaScSP5MMsz72jcjKYfqyNwBnnJHTkV77QAUV8paj4y1bw18ZdZvLd7i7aG9uo4LUyMULtuVAVB5ALA4HXGBgnNdU/wa8beMI/7R8UeJxFdTDeLZw0ojzztwCFXHouQKAPoOivNZNUX4P/Ce0i1KSO8vLbdBbpGTiaRmZlGTggAHJ9ADjPGfL9G0L4gfGN5dUv8AWXs9JLlVLFliPPIjiUgNjoSTzjkkg0AfTVFfP7fs+a7pY+0aH4x23Y5B8p7fn/eV2I/KvYfBltrVn4S0+28QymXVYlZJ5C4csQx2ncOvy456+vOaAN+iiigAooooAKKKKACiiigAooooAKKKKACql3YW14uJ4gxxww4I+h61bopNJqzBNrY5W78OTwnzLSTzADkKThh+PQ/pUdvrd9Yt5VypkA6q/Dfgep/GutqC4tYLpNk0SuPft9DWLo21g7M1VS+klcrWer2l4AqSbJD/AANwfw9fwrQrmrzw0Rl7OTI6+W5/kR/UfjVSLUdS0qTyp1YqONsmTn6H/DI9qXtZR0mg9mpaxZ2NFZNnrtpdYVm8l/7rnr9DWpkHvW0ZKWxm4tbjqKKKoQUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAV82ftD669/4p07w9AxZbKLzJFXqZZCMAjvhQpH+8a+kHdY0Z3YKqjJJ4AA618reD1b4h/HUajKC9v9re+bPaKM5jBz2yI1+lAH0d4N0FPDPhDS9HAG62gAkI6GQ8uR9WJNb1FFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAVb//AI8pvpVXR/uS/UVav/8Ajym+lVdH+5L9RU9Toj/BkalFFFUc4UUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABXm3xl/5Fyx/6/B/6A1ek15t8Zf8AkXLH/r8H/oDVhif4UvQ9PJf9/pepr/C//kQbD/el/wDRjV2Ncd8L/wDkQbD/AHpf/RjV2NVR/hx9DLM/99q/4n+YtFFFanCFZXiHWrbw54ev9YuyBDaQtIRnBY9FUe5JAHuRWrXgH7RPi3AsvClrJ6XV4AfwjU/qxH+6aAOZ+Eui3Pjv4mz+IdTHmxWcpvZ2I+VpmYmNR6DIJA6YTFfUtcJ8J/CX/CJeBbSCaPbfXf8ApV12IZgMKf8AdXAI9QT3ru6ACiiigAooooAKKKKACiiigA7V578YP+RSh/6+k/8AQWr0LtXnvxg/5FKH/r6T/wBBascR/Cl6HpZR/v1L/Ei18Kf+RIg/66yf+hV29cR8Kf8AkSIP+usn/oVdvRQ/hR9Cc1/36r/iYtFFFbHnhRRRQAUUUUAFFFFABRRRQAUUUUAFctq1o+n3q3MGVRm3KR/Cw5I+h/xrqar3dsl3bPC/RhwfQ9iKAG2N2t7arMuATww9D3FWq5TTrh9L1FoJ/lRjtcE8A9j9P6GurzmgAooooAK+Xv2gfDv9meNYNXjTEOqQgsf+mqAK3/juw+5Jr6hrzH466D/bHw5nuo03T6bKtyuOu37rj6YbJ/3aAPnr4b+ID4Z8faTqLPtg84Qzk9PLf5WJ+gOfqBX2nXwBX2j4H16XxJ8N9O1OJt129oY3J6mZAVP5sufxFAHE+Mfja9jrz+H/AAlpX9q6hG5iaRgzKZB1VUX5mwQQTkDjjI5rMj8RfHS7HmReH7eJT0VoY0x+DPn86wP2d5rFPGOpx3TKNRktcQeYfmIDZkAz1P3SR1wCegNfSEsscELyzOscaAs7sQFUDkknoAPU+lAHyX4nvPFh+JujXXiy2jtdWR7dkWPaAUEpKn5SRnIPfPFfXVfI3jrxRB4t+LkV9ZsHs4riG2t3/vqrDLD2LFiPYivrmgD5h0Gyivv2np45lDImqXUwB/vIrsp/BgD+FfT1fNXhT/k6O7/6/wC+/wDQJK+laAPnb9pO8kbVNCsc4iSGWbHqWYD+S/rXuPhjTodJ8LaVYW6hY7e1jQAd8KMn6k5J9Sa8k/aM8PzXOlaXr0CFks2aC4IBO1XwVY+gBBGfVhXdfC7xhZ+LPB1lsnQ6haQpDdwE4ZWUAbsejYyD05I6igDuaKTgCoIJ4buETW80c0RJAeNgwJBweRwcEY+ooAsUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABUU0MU8ZSVFdT1DDIqWila+4HPXnhqN8taSeWeux8lT7A9R+tZom1TR3CtuCdArfMh9ge35g+tdnTHRZFKuoZSOQRnNYyoq946GiqPZmPZeIrafCz/uXPGScqfx7fjWwrq6hlYMpGQQc5rGvPDtvMC9ufJfrgDKn8O34VkmLVNGbcpYRg5JU7kP1B6fkD6UuecPiV0PljL4WdlSVgWfiWJ8LdJ5Z/vLkqfw6j9a24po50DxOrqe6nNaxnGWxnKLW5LRRRViCiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigDivitrR0H4bazco2JpYfs0XODmQhTj3AJP4V51+zdom201nXnXl3WziJ6gABn/PKflTv2kdY2WOiaKjf6yR7qUd8KNq/nuf8q9D+E+jDRPhpotuVxLND9qkOMEmQ7hn3AIH4UAdrRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFAFW//AOPKb6VV0f7kv1FWr/8A48pvpVXR/uS/UVPU6I/wZGpRRRVHOFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAV5t8Zf8AkXLH/r8H/oDV6TXm3xl/5Fyx/wCvwf8AoDVhif4UvQ9PJf8Af6Xqa/wv/wCRBsP96X/0Y1djXHfC/wD5EGw/3pf/AEY1djVUf4cfQyzP/fav+J/mLRRRWpwlHVdSttI0u71G8k2W1rE0sjdwqjJ+p9B3NfMPgLTrn4nfFyXV9STdbRzG+uQeVCqQI48nqM7Rg9VU+ld5+0N4t+yaRa+F7aTEt7ie6APSJT8qn6sCf+Ae9dN8FfCX/CNeBYbmePbfaoRcy5GCqEfu1P0U5wehYigD0qiiigAooooAKKKKACiiigAooooAO1ee/GD/AJFKH/r6T/0Fq9C7V578YP8AkUof+vpP/QWrHEfwpeh6WUf79S/xItfCn/kSIP8ArrJ/6FXb1xHwp/5EiD/rrJ/6FXb0UP4UfQnNf9+q/wCJi0UUVseeFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAYmu2Hmxfaoxl4/vgDqPX8P5U/Q777RB9nc/vIxx6le35dPyrXIBGD0rlLyB9I1JZYchCSyE9CO6/rj6EUAdZRUFtcJcwJMh+VhkD09qnoAKq6hZQ6lpt1YXC7oLmJ4ZB6qwIP6GrVFAHwXqVjNpmqXdhcDE1rM8Lj0ZWIP6g19B/s4a15+iavojtlradbiME87XGGx7AqD/wKvOfjhov9kfE29lVdsV/Gl2oHTJBVvxLKx/GnfAzWTpfxNs4WbbFfxSWrZ6ZI3L+bKB+NAHpvjX4FjVtck1rw1qSabdyuZXhkDBBITncrLkrk84weTxjpWbD8GPG+sFbbxP42klsAQWiS5muM49n2gH3Ocehr3qigDxjXPgXHca9pFzod3b2Vhp8MUZikRmeRlkZmYsOpO7/APUABXs9FFAHlWjfCq+034tTeMn1K3e3kuLiYW4Rg4EisAMnjjdz9K9VoooArXlnb6jZTWd3Ck9tMhSSNxlWU8EEeleJ6x+z/Pbakb7whrz2DZJSKdmVo89lkTnA7AjPHJPWvdaKAPAT8GfiFqy/Ztc8cGS0P3l+1XFx/wCOttB/OvY/Cvh+Lwt4YsdEhneeO0QqJHABYlix4+pNbdFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUhAIwaWigDIvNBtLnLIPJc90HB+o6Viy6dqWlSeZAzFRzujyQR7j/EH612FFYyoxeq0LVSS0Zzdn4lxhLyP23oP5j/AA/Kt23uoLpN8MquPY9Pwqre6PaXmWaPZIed6cE/X1/GsKfRb+xfzbZmcDo0fDfiOp/DNTzVIb6oq0JbaM66lrlrTxHNEdl5HvAOCwwGH1HT+Vb1rf214uYJVYjqvcfUVpCrGREoSiW6KKK0JCiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooppIUEk4A5JNAHyz8WpZPFXxqTR4myEe30+MjsWIJ/JpCPwr6jhiS3hjhiULHGoVVHQADAH5V8t/DRT4r+Ov9qON0f2i4v29h8238mZfyr6poAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAq3/wDx5TfSquj/AHJfqKtX/wDx5TfSquj/AHJfqKnqdEf4MjUoooqjnCiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAK82+Mv8AyLlj/wBfg/8AQGr0mvNvjL/yLlj/ANfg/wDQGrDE/wAKXoenkv8Av9L1Nf4X/wDIg2H+9L/6Mauxrjvhf/yINh/vS/8Aoxq7Gqo/w4+hlmf++1f8T/MWoLq5hsrSa7uZBHBAjSSO3RVUEkn2ABNT14/8fvFv9keFotBtpMXWpk+bg8rApBP03HA9wGFanCeXaJbz/Fz4xtc3KN9ieY3EyHny7ZMBUP1G1eO7E19XgBQAOAOgAryj4D+Ev7D8HHWbmPbeaqRIuRysAyEH45LZHUFfSvWaACiuM8e/EXSfAVgr3YNxfTAm3s42wzgcbmJB2r2zg57A4OPJY/Hvxh8Vxm/0HTGtrI5KGCzUqw9mlB3HscfkKAPo2ivnnwt8cdc0vX10jxxbAJvEcs5h8ma3Y93UYBUcE4AOCSM8A/QasrqGUggjIIOQRQA+iiigAooooAKKKKADtXnvxg/5FKH/AK+k/wDQWr0LtXnvxg/5FKH/AK+k/wDQWrHEfwpeh6WUf79S/wASLXwp/wCRIg/66yf+hV29cR8Kf+RIg/66yf8AoVdvRQ/hR9Cc1/36r/iYtFFFbHnhRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABVPULNb21aI43DlD6GrlFAHMaLeNaXTWs2VV2xg/wsOOfrjB98V09c/r9jgi8iHoJAB+AP9D+FXtIv/tlqA5/fR4DZ7jsfxoA0qKKKAPBv2k9I3WOh6yi48uSS1kPruG5f/QX/OvCdF1J9H13T9TjyXtLmOcD12sDj9K+r/jRpY1P4W6ttXdJbBLlPbaw3H/vktXyBQB99RSpPEksbBo3UMrDoQRkGpa5P4aan/bHw30C73bmFosLEnktH8hJ/FTXWUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQBSu9Ntb0HzYhuxww4YfjWDdeH7m3bzLRzIAcgZww/x/SurorKdKMi4zlHY5K2168s38q6QyAcEMCGH445/H863rTVbS9AEUgDn+BuD/APX/AAqa5sre8TbPEr+hI5H0PUVgXnhp1y9nJuHUI/BH0P8An61FqkNtUVeEt9GdPRXIQ6tqOmyCK4VnH92QEH8D6e/IrbstatLvAL+VIf4X4z9D0NXGtF6bEypyWpq0UUVqQFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAVz3jjUv7J8Ca7fK214rKXYfRypC/qRXQ15p8db/7F8Lb2IHBu54oAf8AgQc/ohoA4D9mzTQ+ra7qhHMMEdup/wB9ixA/79r+dfRVeQfs7WH2fwFd3jDDXV8xB9VVVA/XdXr9ABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFAFW//wCPKb6VV0f7kv1FWr//AI8pfpVXR/uS/UVPU6I/wZGpRRRVHOFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAV5t8Zf+Rcsf+vwf+gNXpNebfGX/AJFyx/6/B/6A1YYn+FL0PTyX/f6Xqa/wv/5EGw/3pf8A0Y1djXHfC/8A5EGw/wB6X/0Y1djVUf4cfQyzP/fav+J/mMkkSKNpJGCooLFicAAck5r5RuXn+L/xlCIXNjLNsQ8jy7SPJJ9iRk/7zYr2D45eLf8AhH/BLabBJtvdWJgXB5WIDMh/EEL/AMCPpWT+z94T/s3w9ceJLiPFxqJ8uAkcrCp5I9NzA5Hoikda1OE9ighitoI4IUWOKNQiIowFUDAAHoBiqet6va6Bol5qt6xW3tImlfB5IA4Az3JwB6kitKvGP2itday8JWGjxsVbULgvIB3jjAJB/wCBMh/CgDhPAOj3Xxa+JV3rmvDzbK3ImuIyflOSRHCP9ng/UKe5zX07HGsUaxxoERQFCqMAAcYA9PavA/hB468EeDvBpg1LWBBqVzO8s8f2WZioB2qNyoQRgZ4P8R75r0H/AIXb8PP+hh/8krj/AON0Aed/tIaRbx3Gi6xGgWeYSW8zAfeCgFc/TLc+49K9Q+FGpSat8MNCuZTmRYDCSTkkRsyDP4KK8b+N/jzw94vsNHg0HUPtnkSSvN+5kj25ChfvqM556Z6dq9b+DNu1t8J9DVhhmWWQ/RpXI/QigDvaKKKACiiigAooooAO1ee/GD/kUof+vpP/AEFq9C7V578YP+RSh/6+k/8AQWrHEfwpeh6WUf79S/xItfCn/kSIP+usn/oVdvXEfCn/AJEiD/rrJ/6FXb0UP4UfQnNf9+q/4mLWH4m8V6N4R0w6hrN2sEWcRp1eVv7qr1J/QdyBzWrd3UNjZz3dzII4II2kkc9FVQSSfoAa+R7681n4x/EmOGNmRZ5CkCNytrbjJyRnkgAk4xk8DGQBseedvrH7R1/LcGPQNDgjjzhHvWaRmHrtUgA+2T9az/8AhevxAtR59xo9l5PXMlnKq4+u8V7j4U8CaB4Oskh0uxjE4XD3UihppD3JbGQD6DAHYV0xAIwaAPFPDH7Q+lX8yW/iHT305mwPtMLGWLPqwwGUfTd+Fe0RyJLGkiMGRwGUjoQehrgvGfwj8OeLbeSSO1j0/UyCUu7dAoLf7ajAYe/X3ruLKBrawtrdyC0USoSOhIAFAFmiiigAooooAKKKKACiiigAooooAY8ayIyOAVYEEHuDXKkSaLquRkpnj/bUnp9R/MV1tZ+rWP221woHmpyp9fUfjQBdjkWWNZEIKsMgj0p9c5oN8Uf7HKSATmPPY+n49fz9a6OgChrWnrq2h3+nPjbd20kBz6MpX+tfCToyOUYEMDgg9c19+V8QeONP/svx3rtkFwkV9LsH+yWJX9CKAPoL9njUTdfD+4s2bLWd86qPRWVWH6lq9dr55/Zrv9t9r+nE/wCsjinUHttLKf8A0Jfyr6GoAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKAIZreK4TZLGrr6MM1h3nhpWy1pJtP8Acfkfgeo/HNdFSVEqcZblRnKOxxyXWp6OwSUNszgLIMqfoQf5fiK2bPxBaXGFl/cOePm5Un6/44rVdElQo6qynqCM1i3nhyCbL2zGF+u05Kk/zH+eKy5Jw+F3RfNCXxKxuKwYZUgj1FLXG41TRW43CPP+8h/wJ/A1q2fiOGXC3K+Ux43DlSf5j/PNVGstpaMTpvdao3qKjSRJUDxsrqehU5BqStUzMKKKKYBRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFeIftJXuzw5olhn/XXbzY9diY/9qfrXt9fOX7Sl0X1zQbPr5VtLLj/eYD/2SgD1L4PWP2H4V6GhGGkjeYn13uzD9CPyru6w/B1p9h8E6FakcxafAh9yI1z+tblABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUARyNsRmxnAzgd6z/7YT/nm36Vp9RXOX0Pk3LL0BOR+P+cUnpsdGHhCbtIt3GppNA8flsNwx2qGyvEtFcFWbce2Kp0VN3udqoQUeXoa/wDbEf8Azzb9Kt2twLmMuFKjJxnvXPKpdwqjJPAH6V0sEQhhWNeiiqi2zkxFOFNJLclooopnKFFFFABRRRQAUUUUAFFFFABRRRQAUVHKcQyEHBCkg+nFfH+jeKviR4hvWs9I1rWby5VDIY4rhiQoIBPJ9SPzoA+xKK+WPsvxu/veI/8Av8f8aPsvxu/veI/+/wAf8aAPqevNvjL/AMi5Y/8AX4P/AEBq8h+y/G7+94j/AO/x/wAajnh8fxRg+LjqhtCf3X2yQsu/Hbk84z+tYYn+FI9TJV/t9L1Pefhf/wAiDYf70v8A6Mauxrjvhf8A8iDYf70v/oxqzvjF4t/4RbwLcLBJtvtQzawYOCoI+dvwXOD2JFVR/hx9EY5n/vtX/E/zPEfFt/L8VPjBFYWc3+htOLK2cHIWJSSzj1z8zD1GBX1PYWVvpun29jaRiO3t4liiQdFVQAB+QFfImh/DHxJrXg1vFGlReYsczCO3UkSuq4y6djhsjAOSV4B4r0X4YfGmZbiHw/4vmJJIjh1CXhlPQLLnr6bjyD1zyRqcJ9AV8xftGXrTeObC0BylvYK2PRmdif0C19OcEV8u/tD2zwfEO3nI+SfT4yp7ZDOCP0H50Ad3pn7PnhW50q0nubzVhPJAjyBJowoYqM4BjJxn3NW/+GdPB3/P7rP/AH/j/wDjden6RdRXui2F1CwMU1vHIhHOQVBGPzpmt6xZaBo13q1/J5draxmRz646AepJIAHckCgD5I+JXhfSvC/jY6DoT3VwI44xIJ2Vm81udo2qBjaV7ZyTzX1p4d0saJ4b0zSxg/ZLWOAkdCVUAn8SCfxr5x+F+j3fxC+Kdz4m1CPNtbXBvZupXzCSY4wT2BAP0THcV9RUAFFFFABRRXx7YeK/iLrmsS2Gka3rF1cAswhiuGJ2g8kDI4FAH2FRXyx9l+N397xH/wB/j/jR9l+N397xH/3+P+NAH1P2rz34wf8AIpQ/9fSf+gtXjX2X43f3vEf/AH+P+NMmg+IccQPis6sbHPy/bJCyb+cY5POM1jiP4Uj0snX+3UvVHuXwp/5EiD/rrJ/6FXb1xHwp/wCRIg/66yf+hV29FD+FH0JzX/fqv+JnBfGbUH0/4V6y0TYeZY4AR6M6hh+K7hXmn7NmnRyapr2pso8yCGKBCfRyzN/6LWvQvjlbtP8ACrUmUf6qSGQ/TzFH9a4f9mm5Qf8ACR2pIDn7PIo7kDeD+WR+dbHnnv8ARRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAczrlmbe4F3DkKzZJHG1hzn8f5g+tbGm3ovrUSdJBw4HrVi4hS4haGQZVgQa5i2lk0bVCkh+TOHwOqnoR9Ov5igDra+RvjhZ/ZfirqbgYW4SGUAD/pmqn9VNfW6sGUMpyCMgjvXzP8AtG2gi8babdjgT6eEPuVdufyYflQBn/s/Xn2b4l+Vn/j6spYh7kFX/wDZK+qq+NvhHdGz+KmgSf3p2j/77Rl/9mr7JoAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAaQGGCAQexrIvNAtLjLRDyH65X7ufp/hitilqZRjLdDUmnocbJZ6no7mSIts67oySp+o7fjx71fs/EynC3ke3/AKaJyPxHUfhmuirMvNFs7vLbPLkP8ScZ+o6GsfZSjrBmnPGWkkXYLiG5QPFIrr6g5qeuQm0jUNNkMtszOB/FHwfxH+Gfep7TxJImEu492DgugwR9RTVa2k9GDp9Yu509LVa1vbe8TdBKrY6jPI+oqzWyaeqMmmtwooopgFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFfLn7QcrXXxKtrdOTHYRRge5dz/AOzCvqOvlj4rf6b8eRa9cTWcOPqqH/2agD6ighW3t4oV+7GgUfQDFS0UUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAnes7Vod8AkA5Tr9DWlTHVZEZG5BGKRUJOMlJHL0U6WMxStGf4Tim1B7Caaui9pUO+58wjhP5n/P8q3Kq2EPkWqg/ePLfWrVWtEeVWnzzbFooopmQUUUUAFFFFABRRRQAUUUUAFFFFAEc/8Ax7yf7p/lXy/+zr/yUa6/7Bkv/oyOvqCf/j3k/wB0/wAq+YP2df8Ako11/wBg2X/0ZHQB9R0UUUAFebfGX/kXLH/r8H/oDV6TXm3xl/5Fyx/6/B/6A1YYn+FL0PTyX/f6XqbHwv8A+RBsP96X/wBGNXg/xM1a6+I3xVh0PTH8yCCUWFtjld2f3kn0znkcFUBr0U+LB4Q+BK3sb7b2Yy29pzg+YzuNw/3QC34Ad6539njwp5t1e+K7pMrFm2tCw/jODIw+gIUHvuYdqqj/AA4+iMsz/wB9q/4n+Z7roulWug6LZ6VZrtt7SJYkz1OBjJ9z1PuTXlHxi+FUetWs/iTQbcDU4gXureMf8fKgZLAD+Mdf9r3OM+0UVqcJ4b8DfiS+oxL4T1ebdcxJ/oE0hyZEHWMk91HI9gRxgZ6j4wfD+bxtoEM2nBTqtgWaFGOBKjY3JnoDwCCeMjHGSR5R8YvCk3gjxpa+JNG3W9tdzefG0YwILhSCQO2CfmA/3gBgV9AeDPEsHi7wnYa1DhWnTEsYP3JBwy/gQceowe9AHz34a+K3iz4eWC6BqejGaKA7YYrxXikiGfug91yeAR3wDjAF26T4ifGi8ghnszpuiRuHyY2jgX/a+Y5kbHQDgZ7Ak19MUUAYHhLwrp3g7QINI01D5aZaSRh80rnGWb3OAPYADtW/RRQAUUUUAFfLHwK/5K1J/wBe0/8AMV9T18sfAr/krUn/AF7T/wAxQB9T0UUUAHavPfjB/wAilD/19J/6C1ehV578YP8AkUof+vpP/QWrHEfwpeh6WUf79S/xItfCn/kSIP8ArrJ/6FXb1xHwp/5EiD/rrJ/6FXb0UP4UfQnNf9+q/wCJmZ4g0eLxB4e1DSJyBHd27wlsZ2kjAYD1BwR9K+VvAWvXHwy+JLR6tG8USs1lfoMnauRhgO4BAYEdRnHWvr2vN/iV8J7Hx0v261kSy1pF2rOQSkw7LIB+QYcgdiAANjzz0G3uIbu3juLaVJoJVDJJGwZWB5BBHBFT18sWln8Wvhq7W1lbX5sw2dkEX2q3IzkkAAhc9/un1q+fix8VrsfZ7fSGEp4Bh0t2f8jkfpQB9D6vrOn6Bps2o6rdx2tpFy0khwPYAdST2A5J6CrkEyXNvHPGcpIoZc+hGR/Ovmq1+GvxH+IeoR3fim6ntLcHPmXrDcoPXZCpG0+xCj3r6TtoBa2kMAO4RIqAnuAAKAJ6KKKACiiigAooooAKKKKACiiigAooooAKydbsPtVv5sYzLGD07r3H9R+PrWtRQBhaDf74/skjZdBlCepHp+H8vpXjf7S9viTw3cgdRcRsfp5ZH8zXq+qWr6dfLcwcIx3KQOFPUj+oHpn0rzP9oWRL7wloV4n8N26MO4JTOP0/lQB4p4JuPsnjvw/cE4Eeo25P08xc/pmvuGvgzS5fI1aymzjy50fP0YH+lfedABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFULzS7W95liG/H314P8An61foqXFS3BNrY5K50G8tW821cyY5G0lWH68/nS23iG6tm8q7QyAHBJG1h9e38q6uq11YW14uJ4gx7N3H0NYuk1rB2NVUT0kiO01O1vRiKUbu6Nww/Crtcvd+G5osyWcm8DkKxAYfQ9P5VDBrN/p7iK5VpAP4ZMhvwOOfxzQqri7TQOmn8LOvpKzrPWLS8wqvskPGx+D+HrWjW0ZJ7GbTT1FoooqhBRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAV8seMP9J/aWjX+9q1in5CIf0r6nr5Y1v5/wBpmL/sNWv6FP8ACgD6nooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigBKKY7rGhdyAo5JqD+0bb/nqP1oGoyeyKOrwYkWYdDwfr/wDqzVSxg8+6Vf4Qcn8P84rSurq0nt2TzVyRxwetV9Nlt7eNmeRQ57e1S0mzthOSpNW1Nmiqv9oWv/PYfkalinimBMbhgODVXONwkldoloqCW6hhbbI4BxnFIl5BK4VJAWPQUC5JWvYs0UVDNPHAoMjBQTjJoEk2yWlqoNQtv+eo/WrXWgbi1ugoprusalmICgZzVf8AtG2/56j9aAUW9kWqWo45FlQOhyp6EU/tQLyYUZqqb+2ViDIMjqPSpYriOcExuGx1oG4SSu0On/495P8AdP8AKvmD9nb/AJKLdf8AYNl/9GR19PT/APHvJ/un+VfN37P+l3tr4nn1uaBl017KSBJ8jBk3oduM56A9u1AJN7H0rzS1Wiu4JX2I+W9KsdqAaa0YV5v8ZP8AkXLH/r8H/oDV6HLPHAAZGC5rz/4owS6t4ftksE85orjzHAwMKFbnnHfFY4hXpSXkelk/u42lJ7XPn7xHqN/4iudD8L2iMwtiYoYx/HNK5JP5FBz0wT3r6u8L6Bb+GPDWn6NbYMdrEFLD+NurMfcsSfxr57+HcmgaX8QLnXPEF/FbLaRAWqOrNukYYLcA8KMjnuwI6V7V/wALU8E/9B6D/v2//wATXXh8FiZUouNOTVuzMMznH65V1+0/zOyoxXG/8LU8E/8AQeg/79v/APE0v/C1PBP/AEHoP+/b/wDxNbfUMX/z6l/4C/8AI4eePck+JPhtPFPgPU9PCBrhYjPbcZIlTJUD0zyv0Y15R+zj4gZbrVfDsjHY6C8hBPAIIV/xIKfka9T/AOFqeCf+g9B/37f/AOJr598FapYeGfjH/aAuAmiC5uYxMAcGFg4Q4xnGdp6dqay/F/8APqX3MOePc+s8UYrjv+FqeCf+g9B/37f/AOJo/wCFqeCf+g9B/wB+3/8AiaX1DF/8+pf+Av8AyDnj3OxxRiuO/wCFqeCf+g9B/wB+3/8AiaP+FqeCf+g9B/37f/4mj6hi/wDn1L/wF/5Bzx7nY4oxXHf8LU8E/wDQeg/79v8A/E0f8LU8E/8AQeg/79v/APE0fUMX/wA+pf8AgL/yDnj3OxzXyz8Cv+Ssyf8AXtP/ADFe6f8AC1PBP/Qeg/79v/8AE18//CTVrHw98RH1LVbhba0MMq+awJGWIxwAT2o/s/F/8+pfcw549z6yxRiuO/4Wp4J/6D0H/ft//iaP+FqeCf8AoPQf9+3/APiaPqGL/wCfUv8AwF/5Bzx7nY1598YP+RTh/wCvtP8A0Fqv/wDC1PBP/Qeg/wC/b/8AxNch8RPGvh3xF4fitNK1OO6nW4VyiowIXB5yQB3Fc+KwWJhRlKVOSVuqZ6WTyi8dS16o6r4U/wDIkQf9dZP/AEKu3+leWfD7xboOj+E4rS/1GOCdZHJQqxIBOQeBjmur/wCFh+FP+gxF/wB8P/hXHRqQVNJsyzatTWOq3kviZ1FLXLf8LD8Kf9BiL/vh/wDCj/hYfhT/AKDEX/fD/wCFa+1p/wAyPP8Ab0v5kdTRXLf8LD8Kf9BiL/vh/wDCj/hYfhT/AKDEX/fD/wCFHtaf8yD29L+ZHU0Vy3/Cw/Cn/QYi/wC+H/wo/wCFh+FP+gxF/wB8P/hR7Wn/ADIPb0v5kdTRXLf8LD8Kf9BiL/vh/wDCj/hYfhT/AKDEX/fD/wCFHtaf8yD29L+ZHU0Vy3/Cw/Cn/QYi/wC+H/wo/wCFh+FP+gxF/wB8P/hR7Wn/ADIPb0v5kdTRXLf8LD8Kf9BiL/vh/wDCj/hYfhT/AKDEX/fD/wCFHtaf8yD29L+ZHU0Vy3/Cw/Cn/QYi/wC+H/wo/wCFh+FP+gxF/wB8P/hR7Wn/ADIPb0v5kdTRXLf8LD8Kf9BiL/vh/wDCj/hYfhT/AKDEX/fD/wCFHtaf8yD29L+ZHU0Vy3/Cw/Cn/QYi/wC+H/wo/wCFh+FP+gxF/wB8P/hR7Wn/ADIPb0v5kdTSVy//AAsPwp/0GIv++H/wo/4WH4U/6DEX/fD/AOFHtaf8yD29L+ZHQXlsl5bPC/fofQ+tePfE/wAN3et+FJ7KAE3NnMLlIwP9YVVgVHuQxIx1IA716D/wsPwp/wBBiL/vh/8ACsTXPGnhid4pYNSR5GbY21GxjBIJ46ZGMjnn2o9rT/mD29L+ZHyMMq2RkEV98xPviR/7yg/nXyd4z8GPfa0+o+GoxdWV0S8iodvlSZ+YYbHB6jHTJHAxX0xa+IdKSzhD3ahxGoYYPXA9q0Suro6Y0ak4qUYto3aKyf8AhJNI/wCfxf8Avk/4Uf8ACSaR/wA/i/8AfJ/wp8r7FfVq38j+5mtRWT/wkmkf8/i/98n/AAo/4STSP+fxf++T/hRZ9g+rVv5H9zNaisn/AISTSP8An8X/AL5P+FH/AAkmkf8AP4v/AHyf8KLPsH1at/I/uZrUVk/8JJpH/P4v/fJ/wo/4STSP+fxf++T/AIUWfYPq1b+R/czWorJ/4STSP+fxf++T/hR/wkmkf8/i/wDfJ/wos+wfVq38j+5mtRWT/wAJJpH/AD+L/wB8n/Cj/hJNI/5/F/75P+FFn2D6tW/kf3M1qKyf+Ek0j/n8X/vk/wCFH/CSaR/z+L/3yf8ACiz7B9WrfyP7ma1FZP8Awkmkf8/i/wDfJ/wo/wCEk0j/AJ/F/wC+T/hRZ9g+rVv5H9zNaisn/hJNI/5/F/75P+FH/CSaR/z+L/3yf8KLPsH1at/I/uZrUVk/8JJpH/P4v/fJ/wAKP+Ek0j/n8X/vk/4UWfYPq1b+R/czWorJ/wCEk0j/AJ/F/wC+T/hR/wAJJpH/AD+L/wB8n/Ciz7B9WrfyP7ma1FZP/CSaR/z+L/3yf8KP+Ek0j/n8X/vk/wCFFn2D6tW/kf3M1qKyf+Ek0j/n8X/vk/4Uf8JJpH/P4v8A3yf8KLPsH1at/I/uZrUVk/8ACSaR/wA/i/8AfJ/wo/4STSP+fxf++T/hRZ9g+rVv5H9zNaisn/hJNI/5/F/75P8AhR/wkmkf8/i/98n/AAos+wfVq38j+5mtRWT/AMJJpH/P4v8A3yf8KP8AhJNI/wCfxf8Avk/4UWfYPq1b+R/czWorJ/4STSP+fxf++T/hR/wkmkf8/i/98n/Ciz7B9WrfyP7ma1FZP/CSaR/z+L/3yf8ACj/hJNI/5/F/75P+FFn2D6tW/kf3M1qKyf8AhJNI/wCfxf8Avk/4Uf8ACSaR/wA/i/8AfJ/wos+wfVq38j+5mtRWT/wkmkf8/i/98n/Cj/hJNI/5/F/75P8AhRZ9g+rVv5H9zNaisn/hJNI/5/F/75P+FH/CSaR/z+L/AN8n/Ciz7B9WrfyP7ma1FZP/AAkmkf8AP4v/AHyf8KP+Ek0j/n8X/vk/4UWfYPq1b+R/czWorJ/4STSP+fxf++T/AIUf8JJpH/P4v/fJ/wAKLPsH1at/I/uZrUVk/wDCSaR/z+L/AN8n/Cj/AISTSP8An8X/AL5P+FFn2D6tW/kf3M1qKyf+Ek0j/n8X/vk/4Uf8JJpP/P4v/fJ/wo5X2D6tW/kf3M1ahntYblNk0auvuKz/APhJNI/5/F/75NH/AAkmkf8AP4v/AHyaTjfRoFh6y2g/uZRvfDQ5ezk9/Lf+h/x/OqcV/qWkuIpVYoONsmSPwPp9CfpW3/wkmk/8/i/98n/Co5df0SZCklzEynqGUkH9KxeHe8dDVU620oNr0H2ev2lzgOTDIeznj8+laoORkdK4y8/sOTLWt+sbHnawJU/1FV7PVp7N9tvcK6A8oTlSPYdRn8KXNUh8aE8LO10mvkd7RWJYa/DdOsUqGOVsAYGVJ7f5/WtqtYyUldHNKLi7MWiiiqEFFFFABRRRQAUUUUAFFFFABRRRQAV8saz8n7TMf/Yatv1KV9T18seKf9G/aXiJ6DWLJvz8o/1oA+p6KKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAiniE0LR5wGGMiqH9jp/z1b8hWpSUblxqSh8Jmf2On/PVvyo/sdP8Anq35Vp0UrIv29TuZn9jp/wA9W/IVatLRbRWCsWyc81apKEiJVZyVmyldael1KJC5BxjAptvpiwTLIHYlc8H3GKv0tFkHtJ8vLfQSq13ardIELEYOeKs0UyU2ndGYNHQY/et+QrT6CiijYc5yn8TI5oxLE0eSAwIzVD+x0/56t+QrUpKQ41JQ+Eit4RBCsYOQvc1LS0lMhtt3ZmvpKM7N5rZJJwAO9WLSzW1DBWLZ9e1WqyvEGt2fhvQbzV79ytvaxl2x1Y8AKM9ySAPcikW6s5KzehY1HU7HSbF7vUrqC1tV+9LPIEUe2T3PpXldx8VPhvpJNtpskiwgk+Xp9j5cYJ6kAhRn3Aryhp/FHxr8bCDzNsYy6xlj5NnF0Jx3PIGerEjoOnsuj/ATwbYWqpqENzqc+PmklmaMZ74VCMD2JP1psUZOLuh+h/FrwHd3aj+2JbSQ/Kou4WjU/VgCoH1Ir0qGeK5hSaCVJYnAZJI2DKwPcEcH8K8k8Sfs/eHb60kbQZJtMvACY1eRpYWPo27LDJ4yCcdcHpXmXgnxrrfwr8WS6JrKyjTkm8q8tGJbyicfvY+2cEHjhh+BCQSk5O8j6lu7RbpVDMVCnPFcf42nPh/RVmjUTGeTyCH4ABVjkY78V2kMsdxBHPE4eKRQyOpyGU8gg/TFYfizw3/wk+nRWn2v7N5cwl3+XvzgEYxkev6VUeXmXNsZVqtZUnGi7M8A8K+FtK8ZeMdR0i7vprK4iiSWARqpEgAAYc9CMggDtnpiu9/4Z+0z/oOXn/fpa808YWepfDD4rWepRyecE8u5hlC7RKmNrqRk4yAynnOCD3FfUWnX1vqmm21/aSb7e5iWWJvVWGR9ODXqRzrG04qFOo1Fbbf5GVKn7i59X19Tyj/hn3TP+g5ef9+lo/4Z90z/AKDl5/36WvZKKr+3sx/5+v8AD/I09lDseN/8M+6Z/wBBy8/79LR/wz7pn/QcvP8Av0teyUUf29mP/P1/h/kHsodjxv8A4Z90z/oOXn/fpaP+GfdM/wCg5ef9+lr2Sij+3sx/5+v8P8g9lDseN/8ADPumf9By8/79LR/wz7pn/QcvP+/S17JRR/b2Y/8AP1/h/kHsodjxv/hn3TP+g5ef9+lo/wCGfdM/6Dl5/wB+lr2Sij+3sx/5+v8AD/IPZQ7Hjf8Awz7pn/QcvP8Av0tH/DPumf8AQcvP+/S17JRR/b2Y/wDP1/h/kHsodjxv/hn3TP8AoOXn/fpaP+GfdM/6Dl5/36WvZKKP7ezH/n6/w/yD2UOx43/wz7pn/QcvP+/S1keIPg7ZeHdPS9g1i6dzKse0oo6gn69q957VyfxD/wCRcj/6+V/9BaonnWPqRcZ1Lp9NP8iowUXdaHD+HvhdZ61pCXr6jPGzMy7VRexxWr/wpjT/APoLXX/fta6nwF/yK0P/AF0f+ddPXh/VaXYwlhKMm5SV2zzD/hS9h/0Frn/v2tH/AApew/6C1z/37WvT6KPqtHsL6lQ/lPMP+FL2H/QWuf8Av2tH/Cl7D/oLXP8A37WvT/wozR9Vo9g+pUP5TzD/AIUvYf8AQWuf+/a0f8KXsP8AoLXP/fta9Poo+q0ewvqVD+U8w/4UvYf9Ba5/79rR/wAKXsP+gtc/9+1r0+ij6rR7B9SofynmH/Cl7D/oLXP/AH7Wj/hS9h/0Frn/AL9rXp9H4UfVaPYPqVD+U8w/4UvYf9Ba5/79rR/wpew/6C1z/wB+1r0+jNH1Wj2H9SofynmH/Cl7D/oLXP8A37Wj/hS9h/0Frn/v2ten0UfVaPYPqVD+U8v/AOFL6f8A9Ba5/wC/a0f8KX0//oLXP/fta67xrqF3pXhG/vbCQxXUYTY4UNjLqOhBHQkVQ+HWsalrnht7rU5zNOLhkDFFX5QFwMKAO55xWfsaKnycpl9Xw6qez5TB/wCFL2H/AEFrn/v2tH/Cl7D/AKC1z/37WvT6K0+q0exr9SofynmH/Cl7D/oLXP8A37Wj/hS9h/0Frn/v2ten/hRR9Vo9g+pUP5TzD/hS9h/0Frn/AL9rR/wpew/6C1z/AN+1r0/8Ka7hEZz0UE0fVaPYPqVD+U+bfhRrEniPxHJ4fljWKIRyTiVSSwIKjGDxjmvaP+EIgz/x9y4/3RXhH7PSGT4kTv3TTpW/8fjH9a+o+9dMXyx5Y7Hp0sXWpQUISskcp/wg9v8A8/kv/fIo/wCEHt/+fyX/AL5FWvFnjHSfBenw32sPKsE0vkr5UZY7sE9PTANcj/wv3wN/z3vv/AU/40+eRp/aGJ/nOk/4Qe3/AOfyX/vkUf8ACD2//P5L/wB8isCH47+A5WAe/uYR6vauR/46DXVaJ448MeI2VNJ1uzuZWGREH2yH/gDYb9KOeQf2hif5yp/wg9v/AM/kv/fIo/4Qe3/5/Jf++RXV0Uc8hf2jif5zlP8AhB7f/n8l/wC+RR/wg9v/AM/kv/fIrq6KOeQf2jif5zlP+EHt/wDn8l/75FH/AAg9v/z+S/8AfIrq6KOeQf2jif5zlP8AhB7f/n8l/wC+RR/wg9v/AM/kv/fIrq6KOeQf2jif5zlP+EHt/wDn8l/75FH/AAg9v/z+S/8AfIrq6KOeQf2jif5zlP8AhB7f/n8l/wC+RR/wg9v/AM/kv/fIrq6KOeQf2jif5zlP+EHt/wDn8l/75FH/AAg9v/z+S/8AfIrq6KOeQf2jif5zlP8AhB7f/n8l/wC+RR/wg9v/AM/kv/fIrq6KOeQf2jif5zlP+EHt/wDn8l/75FH/AAg9v/z+S/8AfIrq6KOeQf2jif5zlP8AhB7f/n8l/wC+RR/wg9v/AM/kv/fIrq6KOeQf2jif5zlP+EHt/wDn8l/75FH/AAg9v/z+S/8AfIrq6KOeQf2jif5zlP8AhB7f/n8l/wC+RR/wg9v/AM/kv/fIrq6KOeQf2jif5zlP+EHt/wDn8l/75FH/AAg9v/z+S/8AfIrq6KOeQf2jif5zlP8AhB7f/n8l/wC+RR/wg9v/AM/kv/fIrq6KOeQf2jif5zlP+EHt/wDn8l/75FH/AAg9v/z+S/8AfIrq6KOeQf2jif5zlP8AhB7f/n8l/wC+RR/wg9v/AM/kv/fIrq6KOeQf2jif5zlP+EHt/wDn8l/75FH/AAg9v/z+S/8AfIrq6KOeQf2jif5zlP8AhB7f/n8l/wC+RR/wg9v/AM/kv/fIrq6KOeQf2jif5zlP+EHt/wDn8l/75FH/AAg9v/z+S/8AfIrq6KOeQf2jif5zlP8AhB7f/n8l/wC+RR/wg9v/AM/kv/fIrq6KOeQf2jif5zlP+EHt/wDn8l/75FH/AAg9v/z+S/8AfIrq6KOeQf2jif5zlP8AhB7f/n8l/wC+RR/wg9v/AM/kv/fIrq6KOeQf2jif5zlP+EHt/wDn8l/75FH/AAg9v/z+S/8AfIrq6KOeQf2jif5zlP8AhB7f/n8l/wC+RR/wg9v/AM/kv/fIrq6KOeQf2jif5zlP+EHt/wDn8l/75FH/AAg9v/z+S/8AfIrq6KOeQf2jif5zlP8AhB7f/n8l/wC+RSjwRAMEXkoPqFFdVRRzMHmGJf2jyPxy134emtrW1vJQZULmRfldcHoCCMA//W7mvTNHd30axkkZndoELMxySdoyc1g+LfBZ8UXdvOL/AOzeShXb5O/OTnOdwxXSWVt9ksLe237zDGse7GM4GM4/Cm+RRXLueRBVpYmc6mz2LdFFFQdYUUVheKfFWm+D9IGqas0i2xlWLMaFjuIJHH4GgDdory//AIX74G/5733/AICn/Gj/AIX74G/5733/AICn/GgD1CivL/8Ahfvgb/nvff8AgKf8a9Is7mO9soLqEkxTRrIhIx8rDI4+hoAsUUUUAFFFFABXyx8TP9D/AGghcnp9qspQfYLGP/Za+p6+Wfj2rWPxThuQOXs4Jh74Zh/7LQB9TUUxGV0V1OVYAg+oNPoAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACvC/wBo/WpIdJ0fRY2wtzLJcSgHqEAC59RlifqB6V7pXzb+0kGHifRj/CbNgPrvOf6UAd18AdAi03wCNVKD7RqczOWxyEQlFXPpkMf+BV6xXF/CYofhZ4fKdPs5B+u5s/rmu0oAK+fP2jtAijl0nxBFGFklLWk5AxuwNyEnucbx9APSvoOvH/2jCv8Awr6wB+9/ake3/v1LQBsfBDWn1j4Z2aSuWksJXsyT6LhlH4Kyj8K9Hrxr9nAN/wAITqbH7h1EgfURpn+Yru/HOv3fh3SILmzWJpHnEZEqkjBVj2I54FNRcnZGdWpGlBzlsjnPjd4THiPwQ97Am690vNxHgctHgeYv5AN/wEDvWF+z54t+36Jc+GrmTM9h++twTyYWPzAf7rH/AMfA7V6X4W1ObXfDNve3iR+ZNvDqikLgMV6EnsK4rwd8Grfwp4zm1+PVZfLSWT7JaRIAojbICyMclsA9AByAcnpQ1Z2HTmpxUlsz1WiiikWJTWYKpLEBR1Jp1eR/HLxPPpmj2uiWkpje/wBzTspwfKXA2+wYn8lI7104LCSxdeNCG7JlLlVzV134z+F9HuXt4GuNRlUkMbVQUBH+0SAfqMisy0+Pnh+WUJdabqFuhON4CuB7kAg/kDVr4cfDLSNM0K01DVbGK81K5jEp89Q6whhkKqngEDGTjOc4OK7W+8J+H9RgMV3otjKhGOYFBH0IGR+FelVlldGbpKEpW+1e33Ihe0Ze0zUrXWNNg1Cxl8y2uE3xvtK5H0IBH5VleJ/GeieEbdZNVu9kj5McCDdJJj0Udvc4FaFlZWPh3RFtrZTDZWcR2gsW2qMnqSSce5r588J6bL8VPiNd3+rs7WaZnljDYwmQEiBHQeuOSAecnNY4HA0a7qVqjapQ1832Q5yasludv/wv/RPOx/ZGo+X/AHvk3flu/rXdeF/Guh+L4HbS7omVBmSCRdsiDPUjuPcZFWv+EU8Piy+xjRNP+zYx5f2ZMfyrwTxpo8nww8f2WpaKWjtZf38CFicAHDxE9SvI/Bu5Ga6qGGwOPbpUE4Ttpd3Tt08iW5Q1ex9K1wXif4s+G/DN5JYu817eRkrJHaqGEZ9GYkDPqASR3FdRdX73HhiXUNP+Z5LNpoPclNy/0rwn4L2Hh/VNa1BtaW3ub/CG1jusNuyW3sA3DNkL1GRnI6mubL8FSnSq1692oW0W7v8AoVOTTSR1kX7QGiGTE2kagieqFGP5Ej+deg+F/Fel+L9Na+0t5THG/lyLIhRlbAOD2PBHQkVam8P6LcReVNpNjJHj7r26Eflim6L4e0vw9FPFpNmlrHPJ5rxoTt3YAyATgcAcCscTVwU4fuabjL1uhxUk9Wa9ct46tbi70BI7eCWZxOpKxoWOMMM4H1rqaK88s5zwVbz2vhuOK4hkikEjErIpU4J9DXR0UUAc74o8V2nhWG3mvba6ljnYoGgVSFIGcHLDrzjHoa09L1KDVtMt7+2J8mdA65HIB7H3HQ+4NZHjjRRrvhK8tkXdPGvnQ4GTvXkAe5GR+Ncv8H9Z+0aTdaRI2XtX8yME/wADdQB7Nk/8CFc7qSjVUHszmdWUa6g9nsem1yVx490y38Ur4fS3u5rsyrEWiRSgYgHklhwM88cYPpW/quoxaXpdzfTfcgiaQjucDp9TXlPws0+XV/Et/wCILsBmjLYYjrK+SSPoCQR/tUVaklOMIirVZRnGEN3+R7HkAZPFchrvxG0LQp2tmlku7lCQ8duoOwjsSSBntgEkdwKZ8SNfl0Lww32Zyl1duIUYHBQHJZh74GB6Eg9qxvh94I01dEt9W1K2jurq5HmKsoBWNT0wOhJHOTyM44xyqlSbn7OG4qtabqeyp7klt8YtGkl2T2V7CpON4CsB7kA5/IGu607U7PVrJLuxuEngfo6nv6EdQfbrVLUfDGiaraPbXOn2xBGAyxgMv0YcivNfAk1x4Z+IV34ceUvbys6DJ43KCyt7EqDkD1HoKlTqU5JTd0yVVq0pxjUd0z1HXtYg0DRp9TuUleGHbuWIAtywUYyQOp9axYviFoT6ANYlkmghaRo0ikUeY7ADoATxyOpwM84pPiYP+Lf6n9Yf/RqVwnwz8JW2vJLqOqKZ7W1k8qCBjlSxAZiRnpgjjoSTnOKKlWoqqhEKtaoqypw6o6vSfinp2sa1b6db2F0n2hwiySbRg4PUAn0rf8Q+LdK8Mxob+Y+a4JSCMbnYeuOgH1wKux+H9Hikiki0yzjkiOUZIFBU9iCBxXj96LO9+ME0fiBwLQTlSJWIXAX5AecAEgexzz1NE51KcbN3bFUqVaUUpO7bOnb4zaWHwNMvNnqSufyzj9a6Lw3470nxPctbWguI7hUMhjmQAlQQCcgkdSO/etqPSNKWARxafaCLHAWJcY/KoLPw5o+n6kdQs7CG3uShjLxDaCpIJyo4JyBzjPFXGNZNNyujSEa6abkmiTXNYg0HRrjUrpJHhhA3LGAWOSFGASB1PrVfw34jtPE+mG+s4po4xIYysygNkAE9CRjkVnfEj/kQNU+kf/oxay/hCf8Aij5f+vt/5LQ6j9tyeQOq1XVPpY2/FHjHT/CbWn26C5k+079vkKpxtxnOWH94VW1n4g6JolvA80ksk00YkW3iUF1VhkFskAduCc+ma5L41ff0T6T/APtOtvwP4LsItGttT1K3S8v7qNZS0679ikAqADnBAxk9fw4qHUqOq4R6GbrVZVpU4dOpFZ/F/RJ5xHc2t3bKxx5hAZR7kA5/IGu/guIrq3jngkWSKRQyOpyGB7g1xPjzwlpd34avbyCzggu7WMzLJGgUkLywOMZGAevQ81W+EGoSXPhq4s5GLfZZ8JnsrAHH57j+NOFSpGpyT1uOnUqRq+yqa3PRqpavN9n0W+m/5528jfkpNXawPG9x9l8B+IJ84KadcEfXy2x+tdR2ngn7OEWfHGpzdl01l/OWM/8AstfTVfOv7NVvu1XxBc9o4YY8/wC8zH/2WvoqgDxn9pD/AJErS/8AsIj/ANFvWB8Ivhl4W8W+CTqWr2Us119qkj3LO6DaAuBgEDua3/2kP+RJ0v8A7CI/9FvWj+z5/wAk0/7fpf5LQBPP8BfAssZVLS8gJH3o7piR/wB9ZH6V5340+Ad7otpJqXhm9lvo4QXa1lAEwA5yrLgMe+MA8cZPFfSVFAHz98G/ixeXOpQ+GPEVy1wJ/ksruU/OG7RsTywPYnJzxyCMfQNfIPxY0r/hFfiletYZgV3S+tyvGxm5JHphw2MdMYr6w0i/XVNFsdRUALdW8c4A7BlDf1oAvUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAmKjlljgiaSV1RFGSWOOKkNcT4ou5b7V4dKhbChlDe7H19gOaqKub4ag61Tl2XU0bjxlYxSFYo5Zh/eUYH68/pUll4t0+6lEb74GPeTGOfcdPxq5Y6LYWUKpHAjNjl3ALH8az/EGi2k2nyzxRJHPEpcMgxuA5IPr0qlyvQ6Y/VJS5LNeZ0gIIrDPiS1TUzYzxTRSbtu6QKBnt0PQ9vrUPhG+e60topWLNAdoJ/u9v8PoKXxNoo1G2+0QLm5jHQfxr6f1H/16SSTszOFGEK7pVvvOh/lWTqmvWmkyJHMHeRhnbGASB78isTS/FSw6VIl2S1xCMJnrJ2/Md/zqHQNNl1e/fVL75kDZXP8AE3+A/oPSnyW1ZpHBezcpV/hX4+h2FtObi3SXy3jLDdskGGH15rO1LxHY6a5id3km7pGM4+p6frWs+Qh29QOlcB4aitbrVZjqG1pW+ZFk6Fj169/b9KUUnqZ4WhCop1J7R6I2B43ts82s2PbH9TWzpur22qxM1uW+Xhgy4x6VYNjaOmw28RXHTaKZaafa2LSG2hWLzMFgvT8qTasRVnh5RfJFp+pZZgq5Y4AHU9qwLrxfp9s5jjEk5HVkAx+Z6/hVPxjqMiCKwhOPM+Z8dSM8D8efyrT0rQLKxtk3xJLPjLOwBOcc49KaSSuzWFGlTpKrWu77JFW38ZWE0gSWOWHP8TDI/Q5rokkWRQ6MGUjII5yPrWRqmh2V/bOqxRxzAfK6jBB7ZrL8F3zsk9k5yI/mTPUZ6/rz+JoaVroc6NKpSdWldW3TOsZgoLMcKO5rn7zxdp1vIY4xJORxuQDH69fwql4y1F0EVjG2N43yY7jPA+mc5rQ0bw7a2VrG80Sy3BALF1zt9h9OlCSSuwp0KVOkqta7vskV4fGlk7BZYJowe/BA/I5/KuigmjnhSaM7kdQyn1BqtPpVhcLiW0iYf7uCPoasQQpb28cMYwkahVHsBgUm09jnrSotXpponoooqTAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigBD7UYrhPHXi7UfDl9aQ2SW7LLGXbzUJPB7YIrr9Nne60y0uJMb5YUdgOmSoJxVOLSTMIV4TqSprdF2iiipNwryn9oT/AJJov/X9F/Jq9Wryn9oT/kmi/wDX9F/JqAOD+Dnw38OeM/DF7fazbzyTw3hhQxzMg27FPQdeWNei/wDChfAn/Pjd/wDgU/8AjXPfs9alY2XgvUo7q9toHbUGYLLKqkjy0GcE9Mg169/b2kf9Bax/8CE/xoA4L/hQvgT/AJ8bv/wKf/GvRbS2isrOC1hBEUMaxoD2VRgfoKrDXNIJAGqWRJ4AFwp/rWjQAUUUUAFFFFABXzZ+0jalfFGjXeMCWyaPPrtcn/2f9a+k68J/aUsy+l+H70DiKaaEn/eVSB/44aAPYPDN0L7wpo93nPn2MMmfXcgP9a1q4z4UXn2/4XeH5Qc7bbyfpsYpj/x2uzoAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACvEv2jdDkuvD+l63EhYWUzQzYHRZMYJ9gygfVhXttZ+raVaa5pN1pl/F5trdRmORT3B9PQjgg9iAe1AHl/7P3iOHUPBsmhvIPtWmysVTPJic7gR64YsD6ceor2CvkvW/Dnir4N+LE1SwZ2tFYiC9VCY5UP/ACzkHYnHIPpkHjI9J0f9ozQprZf7Y0u+tbkD5vs4WWMn1BJBGfTBx6mgD2uvnP8AaL8Rw3Op6b4egcM1oGuLkA5CswART6ELk/RhWp4j/aKtPsbxeG9NnNywIFxehVWM46hVJLH6kD61y3w6+Gur+Ote/wCEj8SpMNMeTzpJJwQ943XC/wCyT1PTHA9gD1/4MaG+ifDSwEybJr1mu3U9cPgL+aBa0viBot/rei29vp8PnSpcB2G9VwoVhnkjuRXWIiooVVAA4AAwBT6qMnF3RlWpRqwcJbM57wZp11pXha1sryPy7iMuWXIbGXJHIOOhFa99e22mWM99eTCG2gQySyNnCqOSTirXFQ3EEN3bS206LJDKjRyI3RlIwQfqCaTd3cqnBQgoLZHM+EfiHoXja81C30eWVjZFcmWPZ5qtkBlGc4BHOQCMjIGRXW18m6bNN8IfjI0MzP8AYY5jDKx/5aWsmCGOOpA2tgd1xX1cjq6hlYFW5BBzmkWPr56+P0Ui+KtMlOfLaz2r6ZDsT+hFfQ1cB8U/BUni/wAPIbIA6lZMZIA3HmA/eTPQZwCCe4A4BJr1MlxMMNjYTqaLb71Yiom42R21lNFcWNvNDgwyRqyEd1IBFWK8C8E/Fl/Ctkvh/wATWN0Bafu45FTEkY7I6tjp0BHbAwetdZe/HXwvbwFrWG+upeyCIIPxJPA9wDVV8lxkKrjCDkujWzXqJVI2O78TRvN4U1eOIZkeymVcepQgV49+z3JGt7r0RI8xo4GUdyAXB/UivXvDernxF4astVkt/I+1xeZ5W7dtB6DOBn8q8I1Ow1b4QePjqlpbtLpUrMIzyFkiY5MbHnDDjB7lQcEZFdeWQ9pQxGBbtN2t5uL2Jno1PofSFeG/tCyoX8PxAgyAXDH2B8v+eP0roR8dfCpsvOMOoCbH+o8obs/Xdj9a89tbTV/jF48W+nt2g0qIqkhzlYYgc7A3GWbJ/E5xgYF5Rga2ExH1rErljBN69dLWXcKk1Jcsep7t4NieLwToUcg+ddPgDA9j5a8Vwvif4I6Xq97Le6TeNps0rFmi8sSREnrgZBXJ9Dj0Ar0PWrxtH8N6he20SM9naSSxRkHBKISBx24HSvNtJ+Pei3Earqmn3VpL3MQEqfnkH9K4cD9fcp18Hfzt5+RUuWyUjnLrwx8T/BFu95YatLeWcA3MsMxlCqPWNxjp/dBP9O++GPxBk8a2NxDexRxalabS/l5CyocgMAehBGCOe2OuBj678ctAi02ZNKiubu7dCsYePYik8ZYk5I5zgDnHbrVH4F+GL+wivddvIngiukWK3VxgyLnJbHpnGD357Yz6WKhKrgZ1cbTUJprldrN99CFpJKL0Paa53xjql5pOircWcgjlMyoSVDcEEng/SuirkviJ/wAi5H/18r/6C1fLm5f8Kajc6poMd1dyB5mdhkKAMA4HArermPAX/IrQ/wDXR/5109ADcV4lH/xQ/wAWiv3LO4kx6DypD/JW/wDQTXt1eX/GHRfO0201iJcvbv5UpA/gbpn2Dcf8CrmxUXyqa3Rx4yL5FOO8dSb4vaz9l0W30uJvnu33SAf3F5/Vsfka6PwFo39ieEbOB12zSr583GDuYZwfcDA/CvJtLkuvHvjfTVvBuSKONZRnIKRgFif95s/TcB719AAYAAqKD9pN1fuIwz9rUlW+SPK/jQj/AGPSXA/diSRT9SAR/I1R0P4WWOs6HZaiurTKbiFXZRGCFYjkdexyPwr0Hxh4eTxLoE1juCzBhJA5zhXGeuOxBI78E8V5l4a8YX/gSWXRdbsZzbqxZVXG+Mk87cnDKTzwQOpBOazqwjGtzTXusyrU4RxHNVXus3P+FL2n/QYn/wC/I/xrR0L4XW2h61a6lHqc0rW7FghjAByCME/jUj/Frw0kW9ftjt/cEPP6nH607wz4/bxT4jeytdPaGzjhZzLIcsSCAAQOF6nuc4q4xw91bc0jHCcy5dy58Tv+Sfal9Yv/AEalUfhGAPBhx3uXP8qvfE7/AJJ9qX1i/wDRqVS+En/Imf8Aby/9Kp/7yvQt/wC9/I7yuQ8U+ANM8TyfapGe1vQu3zowDux03KeuPwOOM11xPHvXmz/Fa30/W77T9T0+ULb3DxJLAQcqGIBKnHYZ4P4VrWcLWqbG1eVJRtV2Mhvh74w0IF9D1nzUXkRxytEW/wCAklfzNaPgzx7qc2ujQPEMY+0liiylQrBwCdrAYHOOCAO3XORqS/Fnw0kJdWupH7IsOD+pA/WuQ8L2974x+Ip8QfZjDZxS+azdhtUBVBxyxwCfbJ4yAeT3YziqT3OH3ITiqEr36HoHxI/5EDVPpH/6MWsr4Qf8ifJ/19v/AOgrWr8SP+RA1T6R/wDoxayvhB/yJ8n/AF9v/wCgrW7/AN4XodEv97XoYnxr+9of0n/9p16Xof8AyANP/wCvaP8A9BFeafGv72h/Sf8A9p16Xof/ACANP/69o/8A0EUqf8eYUf8AeanyK/iv/kUdY/68pv8A0A1wnwW/48tW/wCukf8AI13fiv8A5FHWP+vKb/0Bq4T4Lf8AHlq3/XSP+Rpz/jx+YVP95h8z1SuJ+Ll0LT4V6/J/egWP/vt1X/2au2ryz9oC8+zfDN4c83V5FCB64y//ALJXUdpz/wCzXa7NE167x/rbmKPPrtUn/wBnr3OvKf2fbM23w1MxGPtV9LKPoAqfzU16tQB4z+0h/wAiTpf/AGER/wCi3rR/Z8/5Jp/2/S/yWs79pD/kSdL/AOwiP/Rb1o/s+f8AJNP+36X+S0Aeq0UVBdXUFlay3VzKkVvEheSRzhVUDJJPYACgD5i/aIkV/iNbqvVNOiVvrvkP8iK+g/AqNH8P/DiPkMul2wOe37peK+WfEd9cfE34qynT1Yrf3KwWwIPyxKAoYjqPlBY+mTX2Ba20dnaQ2sIxFCixoPQKAAPyFAE9FFFABRRRQAUUUUAFFFFABRRRQAUUUUAJnivOtXt1uPFslvK5QSSKu4DpkDFei965TxVostyy39qpaVBh1XqR2I9/89quDSZ35dVVOq7u11a43/hCIf8An8k/74FL/wAIRD/z+Sf98Cmaf4wjWIR6gkgkXguq9fr/AFxx/KrU/jLT0X90k0jY/u4H603zpnRKWYKVv0Re0bRE0cTBJmkEuOoxjFaNxcR2sDzSuFRBkk9qo6LqMuqWRuJIvKG8hR7DHfv3rmte1GbWdQTS7L5kDYJB+83v7D+n0pJXepyxo1K9d+0eq3Zi3pfULq7voLcrAGy23ouehPv3P1rvNAvra80uL7OojKDY0Y/hNS2Gl29jpv2LaGUj58/xk9c1yciXHhTWw6Za1k7f3l9PqO3/ANc1TfMrHZUqQxkXSho47eaO+rm9S8J219O08MjQSNy2BlSfXHHJraW6SSx+0wkOpTep7HuK5+18a27gC5t5I26Ephh/jULm6HDho4iLcqO63KL6R4g0pTJbXTSIvZHzwP8AZbj8BWt4c199U3wXAAnQbty/xDODx2I4z9aZc+MbBIW8hZJXxwCu3n3z/TNUfCNhObqXUZUKIylVzxuOcnHsMVbV43kdtRSnQlOvFJrZ7NlPxco/t5N5wjRrz6cnJrSHgiEgEXj8+iirvibRm1O1WaAA3EOcD+8O4+v+e9ZOleKTZQrZ6hFKTH8ocD5gB/ez/n270XbjoVCrWnho+wesd0Wv+EIh/wCf2T/vgVoaP4dj0i5eZbhpNybcFQO4P9Kgl8Y6ai5jWeQ+gTH88VZ0PWZNX8+QweVGhATnJPXPPSpblbU5q08b7J+00ic54r+TxFC7D5diH8mOa7tcbB9KwPE+jvqNqk1uuZ4c4X+8p6j6/wD6u9ZeleKvscC2t/HJmP5Q4HOPcHn29ab96Ohc4PE4aHs9XHRo7X+dGK5qfxlYIv7qOaVsdMbf51uWVwbqyhuCu0yxqxX0yM4qGmjgqUKlNJzVi1RRRSMgooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKAPO/iF4a1bXL+yl061EyRxlWPmKuCTx1IzXbaZDJbaTZwSjbJHAiMM5wQoB5/Crhpe1U5NpJnPTw8YVJVFvIWiiipOgK8p/aE/5Jov/AF/RfyavVq8p/aE/5Jov/X9F/JqAPHfAHwmu/H2i3Go2+qwWaQXBgKyRFiSFVs5B/wBrH4V1n/DNWpf9DHaf+Azf410/7N//ACI+p/8AYSb/ANFR17LQB88W37OOpW93DMfEVoRG4cgW7c4OfWvoeiigAooooAKKKKACvLPj/Ym7+GbzgZ+x3kUxPoDmP+bivU65T4k6f/anw48QWoXc32N5VGM5KDeB+aigDk/2fr/7X8Njbk82l7LEAewIVx+rH9a9Xr5//Zq1EZ1/TGbn91cIP++lY/8AoFfQFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAQzQx3ELxTRJLE4wyOoIYehB61yF78JfAmoymSfw3bKx5PkO8I/JGA/Su1ooA5HS/hl4L0aVZbPw7ZiRcbXmBmKn1BcnB+ldbwBS0UAJWJ4l8RW/hqwju7iGWVXlEYEeMgkE55I44rbrg/iqjP4dtQqsxF2vQZ/geqgrySZz4qpKnRlOO6Op0PV4td0mHUYY3jjl3AK+MjDEHoT3Fadct8PQV8E2IZSpzJwRg/6xq6miStJ2KoTc6UZS3aPFP2hPCX27RLbxNbR5nsT5NyQOTEx+Un/dY4+jn0rf+CPi3/hI/BEdlPJuvtKIt5Mnlo8fu2P4Ar9VJ716DqNhbarptzYXaCS2uYmhlX1VgQfocGvl/wAEXl38MfjE2kXpYwPMbG4wDhkYgxyAemdjeuCR3qTY+rKKKKAMnVPDuja3g6npVpdsBgNNCrMB7HGRVKz8C+FrGUS2+gaesgOQxgDEH1BIOK6OkrWNerGPIpO3qKyAAAAAYHpUNzbQ3cDw3EMc0TjDJIoZWHoQeKnorK7TuhnMf8K98IGbzf8AhHdP3dceQNv/AHz0/St+2tYLK3WC1gjghQYWONQqqPQAcCp6K0nWqVElOTfqxJJBWJf+EPDuquZL3RLCaQ9ZGgXcf+BYz+tblJUwqSg7wdmM52y8DeFrCYTWug2CSryrmBWKn1BIOD9K6IDA4FFFOdWdR3m235islsLXJfET/kXI/wDr5X/0Fq62uS+ISs3hyMKCT9oU4AyfutUDJvAX/IrQ/wDXR/5109cz4EBXwvEGBB8x+CMHrXTUAFVrm0gvIGguYY5oXHzRyKGVvqDxVmkpWvuJpMzbLRdL06YzWWm2ltIRtLwQKjEehIHTjpWlRRQklsCSWwVTvtMstSiEd7aQXKDkLNGGAPrzVyihpPRg0mtTn08FeGo5N40SyJ9DECPyPFbFta29pCIraCOGMdFjQKB9AKsUUlCMdkTGEY/CrFa6tLe+tmt7qCKeFsbo5UDKcHPIPB5H5iks7C00+DybO2htosk7IYwi5PU4GBVqinZXuVZXuFUL3SNO1ID7bYW1xjp5sSvj6ZFaFJQ0nuDSejRz6eCvDSSBxolnn0aIEfkeK24YIreJYoY0jjUYCooAA9gKlopKMY7ImMIx+FWK11aQXtu1vdQRzQv96OVAytjkZB4Pr+FNstPs9PhMNlaw20WdxSGMIuT1OBgZ461bop2VyrK9yjfaVp+pGP7dYW115ednnwq+3PXGQcZwM/SrMcSQxrHGoVFACqowAPYVLQaLa3Cy3IZ4Y7iGSGZFkidSrowyGB4IIPUdqgstLsNNDLY2VtahyCwgiVNxHc4AzirtFFle4WV7i14T+0pf7NN0HTgc+bNLOw/3VVR/6Gfyr3avmH9oW+a++INlp0WWNtZou0dfMdmOPxBSmM9r+FFidO+F3h+EjBa287/v4xkH6NXZ1T0uyTTdJsrFMbbaCOEfRVA/pVygDxn9pD/kSdL/AOwiP/Rb15t4D+Mdz4G8OHR4dGiu185pvMecocsBxgKfT9a+prmztr1BHdW8U6KchZUDAH15qD+wdI/6BNj/AOA6f4UAeAz/ALSeqshFv4eso37GSd2H5AD+dYN/qfxN+K5W1WzuWsHIbyoITBbA5zlmY4bHUAsenAzX1BDpen2zboLG2iYdCkKqR+IFXKAPMvhh8KLfwMh1G/lju9alTYXQfu4FPVUyMknuxA9AAM59NoooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKAKVxpdjdNuntInb+8UGaZFo2nQkMllCGHfYM/nV80U7vuX7WaVruw0qu3bgYIxiq0Gn2ls5eC2hjcjG5Iwpx9QKt0tFyVJiVBcWsF0gW4hjkUHIDqGGfxqej8aQk2tUQw28NvGI4YkjQdFRQB+QqG40yyum3TWsLt6lBn86uUU7sanJO6ZnRaJpkTbksocjoSorQAAGBwKWii7Y5TlL4ncKqXOn2l0QZ7aOQjuyAmrdFCdhKTWqZnR6JpkZ3LZQZ9Smavqiou1VAA7AU6lobbHKcpfE7iAVUudNs7tsz20ch9WUE/nVuildrYUZOOqZnxaPp1uwaKzhDDvsGRWgBgdKBS022wlOUneTuFFFFIQUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFAHMeJfGVp4ZuYILm3nlMylgY8cAeuSK3rO4W7s4LlQQs0auAewIzg/nXmHxXjd9VsCqMwELZIGcc16RogxoWngjn7NHx/wABFaSilBNHFRrTliJweyNCiiisztCvKf2hP+SaL/1/RfyavVqr3Frb3cXl3MEc0ec7ZEDDP0PFAHyf4A+LN34B0W40630qC8Se4M5aSUqQSqrjAH+zn8a6z/hpXUv+hctP/Alv8K98/sHSP+gTY/8AgOn+FH9g6R/0CbH/AMB0/wAKAPA/+GldS/6Fy0/8CW/wr3bw5qr654Z0zVpIxE95axztGpyFLKDgHvjNTf2DpH/QJsf/AAHT/CrccSQxLHGioijaqqMAAdAB6UAS0UUUAFFFFABUU0KXEEkEo3RyKUYeoIwRUtFAHyz8GJn8PfGGTSJ2IeVbixcHj5kJb+cePxr6mr5V8c/8Ud8fTqQykAvYL7PTKNtMn5neK+qcgjjpQAtFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFACUfhRVLUNTstLhWa+uY4Iy20NIcAnBOPyBoWopNJXZdGMUtVbO9t9QtUubSZJoXztdDkHBwf1BqzTYJprQWs4aNpo1dtW/s+3/tFkEZuvKBk2jOAGxkDk/Xj0FaNIenHWkMWivA9B+LHiOP4uHRfE7QQWjTNYm3hj2pFJuARwT8xBIAyTjDZAFe+UAFFFFABRRRQAUUUUAFFFFABRRRQAUUVg+KtYudE0lbq2WJpDKExICRjBPQEelAG9RWL4Z1S41jRY7y5WNZGdlIjBA4OBwSf51tUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABXytef8Vd+0ftHzx/2sqEdmjgwD+BEZ/OvpzVr+PStHvtRlx5dpBJO30VSx/QV82/ADT5NU+It5q0+XNrbPIXP/AD0kYKPzBegD6fooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKAG4B6gUvWs3UNc0zSpEjvryG3ZwSokbBI9auxSpNEksbBkcBlYdwelPW1yFKLdk9SaiiikWFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAfPP7SWj7b7RNaRc+ZG9rIw7FTuUfjuf8q9f+H2sf274A0TUC253tVSQ9y6fI3/AI8prC+Nei/2x8MdQZU3S2LLeRgdtpIY/gjMfwrmP2dNa+1eGdS0Z2y9ncCZAeySDoPoysT/ALw9aAPa6KKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKAErgfix/yLlp/wBfa/8AoD13o9+tUNT0mx1i3WC/t1niVt6qxPBwRnj2JqoSUZXMMTSdWk4LdmL8Ov8AkSLH6yf+jGrqqp2Fha6ZZpaWcQigjztQZwMkk9fck1cpSd3cqjBwpxg+gtFFFI1Pnb9oXwmbXUrPxXartW4xb3RXjEijKN9SoIz22D1r1j4aeKx4w8D2OoO+buMeRdjuJVAyT/vDDf8AAq1fFnh6DxV4Xv8ARrjAW5iKo5GdjjlW/BgD+GO9fPvwT8QT+E/H1z4Z1PMMd85t3Rj/AKu4QkL+fzL7kr6UAfT1FFFABRRRQAUUUUAFFFFABRRRQAVyXxE/5FyP/r5X/wBBautrkviJ/wAi5H/18r/6C1AE3gL/AJFaH/ro/wDOunrmPAX/ACK0P/XR/wCddPQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAecfG/WP7J+GN9GrbZb6SO1THudzD8VVh+NYH7Omj/ZfCOo6q64e+uhGpPdI1wD/AN9M4/Cub/aP1sS6po+iI3EETXUoHQljtX8QFb/vqvZvAWi/8I94E0XTCmySK2Uyj0kb5n/8eY0AdJRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAeS/Fr/kLaf8A9cW/nXpOif8AIB0//r2j/wDQRUWqeHtL1mSOS/tFneMFVLEggHqODWhBDHBDHDGoWONQqqOwAwK0lNOKXY46WHlCvOo3oyaiiiszsCiiigAooooAKKKKACiiigAooooAKKKKAK95aQ39jcWdwu6CeNopF9VYEEfkTXzB8JbyXwd8YpNFu22iZ5dOlzwN4bKnHuygA+je9fU9fL3xx0ubw38TLbX7LMZvFjuo3HQTRkA4+mEJ/wB6gD6horO0PVYdb0Ox1S2/1N3AkyjuNwBwfcdD9K0aACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKAEpOB7Uua4T4ozzQeH7VoZXjY3aglWIONj8ce+KqMbuxjXqqlTc30O6BzyKWuX+H8sk3gyyklkZ3JkyzkknDsOprqKUlZ2KpT9pBT7i0UUUjQK8J+Jnwn1vWviBa6z4Zjjj+1BZLiZ5QiwSoQA57nI2nABOVJ717tRQBWsxcLZQC7ZGuRGomaMEKXx8xAPbOcVZrOuda0y01O10241C2ivbokQ27SDzJMAnhc5xwefoOpFaNABRRRQAUUUUAFFFFABRRRQAVyXxE/wCRcj/6+V/9BautqKSKOVdskaOvXDAEfrQBzvgL/kVof+uj/wA66eo440iQJGioo7KMAfgKkoAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKK5X4ieIB4Z8BatqSvtnWExQEcHzH+VSPoSD9AaAPnuUj4i/H7A/e2kl+FHcGCHqfYFUJ+re9fV1fO/7OOgebf6t4hkT5YkW0hJ6Fmwz/iAF/wC+q+iKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAaTj0pa8r+Kd1cW+qWAhnliBhYkI5UHnvivRNGYtolgzHLG3jJP8AwEVcoWin3OaniFOrKnb4TRoooqDpCiiigAooooAKKKKACiiigAooooAKKKKACvLvjv4d/tn4fPfxJuuNLkFwMDkxn5XH0wQx/wB2vUagu7WG+sp7O5QSQTxtHIh6MrDBB+oJoA8l/Z88RDUfB9xokr5m02bKA/8APKTLDH0YP9MivYa+U/AV3N8N/jO+k3jlYHnbT5mPG5WI8t/YEhDnsCa+rKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKAErC8UeHI/EunxWkk7wBJRLuVQSSARjn6/pW7RTTs7oicIzjyy2MrQNHTQdGg05JWlWIth2GCcsT0H1rVpD+lLmh3buOMVGKitkLRRRSKCiiigD5h+NWh3XhL4iW3ibTmaNL1xcxyDny7hCNw/HCtz1yR0FfQvhbX4PFHhnT9ZtsBLqIMyg52N0ZfqGBH4Vi/E/wAJjxh4HvbGJN17CPtFpgcmRQflH+8CV/EeleV/s8+LPJvbzwpdOQs2bq0DHGHAw6/iAGA6Da3rQB9D0UUUAFFFFABRRRQAUUUUAFYviXWn0LTFu44VlJkCbWOOoJzn8K2q5L4if8i5H/18r/6C1AGt4d1Z9a0lLySJYmZmXapyODjrWvXMeAv+RWh/66P/ADrp6ACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACvn79o3xGGfS/DcL525vLgA9+VQf8AoZx7g175JIkMbSSMERAWZicAAckmvlTSEf4qfG/7TIheykuTcOGHAt4sBVI7ZAVT7tQB7/8AC/w7/wAIz8PdKsZE2XMkf2i4BGD5j/MQfcAhf+A12NFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAcp4o8GQ+J7mCeW8kgMKFAFUEEE9810VlbizsoLYMWEMaoCe+BjNWKKbk2rGUaMIyc0tWLRRRSNQooooAKKKKACiiigAooooAKKKKACiiigAooooA+df2ifDBttS0/wAT26YW4AtrhhxiRQSjE+pXI/4AK9e+HPiceLvA+namzhroJ5N1zyJVwGJ9M8N9GFWvG3hpPFvg/UdHcKJJoiYWPRZV5Q/TIGfYmvC/gL4lk0PxZeeGL8tEl8SER+PLuEyCpHYkAg+6qKAPpaiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKAErk/Huu32g6PBc2DokjziNiyhvlKsen1ArrK5Tx5oV7r+jwW1gEMiXAkbe235QrD+ZFXC3Mr7HPiuf2MuTcueD9TudY8M2t9eMrTyFwxVQAcMQOPoBW/WD4Q0u50bwza2F2EE8ZcsFbI5YkYP0IreqZW5tCqHN7KPNvYWiiikbBRRRQAV8r/EzSLn4d/FWHXNMXy4LiUX9tjIUMD+8jOO2c8D+FwK+qK5jxj4I0jxxZ2trqwm2W83nI0LBW6YK5IPB4zj0HIoA1tF1e217RLPVbNt1vdxLKnqMjJB9wcg+4NaNZ2j6NYeH9Lg0zS7ZbezhBEcakkDJJPJySSSTk1o0AFFFFABRRRQAUUUUAFcl8RP8AkXI/+vlf/QWrra5L4if8i5H/ANfK/wDoLUATeAv+RWh/66P/ADrp65jwF/yK0P8A10f+ddPQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQB5p8bvFA8P8AgGezik23eqE20YBwQmMyN9Nvy/VhXP8A7PHhc2Ph688Qzx/vdQfyYCRyIkPJB92yD/uCuA+JWqXHxF+LMOi6Y2+GGUWFt3Xdu/eSHHbOeR2UGvpvSNMt9G0i00u0Xbb2kSxRjvhRgE+pPUn1NAF+iiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKAPP/H/AIq1Xw/f2kWnyRoksZZtyBiSDjjNdnpk73Ol2lxJgySwo7HGOSoJrjfHvhTVPEF/aTWCxMscZVt77cEnNdlpsD2ulWkEuPMihRG+oABrSXLyq25w0fa/WJ83w9C7RRRWZ3BRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAV8w/Gvw9ceFPH1t4n03MMd7ILhHUcR3KEFvxJAbnqS3pX09XJ/ETwmnjLwZe6WFU3QHm2rH+GVQdvPbIJUn0Y0AX/CXiK38V+F7DWbfAFzGC6A52OOGX8GBHuMHvW7Xzf8A/Fz6Tr114T1Bmjju3L26vxsnUYZcHpuA/NQOpr6QoAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigBKxfEXiK18N2Md1dxTSJJIIwIgCQSCeckDGAa2q4H4sf8i7a/9fa/+gPVwSlJI58XUlSoynHdHV6Lq8OuaTDqNvHIkUu7CyABuGIOQCe4PetPvXK/Dr/kR7H6yf8Aoxq6qlJWbKoTc6UZPdoKM1jat4m0jRF/028jSTGREp3Of+AjnHv0rgNY+Kl3MGi0m1WBTkebN8z47EL0B+uRTjTlLZGVfG0aPxS1PULu8trKAz3U8cMa9WkYKB+JrO0fxFp2uzXSafK0y220O+0hTuz0zyeh7Y9K8Gv9SvdTnM19dS3EnPMjEgewHQD2AAr0X4Rj5dX+sP8A7PWsqPJG73OKhmbr4hU4qyZ6dRRRXOeweYfEn4tHwHqlvpsWjyXM8qLMZpHCx7CxBC4yS3B4OMcHmvRbC9t9S0+3vrSQSW9xEssTj+JWAIP5EV5x8cvCX/CQ+CX1GCPde6STOuBktEQPMH4ABv8AgPvWP+z74t/tHw/ceHLmTNxpx8y3BPLQseR/wFiefRgO1AHtNFFFABRRRQAUUUUAFVrqztr2LyrqCOaPO7bIoIz64P1NWayNf1pdB09bt4TMDII9gbByQTnofSgDQtrWCzhENtCkUYOQiKAM/QVPWZoerLrWmJerCYgzFdpbPQ4rToAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigArifij4uHg/wRd3kUm2+uB9ntMHBEjD73/ARlvqAO9dtXyz8VNeufiF8SbfQNIPnQWsv2O2APyvKTiR/pkYz0wuehoA6H9njwmZbq88V3UeViBtrQsOrHBdh9AQoPfcw7V9C1k+HNDtvDXh6w0ezH7m0iEYOAC56sx9ySSfc1rUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAZur6rb6Npst/d7/ACYiobYMn5mC+o6Z59qZpmv6VrCg2F7FMcZKA4YfVTgj8qy/iH/yI+o/9sv/AEYteGo7RuHRmVwcqwJBB9QRyDW9OkpxueTjcwlhqyja6sfTVGa8O0n4ha7pmEknF5COCtxksB3wwOc/UkCu70n4l6Nf7Uu99jKeMSfMhP8AvDp9SBUyoyibUcyoVdL2fmdtS1BBcQ3MKywSpLGwyrxsGBHsRU1ZHemmro5vxH4ysfDVxBDdw3EjSoWHlKpAA9ckVuWlwt3Zw3KAhZUWQZ6gEZ/ka8u+LP8AyFtP/wCuLfzr0nRP+QDp/wD17R/+gitJQSgpI4qNec8ROm9kaNFFFZncFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQB8y/G7wtP4X8Y23ivSt0MN7KJd8Yx5NypBz/wLG4e4avdPA3iuDxl4Ss9Yi2iVl2XMa/8ALOUY3D+RHsQan8X+GrXxd4XvdFusATpmOQjJjkHKsPocZ9Rkd6+evhR4muvh949ufDmtEwWt1N9mnVzxFMCQr56YJ4J6EEHOAKAPqSiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAK4D4sf8AIuWn/X2v/oD139cB8WP+RctP+vtf/QHrSl8aOPH/AO7TMnw94603w/4PtLRkluLxPMJiQYC5diMsegwQeMnnpWDrHxB1zVd0ccws4D/Bbkhvxbrn6YB9K7Dwp4X0jXfBFk17aKZv3gEyfK4w7Acjkgdgcj2rH1j4WXtuGl0m5W5QZIilIVwOwB6E+5xW6dNSd9zyalPGSoRcH7tuh58zFmLMSxOSSTkk98k02rV7Y3mnTmG9tpYJOu2RSMj1B6Ee/IqrXSmnseNJNO0twrsfBHiy08Lpem7gnl+0FNvlAHG3dnOSP7w6Zrjq7v4d+HtL15NQ/tK2M3kmPy/3jLjduz90jPQdelZ1bKPvbHTglUddezdpHRf8LZ0n/nxvf++V/wDiqP8AhbOk/wDPje/98r/8VWx/wrzwt/0DD/4ES/8AxVH/AArzwt/0DD/4ES//ABVcvNS7HvezzD+Zf18jFf4qaNKjJJp96yMCGUqhBB4I5bnvXjHh2zl8JfEBNc0iXGnxztiCQ4drdiQUOMgkA8HOMgGvoH/hXnhb/oGH/v8Ay/8AxVcJ8VvBaaR4QfV/DMTW81m4a4QEyb4jwSA2cFSQeMcZ9BRekP2eP/mX9fI6P/hbOk/8+N7/AN8r/wDFUf8AC2dJ/wCfG9/75X/4quf+FvhZNb8JCfxRoE8N6sp8uaVniM8ZwVbaCMdSOgyADzk13H/CvPC3/QMP/gRL/wDFUc1LsL2eYfzL+vkY/wDwtnSf+fG9/wC+V/8AiqP+Fs6T/wA+N7/3yv8A8VWx/wAK88Lf9Aw/+BEv/wAVR/wrzwt/0DD/AOBEv/xVPmo9g9nmH8y/r5GP/wALZ0n/AJ8b3/vlf/iqP+Fs6T/z43v/AHyv/wAVWx/wrzwt/wBAw/8AgRL/APFUf8K88Lf9Aw/+BEv/AMVRzUewezzD+Zf18jH/AOFs6T/z43v/AHyv/wAVWL4o8fafrmlraQWt1G4lD5kCgYAIxwT612X/AArzwv8A9Aw/9/5f/iq53xj4P0LStGW4srIxSmZVLec7cEEkYLEdhRzUuwezzD+Zf18in4b+IenaNo6Wc1rdO6szZQLjk57kVrf8LZ0n/nxvv++V/wDiqi8J+DNB1TQY7q8sTJKXYFvOdcgHA4DAVu/8K88L/wDQMP8A3/l/+KovS7B7PMP5l/XyMf8A4WzpP/Pje/8AfK//ABVH/C2dJ/58b3/vlf8A4qtj/hXnhb/oGH/wIl/+Ko/4V54W/wCgYf8AwIl/+Kpc1HsHs8w/mX9fIx/+Fs6T/wA+N7/3yv8A8VR/wtnSf+fG9/75X/4qtj/hXnhb/oGH/wACJf8A4qj/AIV54W/6Bh/8CJf/AIqnzUewezzD+Zf18jH/AOFs6T/z43v/AHyv/wAVR/wtnSf+fG9/75X/AOKrY/4V54W/6Bh/8CJf/iqP+FeeFv8AoGH/AMCJf/iqOaj2D2eYfzL+vkY//C2dJ/58b3/vlf8A4qj/AIWzpP8Az43v/fK//FVsf8K88Lf9Aw/+BEv/AMVR/wAK88Lf9Aw/+BEv/wAVRzUewezzD+Zf18jH/wCFs6T/AM+N7/3yv/xVH/C2dJ/58b3/AL5X/wCKrY/4V54W/wCgYf8AwIl/+Ko/4V54W/6Bh/8AAiX/AOKo5qPYPZ5h/Mv6+Rj/APC2dJ/58b3/AL5X/wCKo/4WzpP/AD43v/fK/wDxVbH/AArzwt/0DD/4ES//ABVH/CvPC3/QMP8A4ES//FUc1HsHs8w/mX9fIx/+Fs6T/wA+N7/3yv8A8VR/wtnSf+fG9/75X/4qtj/hXnhb/oGH/wACJf8A4qj/AIV54W/6Bh/8CJf/AIqjmo9g9nmH8y/r5GP/AMLZ0n/nxvf++V/+Ko/4WzpP/Pje/wDfK/8AxVbH/CvPC3/QMP8A4ES//FVHL4C8KQRPNLYBI0XczPcyAKBySTu4AFLmo9g9nmH8y/r5HL+Iviet5oF7baLBPb6hNGY4ppgAsZPBbIJOQMkcdcZ4rzj4Y22n+C9dn1jVo5Lq5WIx2vkAERlshmyxHJHA9ifasiG9u/GvxH/snwqPsemzTbYvl37IV+9KxbJyQCcZ6kDrX0Onw68MqgU6ezkADcZ5AT78MBz9BRekP2eP/mX9fIyv+Fs6T/z43v8A3yv/AMVR/wALZ0n/AJ8b3/vlf/iq2P8AhXnhb/oGH/wIl/8AiqP+FeeFv+gYf/AiX/4qjmo9hezzD+Zf18jH/wCFs6T/AM+N7/3yv/xVH/C2dJ/58b3/AL5X/wCKrY/4V54W/wCgYf8AwIl/+Ko/4V54W/6Bh/8AAiX/AOKp81HsHs8w/mX9fIx/+Fs6T/z43v8A3yv/AMVR/wALZ0n/AJ8b3/vlf/iq2P8AhXnhb/oGH/wIl/8AiqP+FeeFv+gYf/AiX/4qjmo9g9nmH8y/r5GP/wALZ0n/AJ8b3/vlf/iqP+Fs6T/z43v/AHyv/wAVWx/wrzwt/wBAw/8AgRL/APFUf8K88Lf9Aw/+BEv/AMVRzUewezzD+Zf18jH/AOFs6T/z43v/AHyv/wAVR/wtnSf+fG9/75X/AOKrY/4V54W/6Bh/8CJf/iqP+FeeFv8AoGH/AMCJf/iqOal2D2eYfzL+vkY//C2dJ/58b3/vlf8A4qj/AIWzpP8Az43v/fK//FVsf8K88Lf9Aw/+BEv/AMVR/wAK88Lf9Aw/+BEv/wAVRzUuwezzD+Zf18jH/wCFs6T/AM+N7/3yv/xVH/C2dJ/58b3/AL5X/wCKrY/4V54W/wCgYf8AwIl/+Ko/4V54W/6Bh/8AAiT/AOKo5qPYPZ5h/Mv6+Rj/APC2dJ/58b3/AL5X/wCKo/4WzpP/AD43v/fK/wDxVbH/AArzwt/0DD/4ES//ABVH/CvPC3/QMP8A4ES//FUc1HsHs8w/mX9fIx/+Fs6T/wA+N7/3yv8A8VR/wtnSf+fG9/75X/4qtj/hXnhb/oGH/wACJf8A4qj/AIV54W/6Bh/8CJf/AIqjmo9g9nmH8y/r5GP/AMLZ0n/nxvf++V/+Ko/4WzpP/Pje/wDfK/8AxVbH/CvPC3/QMP8A4ES//FUf8K88Lf8AQMP/AIES/wDxVHNR7B7PMP5l/XyMf/hbOk/8+N7/AN8r/wDFUf8AC2dJ/wCfG9/75X/4qtj/AIV54W/6Bh/8CJf/AIqj/hXnhb/oGH/wIl/+Ko5qPYPZ5h/Mv6+Rj/8AC2dJ/wCfG9/75X/4qj/hbOk/8+N7/wB8r/8AFVsf8K88Lf8AQMP/AIES/wDxVH/CvPC3/QMP/gRL/wDFUc1HsHs8w/mX9fIx/wDhbOk/8+N7/wB8r/8AFUf8LZ0n/nxvf++V/wDiq2P+FeeFv+gYf/AiX/4qj/hXnhb/AKBh/wDAiX/4qjmo9g9nmH8y/r5GP/wtnSf+fG9/75X/AOKo/wCFs6T/AM+N7/3yv/xVbH/CvPC3/QMP/gRL/wDFUf8ACvPC3/QMP/gRL/8AFUc1HsHs8w/mX9fIx/8AhbOk/wDPje/98r/8VR/wtnSf+fG9/wC+V/8Aiq2P+FeeFv8AoGH/AMCJf/iqP+FeeFv+gYf/AAIl/wDiqOaj2D2eYfzL+vkY/wDwtnSf+fG9/wC+V/8AiqP+Fs6T/wA+N7/3yv8A8VWx/wAK88Lf9Aw/+BEv/wAVR/wrzwt/0DD/AOBEv/xVHNR7B7PMP5l/XyMf/hbOk/8APje/98r/APFUf8LZ0n/nxvf++V/+KrY/4V54W/6Bh/8AAiX/AOKo/wCFeeFv+gYf/AiX/wCKo5qPYPZ5h/Mv6+Rj/wDC2dJ/58b3/vlf/iqP+Fs6T/z43v8A3yv/AMVWx/wrzwt/0DD/AOBEv/xVH/CvPC3/AEDD/wCBEv8A8VRzUewezzD+Zf18jH/4WzpP/Pje/wDfK/8AxVH/AAtnSf8Anxvf++V/+KrY/wCFeeFv+gYf/AiX/wCKo/4V54W/6Bh/8CJf/iqOaj2D2eYfzL+vkY//AAtnSf8Anxvf++V/+Ko/4WzpP/Pje/8AfK//ABVbH/CvPC3/AEDD/wCBEv8A8VR/wrzwt/0DD/4ES/8AxVHNR7B7PMP5l/XyMf8A4WzpP/Pje/8AfK//ABVH/C2dJ/58b3/vlf8A4qtj/hXnhb/oGH/wIl/+Ko/4V54W/wCgYf8AwIl/+Ko5qPYPZ5h/Mv6+Rj/8LZ0n/nxvf++V/wDiqP8AhbOk/wDPje/98r/8VWx/wrzwt/0DD/4ES/8AxVH/AArzwt/0DD/4ES//ABVHNR7B7PMP5l/XyMf/AIWzpP8Az43v/fK//FUf8LZ0n/nxvf8Avlf/AIqtj/hXnhb/AKBh/wDAiX/4qj/hXnhb/oGH/wACJf8A4qjmo9g9nmH8y/r5GP8A8LZ0n/nxvf8Avlf/AIqj/hbOk/8APje/98r/APFVsf8ACvPC3/QMP/gRL/8AFUf8K88Lf9Aw/wDgRL/8VRzUewezzD+Zf18jH/4WzpP/AD43v/fK/wDxVH/C2dJ/58b3/vlf/iq2P+FeeFv+gYf/AAIl/wDiqP8AhXnhb/oGH/wIl/8AiqOaj2D2eYfzL+vkY/8AwtnSf+fG9/75X/4qj/hbOk/8+N7/AN8r/wDFVsf8K88Lf9Aw/wDgRL/8VR/wrzwt/wBAw/8AgRL/APFUc1HsHs8w/mX9fIx/+Fs6T/z43v8A3yv/AMVR/wALZ0n/AJ8b3/vlf/iq2P8AhXnhb/oGH/wIl/8AiqP+FeeFv+gYf/AiX/4qjmo9g9nmH8y/r5GP/wALZ0n/AJ8b3/vlf/iqP+Fs6T/z43v/AHyv/wAVWx/wrzwt/wBAw/8AgRL/APFUf8K88Lf9Aw/+BEv/AMVRzUewezzD+Zf18jkPFHxB07XPD1zp0FrdRyTFcNIq7fldWOcEnnHpXnXQ16r4x8G6DpXha8vbKyMVxF5ex/OdsZdQeCxB4JHPrXlXfmuii4uPuo8bMVWVVe2d3YSiiitTzy7p+q3+lS+bY3ktu2QTsYgHHqOhHsQRXb6T8VLyHbHqtqtwgwDLDhXHqSDwT7DFc3pPgzXdZw0Fm0cJxiWf5Fwe4yMke4Bru9J+Flhb7ZNUuHun/wCeceUQe2RyfqCPpWFSVLruerg6eNunTul57HKePdesPEFzY3NjIzBIirqylWUk5we34jj3r13RP+QDp/8A17R/+givLPiVp9npt7p0FlbRwRCFjtRQOc9T6n3r1PRP+QDp/wD17R/+gisaluSNj0cEpLE1FN66GjRRRWB64UUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABXg/x98CfaIF8X2EWZIgsV+qjkr0WT8OFPsVPQGveKguraG8tZrW4jWWCZDHJG4yGUjBB9iM0Aec/Bnx3/wAJZ4YFjezbtV01RHLuPzSx9Ff1JwME+oyeor02vk3WLDU/gx8T4rqy3vZ7jJbljxPbscNGx6EjofcBsDivqDRNYsfEGjWmrafKJLW5QOjdx6g+hByCOxBFAGlRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAlcD8WP8AkXLX/r7X/wBAeu+x3rO1XR7DXLZbfUIPOiRw6qWZcMAQDkEdifzq4S5ZXOfE0nVpShHqY3w6/wCRIsfrJ/6MauqqlpunWulWSWdlH5UEedqbicZJJ5Jz1Jq7Uyd5XLoQdOnGD6Iq3ljbX8Bhu7eKeI9VkUMPyNcRrHwtsLnMmlzvaP8A883y6H6dx9cn6V6DRTjOUdmRWw1KqrTifP2seEta0Qs11Zs0IyfOiy6Y9SQMgfXFdp8Ivu6v9Yf/AGevTCARggEVTtdMsrGaaW1tYoJJ8GQxrt3EZwTjvya1lWco8rOKjlkaNdVIPRF6iiisD1QooooAKK8o+O416HwZFf6RqNzbWsMuy+igbaXRsBWLDnAPBAODu56Vc+Cvi3/hJfA0VrcSbr/SyLaXJyWTB8tvxUY9ypPegD0uiiigAooooAK5L4if8i5H/wBfK/8AoLV1tUtQ0201W3FvexebEGDBdxGCMgHIIPc0AYvgL/kVof8Aro/866eqlhp9tplqLa0i8uEEkLuJ5PJ5JJq3QAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFeJfHrx2NO00eFNPmxd3ih7xlPMcJ6J9WI5H90c8MK9M8Z+K7Pwb4ZudXvCCYxshizgyykHao/Ik+gBPavnn4ZeFrz4leO7nxBrmZ7KGbz7pmHE0p5WID04GQOAoxxkUAenfA/wACnw54c/tq+i26nqaBlDDBhg6qv1bhj/wEEZBr1mkAwMCloAKKKKACiiigAooooASjNVru5hs7aW5uHEcMSlnc9AAMk153c/ErUb66eHQtHacKero0jEdiVXoPxNXGDlsc9bE06Ok3qz02jpXmH/CfeKbIeZqHh7bCOpMEkQ/M5/lXe6JqY1nRrbUBEYhOu7YTnHPrx6UpQcVqKjiqdWXLHc0jQKxNf8RWPh2yFxeOSzHEcSfec98Z7DjJPA/EVxX/AAsLxHqBMmlaDvgzjIikl+vK4H6U4wk1dCq4ulSlyt6nqAorzvSviV/pws9dsTZPnBkXOFJ/vKeQPfn3wOa9BVwwypyCMgilKLjuXRxFOsrwY+jNYmv+I7Hw7aie9cl3JEcSfef6A+mRk9OncgVxP/CxfEOoszaToIeMHHEbzY+u3GKcacmrkVcXSpS5W9fI9RzRXnWmfEHUjqdrp+r6K0ElxKsSuA0ZBY4ztYcjJGeePevRM/hSlFx0ZdGvCsrwHUUUVJuFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAcr8Qz/wAUPqH/AGy/9GLXi9hpd/qkvlWNpLcPkfcU4GfU9APckCvoe9srbULVra7iWWByC0bDg4II/UCn29tBawrFBCkMajhEUKB9AOlbU6vJGyPMxeX/AFmqpt2SR5ZpHwrvZwsmq3S2ycExRfO5HcE9AfcZru9J8IaJo21rayVpxgiaX53z6gngH6YrfoqZVJS3ZvRwNCj8MdRQMUUUVmdh5L8Wc/2tp/8A1wb+dek6J/yAdO/69o//AEEVX1bw3pOtyxy6jaCd4wVQ72XA9OCK0reGO3gjgiG2ONQij0AGAK0lO8VHscdHDyhXnUe0ieiiiszsCiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKAOO+I3gi38c+F5bEhEvocy2czD7kmOhPXa3Q/gcEgV4p8H/HM/gvxJP4W10vBZTzGMiXj7LcA4OfRSeD2BAPAzX05Xh3x0+HP9oWz+LNKgJu4F/0+NBzJGBxIB6qBg+oGe3IB7jRXj3wU+JH/AAkWmL4d1WfOq2ifuZHPNxEPfuyjg9yMHnBNew0AFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAUdU0621fS7rTrxN9tdRNDIvcqwwceh54NfMHgTUrn4YfF2XSdSk227zGxuWbhSrEeXJz0H3Wyf4SfWvq2vAf2iPCWVsvFdrH0xa3mB26xsf1Un/dFAHv1FcH8JfFv/CW+BbSaaTffWeLW6yckso+Vv8AgS4JPrkdq7ygAooooAKzNZ1m30OyF3cpK8ZcIBGATkgnuR6etadcl8RP+Rcj/wCvlf8A0FqAN3SdVg1mwW8tkkWNmK4kAByDjsTWhXMeAv8AkVof+uj/AM66egAooooAKKKKACiiigAooooAKKKKACiiigAqGaaOCF5pnWOKNSzsxwFA5JJ7AYqavn/45/EfeZPB2jykkkf2hLGc89RCD+Rb8B6igDkfG/iPUfi58QLXSdGVmskkMNkhyAR1eZvQEDPThQOM5z9I+E/DNl4R8O2uj2C/u4R88hGGlc/ec+5P5DA6AVxXwb+HX/CIaL/ampQgazfINwYc28ZwQnsTwW98Dtk+pUAFFFFABRRRQAUUUUAFFFFAHM+PIJ7nwZqCQKWYKrkDrtVgW/IAn8K5f4eeJNFsNI+wXU8drc+YWZ5flVwcYO48AgYGCe3Ga9M9q5PVPh3oOpSNKIHtZG5LW7BQf+AkED8BWsJLl5ZHBiKFX2qrUrNrozpoLiC6jDwTRyoejIwYH8qfHGkKBI0CqMkBRgc815JrfgnUPCts+r6VqcjRxHL4zG6jOOoPzDPUccdjXb+Cdem8QeHxPc4NxFIYpGUYDEAENj3BGccZzjHSlKGl09B0cU5VPZ1I8sjz/VL201z4jP8A2tcCLT7eVojuOBtTPH/AmB6c8n0FeixeLvDMMSxRanapGowqrwAB7AcV5nZadYy/Ee40/V4t0EtzKgBcrySSpyCDzwB65Fei/wDCuvC//QOb/wACJP8A4qtanIrJnDhPbtzlBK9+pzvj7UfDutaGZba+t5L+Bh5W0/MwJww6dMc/UVv/AA8v3vvCNuJG3Pbs0GSecDp+QIH4U/8A4V34X/6Bzf8Af+T/AOKrZ0rRrHQ7RrbT4TFCWLld5bkgDqST2FZuUeWyOujQrKu6s7LToeV3qHxf8THtJmb7OkzRYyeI0ByB6ZIPP+1Xr1vbw2lukFvEscSDCogwAPYV5H4fcaZ8VJop/l33E0YLH+8SVP48AfUV7HTraWS2Iy5KXPN/FchkgjlCiWNH2sGAZQcEHII9wRmp6SisT07IWiiigYUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABTWAYEMAQeoIp1FAHy78UfA978PPE0PiXw8zwafJMJIXi62kvXYf9k8kdsZBHHPt3w58eWvjvw8tyuyLUYAEvLdT9xuzAH+FsZH4jJIzXS6tpdlrel3GmahAs9pcoUkRh1HqD2I6gjkHBr5b1XTtd+CfxAhurVmltGyYJW4S6hyNyPjuOMjscEdqAPrOisPwt4n07xfoVvq2mS7opBh4yfmifujDsRn8Rgjgg1uUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAVl+IdFtvEfh++0i7GYLuExk4yVJ6MPcEAj3FalFAHm/wu+GM3gBbuefVmuri7RVlhiTbCpUnBGeWIyQDwME8d69IrJ13xBpfhrS31LV7xLW1Uhd75O4nJCgAEknB4A9areFPFumeM9H/ALU0lpDB5rxMsihWVlPcAnGQQRz0I6HigDfooooAK5L4if8AIuR/9fK/+gtXW1yXxE/5FyP/AK+V/wDQWoAm8Bf8itD/ANdH/nXT1zHgL/kVof8Aro/866egAooooAKKKKACiiigAooooAKKKKACiiuS8f8Ajmw8C6A19cYkvJQVtLbODK+O/ooyCT2HHUgEAwfi38SU8F6P9hsJFOt3iHyhwfIToZCPXqFB4JBPIBB4D4J/DmXVLxPGOuxs8CuXso5eTNIDzK3qAc4z1PPbnn/AXg7U/it4tude16SR9PWXfdzcjzW4xEnoAMZx0GBwSK+o7eCG1t47eCNY4YlCJGgwqqBgADsAOKAJ6KKKACiiigAooooAKKKKACiiigDB8Vzatb6I02jKzXaupCqoYlc8jBznj05rjE+Juq2I8vVdCIk7nLRfowP869Q+tJgegq1JLRo5K1CpOXNCdjyTVfFWueMLQ6ZpujyRwykCQqS5IyDgsQAozjJPp19e78H6C3h3QUtJGDXEjGWYr0DHAwPoAB7kE966DGOgFB6U5TuuVKwqOFcJ+0nLmkcF438FT6tONW0vi+UAPGCFMmMYIORhhgdT0x0xzkW3xD1zRoxbazpDSyIMb33RMR6ngg/UYH8z6pRgelCqaWlqTPBvndSlLlb3PMH+ImvaovlaToZDnjcA02PfgDH6iu78PjUf7Dtjq2ftxUmXOOpJx046Y6dK1MDtilpSknsrGtGjUhLmnPmPP/HPgy51O4XV9K/4/EAEkYbaXxjDKePmGB1PQdeOcq1+I+s6TELbV9IaWZBje5MLHtkjaQfqMfSvVO9GAe1NVNLSVzKeDfO6lKXK3uec2HjXxDruqWkVjpBgtGmTz5NrPhNw3fMQFHGff05r0YZxQOtLmpk09lY3o05wXvy5mLRRRUm4UUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAVz/i3wppnjLQJtJ1JPlb5o5VHzQyDoy+/X6gkd66CigD5M0nVPEHwS8dy2d5E0lo5AniGQl1Fk7XQnjI5wexyD3r6h0XWrDxDpFvqmmXCz2k6hkYHkeoI7EHIIPQisXx54F0/wAdaE1jdgR3UeWtblRloX/qpwAR347gEfPfhbxPr/wb8Xz6Tq1vIbFnH2q1zkMOgmiJ4JwOOgIGDggEAH1hRVDStVstb0y31LTbiO4tJ0DpIhyD7EdQR0IPIIIPIq/QAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFAGD4v8OQeK/CuoaLPgfaIyI3I+5IOVb8GAz6jI714D8D/EU/hjxzdeGNRzDHfMYSjn/V3KEgD2J+ZeOp2+lfTlfM/x38NTaB4wtPFGn7okvmDM6DHl3CYOfQEgAjuSGNAH0xRXO+CfEkPi7wlp+sx7Q80YEyDokq8Mv0yDj2wa6KgArP1bSbbWbMW13vMYcP8AI2DkAj+prQqhqmqWmkWoubxykRYICFJ5IJ7fQ0ALpemW+kWS2lrv8pSSNxyck561eqlp2pW2q2YurRy0RJAJUjkHB4NXaACiiigAooooAKKKKACiiigAoorE8TeJtM8JaLNq2qz+XDHwqDlpWPRVHcnB+gBJwATQBF4t8V6Z4N0KbVdTk+VfliiUjfM/ZV9/5AEnpXzbpmneIPjd48kubuRo7VCDNKoJjtYc8IuerHnA6k5J4Bpsj+Jfjh46CqPKtY+g5MVlCT1PTLHHsWPoBx9MeF/DGm+EdEh0nS4dkKcu5wWlcjlmPcnA9gAAMAAUAWtG0ax8P6TbaXptusFpbrtRB37kk9yTkknqSa0qKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigArjfiB8P9O8eaMbe4Ahv4QTa3YXLRn0Pcqe4/Ec12VFAHyf4Y8U+Ifg34tn0jVreRrFnH2m1zkMOgliJwM4HXgEcHBAI+ntF1rT/ABDpUGp6XcpcWkwyroenqCOxHQg1ieOvAWl+O9INrer5V3Hk214i5eFv0yp4yp69sEA1886VrHir4J+LZLK8gL2rnMtuWPlXKdBJG3Y46HGR0I4IoA+s6Kw/DPinSvFujR6npFwJYW4dDw8T4BKsOxH5HqCQQTuUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABXLfEDwsnjHwZf6VtH2kr5lsxx8sq5K8npnlSfRjXU0UAfN/7P3ieTTPEF54UvCypd5lhRgQUmQfMuOxKjn/cA719IVl6foGk6VdXN3Y6dbW9zdSNJPNHGA8jMcnLdSCecZxWpQAVyXxE/5FyP/r5X/wBBautrkviJ/wAi5H/18r/6C1AE3gL/AJFaH/ro/wDOunrmPAX/ACK0P/XR/wCddPQAUUUUAFFFFABRRRQAUUVyvjfx1pPgbSfteoSb7iTIt7RDh5mHp6KDjLHgD1JAIBc8VeKtL8HaLJqeqz7IxxHGvLytjhVHc/oOpIFfNU03in44eNQiL5VrH91eTDZRE9SeMsfXqxGBgDgs7LxZ8bvGDXEz7LWMgPLg+TZxnnaozyx9M5J5JABI+lfC3hXS/B+ix6XpMAjiX5nkbl5XxyzHuT+QHAAAxQAzwj4R0zwXokWmaZFgD5ppmHzzPjlmI/QdAOK6GiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigArn/ABZ4R0rxnoz6bqsG5eWimTiSFum5T/ToehFdBRQB8mX2m+Lvgl4rW6t5S9rK22OcA+RdoOdrrnhsdicjkgnqfoHwL8RdH8d2HmWbCC/jXM9lIw3p7j+8ue49sgHiui1bSLDXdNm07VLWO5tJhh45BkH3HcEdQRyDyK+bPG/wx134c6mPEPhq4uZNOhbek8X+ttfZ8DlccbuhGQQO4B9R0V5D8N/jVZeJVh0rX3jstWOFSbO2K4PbB/hY+h4J6HkAevUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFAGbrc9/aaHfXGl26XF9FA7wQyEgO4BIXjnn9T3HWvJvhB8VNT8WeItQ0rXpozPMvn2YjQIq7fvRgdTxhhkk8Nz0r2uvlX4j6VdfDf4sQ61pibIJpRfWwHC5z+8j47ZJGB0VgKAPqquS+In/IuR/9fK/+gtW7o+qW2uaPZ6pZtutruJZYz3AIzg+hHQjsRUet6NDrtiLSeV41Dh8pjOQCO496AMzwF/yK0P8A10f+ddPWdo2kxaLpy2cMjyIrFgz4zknPYCtGgAooooAKKKKACimO6opZiAoGSScV4b8SPjnHaedpHhKRJrjlZdRHKIe4j7Mf9rp6ZzkAHY/Eb4q6Z4GtntIDHea2y/u7YNlYsjIaQjoO4HU+wOR4t4V8F+JPi94gk1vWrqZNPL4mvWGCwH/LOJcY4/Ic9Twdv4d/Bm98RTrr/i/z47OVvNW3kY+ddEnJZznKqTzz8x56DBP0Va2sFjaxWtrDHDbxKFjijUKqgdAAOAKAKmh6Fp3hzSYdN0q1S3tYhwqjknuzHqSe5PJrToooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigApjKHUqwBBGCCOtPooA8L+I3wKivjNq3hJEguDl5NO4WNz6xnop/2TwexGMHmfAvxk1fwfcDQvFcFzc2cDeWWkBFxa44wQeWA9DyB0OABX01XGeOPhtoXjm2JvIvs+oKu2K+iUb19A395fY9MnBBOaAOi0nWNP17TotQ0u8iu7STlJIzke4PcEdweR0IFaNfJt3pvjn4La39pgkIs5GwJowXtrkdldeMHGeDgjnB717R4D+MeheL/ACrK6ZdN1ZsDyJW+SU/9M26E/wCycHnjOM0AelUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAV518ZfCX/CUeBbiWCPdf6bm6gwOWAHzr68rk4HUqK9FpCARg96APC/2efFvn6feeFrmTL2+bm0z3jJw6j6MQcf7R9K9qvb+102ATXk6wxlgoZumTkgfoa8L0/4U+JdB+MR1LQIoIdHguROk00gVTE/34gBliQCyjjHAJIzXqXxE/5FyP8A6+V/9BagDpLO9ttQtxcWkyyxEkBl6EjrVmuY8Bf8itD/ANdH/nXT0AFFFISAMngUALWL4j8UaR4U0x7/AFm8S3hGdinl5D/dRRyx+nTqcDmvPPHvxx0nw8JbDQTFqmpDKmQHMER9yPvkeg49SCMV5doPgvxl8XdX/tfVbqVLJjhr65U7cZ+7CgwCAc9MKDnJz1AJ/FvxJ8S/E7UhoOgWlxDYTNtS0gOZJx6yMOAAOSMhR3JxmvSvhx8FbDw0YdU18RX2rD5kjxmG3PbAP3mHqeAegyM13HhLwRongrTha6TbYkbHnXMmDLMR/ebA49AMAdhyc9LQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQBXvLO3v7SW1vLeO4t5VKvFKoZWB6gg8EV4V47+AKuZNQ8Htsblm0+Z+D7Rsen0Y49x0r32igD5e8LfF3xT4FvP7G8TW1xeWsJ2NDcgrcQj/ZY9RjkBsjAGCBXv8A4X8a6D4xtDPo1+kzqAZLdvllj/3l6+2RkHsTR4o8F6D4xtPs+s2KTMoIjnX5ZY/91hyOecHIPcGvA/E/wY8U+D7z+1fC1zPfQQkujWxKXMQ/3Qfm44yvJ9AKAPp6ivnPwh8f9QsHWw8W2jXSKdpuoUCyoQcHenAb8MEY6E17noHifRPFFn9q0XUYbuMAbghwyZ7MpwVP1AoA2aKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigArhfH2q6fLp50yO+t3vo5Vke2WQGRFwRkqDkDJHJ9a7hlDAqehGCK+PvEemz/AA5+J11bsXNssvmRs2SZLd+RknqR0J7spoA+nPAX/IrQ/wDXR/5109ea6P458O+E/BcFxqupRRs7M0cCENLICeNqjkjtngDuRXmHin45eIfElx/ZnhW0lsIpW2I0Y8y6lz0AxnaT6Lk+hoA9q8YfEbw74Kgb+0bsSXmMpZQENK2ehIz8o9yQPTNeB6/8QfGnxT1A6Po1rNDZyHAsrMk7l6Zlk4yOec4Xpxxmtrwh8BtW1mYal4uupLOKQ72gVt1xKTySzHIXPvk9cgGvetC8OaR4Z08WOj2EVpAMZCDlyO7MeWPuSTQB5b4F+A2n6X5V/wCKGjv7wYZbNP8AURn/AGj1c+xwOvB617JHGkUaxxoqogCqqjAAHAAHpUtFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFAHHeLvhp4a8ZKz6hZeVeEcXlthJR9TjDD2YH2xXh+vfB3xl4Kvf7T8NXU19FHkrNZEx3CD3TOT/wEnPcCvqGigD5t8L/ALQGsaU4s/FNib5EO1pogIp1wcEMvCsRjGPlPqTXtfhnx74a8XRj+yNTiknIybaQ7JV/4CcEgeoyPejxP4B8NeL4z/a2mRPPjAuoxsmXHA+YcnHocj2rxbxL+z1q1g5uvDGoreop3JBORFMvphuFY+520AfSFFfK1h8TPiJ8P7pbDWo5541P+o1SNi2B1KyZBI9Dkj2r0/w58f8AwvqoWPVUn0ic9TIPNiJ9AyjP5qB70AetUVS0/VLDVrVbrTry3u7dukkEgdfpkE1doAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKzdW17SdBtvtGralbWUeODPKF3ewBOSfYUAaVFeM+I/2htBsA8OhWk+pzDgSuDFD+o3HHpgZ9a83ufGHxL+JszWmmrdG2Y7Wh09DFEoPZ5M9PZmxQB754p+J/hXwkrpfaik12uR9ktcSS59CAcKf94ivnP4g+OJvidrtkLHQzE8IaKBYt0s8oJBwcDnGCQAOMnk13Xhj9nWZylx4n1IRrwTa2Ryx9mkIwPfAPsa9m8PeEdB8K25i0bTILXIw0gBaR/8Aec5Y/QnAoA8B8JfALXNXMd14hmGl2pAPkjD3DDHTHRePUkj0r3fwt4H8PeD7fy9H09I5SMPcP80sn1Y849hge1dLRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAVb7T7PU7Vra/tILq3f70U8YdT9QQRXmHiL4BeFtXLy6Y9xpFw2cCI+ZFn1KNz+AYD2r1migD5av/AIOeP/CVy17oU7XIXpNps5jlA91JBJ9gTS6d8a/Hnhe4Flrlut0U+9HqFu0UwH1GDn3INfUlU7/S9P1W3+z6jY293Cf+WdxEsi/kQRQB5Tov7RHhm9CJqtje6bIfvMAJox+K4Y/9816Jo3jPw1r+3+y9csrl26RLKBJ+KHDD8RXIa18CvBWrbnt7W40yVud1pKdpP+62QB7ACvPdY/Zw1eEs+ja1a3S9QlzG0LfQEbgf0oA+j6K+VRofxh8F4FqusiBPuray/ao8DvsBYAfUCrFp8evG+kSeRqdtZ3LqcOLm2aKT/wAdKgfiKAPqKivCdO/aTsWwNT8PXEXq1tOsmfwYLj6ZP1rqrD48eBbxR5t7dWRPa4tWJ/NNw/WgD0yiuWs/iN4Nv1zb+JtLBPQS3Cxn8mINb1rqVjfDNpe21x/1ylVv5GgC3RRRQAUUUUAFFFFABRRRQAUVRu9Y0ywH+malaW4H/PadUx+ZFYF78TfBOngmfxNpzeohl80/+OZoA62ivLr/AOP3gezB8ie+vj/072xX/wBGFa5XUP2lIQGXTfDkj8cPc3IXH1VVOfzFAHvdJnHNfLdx8bviDr8xt9Ihht3PRLC0Mr4/4Fu/QCoT4N+LfjTH9ojVDA/JGoXPlIP+2ZII/BaAPoXWPiB4T0AMNR1+yjdesSSeZIPqq5b9K871v9ovQ7Xcmi6Xd3zjgSTMIUPuOrH6ECsHSP2bbx9razr0EQB5js4jJkf7zbcfka9E0T4KeCNGKu+mtqEq9JL6TzAfqoAU/iKAPHLv4sfEfxncNaaJHLAG48rS7cswB6EucsPcggfSrOlfAzxn4iuvtniC8Sx38vJdSm4nI7cAkfmwNfS1rZ21jAtvaW8NvCv3Y4UCKPoAMCrFAHmPhz4F+ENE2S3kEmrXK4Ja7PyA+0YwCPZt1ej21tBZ26QW0EcEKDCRxIFVR6AAYFT0UAFFFFABRRRQAV4Q37StoGI/4Rifgkf8fg/+Ir3evj34RWFnqnxR0u0v7SC7tpPP3QzxiRGxE5GVIIOCAenUUAelf8NLWf8A0LE+P+vwf/E1raV+0T4ZvJ1i1GwvtPDHHm4EqL9cYb8ga9B/4QPwh/0Kuh/+C+L/AOJrz34ofCbw5J4T1DV9H0+LT7+xha4/0cbY5EUEspUcDgHBAByBnigD1fT7+01SyhvbG4juLWZd0csTblYexH5fUEVcr55/Zx1u4N7q2gu7NbeULuNSciNgwVsfUMuf92voagAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKq3dhZ6hF5V7ZwXMf9yaMOPyINWqKAOK1H4T+BtSJM3hy1jJ5zbFoMH2CED8MVy99+zv4RuSWtbvVLQnoFlV1H4MpP6167RQB8/3v7NXJNj4m47JPafzYN/SsG6/Z08VxEm21HSZ1HQGSRGP4FCP1r6eooA+WP8AhUfxR03/AI8mkIH/AD7akE/my0f8Ix8a7HhZNfAHZNU3j8hIRX1PRQB8sbPjbb/9DGf+BF/6mj7f8bU2/J4j9v8ARifz+X+dfU9FAHyx9t+Nrj7niT/wHI/pR5HxtuP4vEY/7aFP6ivqeigD5Z/4RH41X4+eTXWB7S6sF/QyCk/4U38TNS/4/WAz/wA/OoB/5Fq+p6KAPmW1/Zx8TyHN1qulQjvsaSQj8NoH61u2f7NMYIN74mZh3SGzA/Usf5V77RQB5NYfs9+DrUhrqXUr0jqJJwqn8FUEfnXVad8L/BGl4Nv4bsWI6GdTOf8Ax8muvooAggtYLWERW0EcMY6JGgUD6AVPRRQAUUUUAFFFFABRRRQAUUUUAFFFFABXxv8ACzWdP0D4ladqeqXC21nD52+VgSF3ROo4AJ5JA6d6+yK+LPh94bsvFnjux0S/knjtrjzdzQMFcbY2YYyCByo6g0AfTf8AwuHwCB/yMcH/AH5l/wDia4L4lfGnQ77w1e6J4cklvrm+jMDz+UyJGjcMAGALEgkDAxznPAB1v+GcvCH/AEEdc/7/AMX/AMarA8Q/AOTSLV9T8H6zffbrYGRIZSBIxHZJEC4b0GOc9RQBqfAXwPqGhWt7r2qW0ltJeIsNtFIpVxGDksQeRk7cA88Z6EV7VXhvwa+Kt/rmoL4a8QTfaLpkLWl02A77Rko3qcAkHqcHOTXuVABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAV8i/BP8A5K/pH0uP/RL19dV8X6BZ+MvC+vw6xpmhakt3AXCF7CRh8ylTwR6E0AfaFQ3FxFa28tzPIscMSF5HY4CqBkkn0Aya+bP+FofF7/oEXH/gob/CqOoz/F/x9F/Z11Yap9lkPzRfZfssTezMQoI46EkcDvQBh/DhmvvjDpMtmrKr37SgAdEAZj/46DmvsOvKvhT8J/8AhCWfVtVljn1iWMoqx8pbqcZAJ6scYJ6AcDqSfVaACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooA//9k=\"}]}"},{"id":59249,"title":"Compute the total length of lines between all vertices of a regular polygon","description":"Write a function to compute the total length of between all vertices of a regular polygon inscribed in a unit circle. For example, a square in a unit circle would have side length of  and each of the two diagonals would have a length of 2. Therefore, for  the total length is . In the hexagon below, there are 6 lines of length 1 connecting adjacent points, 3 lines of length 2 connecting opposite points, and 6 lines of length  connecting points two away; therefore, for , the total length is . \r\n","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 442.4px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 221.2px; transform-origin: 407px 221.2px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 105.4px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 52.7px; text-align: left; transform-origin: 384px 52.7px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 358.892px 8px; transform-origin: 358.892px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function to compute the total length of between all vertices of a regular polygon inscribed in a unit circle. For example, a square in a unit circle would have side length of \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"23\" height=\"20\" alt=\"sqrt(2)\" style=\"width: 23px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 176.6px 8px; transform-origin: 176.6px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and each of the two diagonals would have a length of 2. Therefore, for \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"36.5\" height=\"18\" alt=\"n = 4\" style=\"width: 36.5px; height: 18px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 56.7833px 8px; transform-origin: 56.7833px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e the total length is \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"66.5\" height=\"20.5\" alt=\"4(1+sqrt(2))\" style=\"width: 66.5px; height: 20.5px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 224.833px 8px; transform-origin: 224.833px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. In the hexagon below, there are 6 lines of length 1 connecting adjacent points, 3 lines of length 2 connecting opposite points, and 6 lines of length \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"23\" height=\"20\" alt=\"sqrt(3)\" style=\"width: 23px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 133.408px 8px; transform-origin: 133.408px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e connecting points two away; therefore, for \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"36.5\" height=\"18\" alt=\"n = 6\" style=\"width: 36.5px; height: 18px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 58.725px 8px; transform-origin: 58.725px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, the total length is \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"66.5\" height=\"20.5\" alt=\"6(2+sqrt(3))\" style=\"width: 66.5px; height: 20.5px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.88333px 8px; transform-origin: 3.88333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 328px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 164px; text-align: left; transform-origin: 384px 164px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cimg class=\"imageNode\" width=\"438\" height=\"328\" style=\"vertical-align: middle;width: 438px;height: 328px\" src=\"data:image/png;base64,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\" alt=\"hexagon\" data-image-state=\"image-loaded\"\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = totalLength(n)\r\n  y = n*(n/2-1+sqrt(n/2));\r\nend","test_suite":"%% Point\r\nn = 1;\r\nassert(abs(totalLength(n))\u003ceps)\r\n\r\n%% Line\r\nn = 2;\r\ny_correct = 2;\r\nassert(abs(totalLength(n)-y_correct)./y_correct\u003c1e-12)\r\n\r\n%% Triangle\r\nn = 3;\r\ny_correct = 3^(3/2);\r\nassert(abs(totalLength(n)-y_correct)./y_correct\u003c1e-12)\r\n\r\n%% Square\r\nn = 4;\r\ny_correct = 4*(1+sqrt(2));\r\nassert(abs(totalLength(n)-y_correct)./y_correct\u003c1e-12)\r\n\r\n%% Hexagon\r\nn = 6;\r\ny_correct = 22.392304845413271;\r\nassert(abs(totalLength(n)-y_correct)./y_correct\u003c1e-12)\r\n\r\n%% Octagon\r\nn = 8;\r\ny_correct = 40.218715937006777;\r\nassert(abs(totalLength(n)-y_correct)./y_correct\u003c1e-12)\r\n\r\n%% Dodecagon\r\nn = 12;\r\ny_correct = 91.149049352701866;\r\nassert(abs(totalLength(n)-y_correct)./y_correct\u003c1e-12)\r\n\r\n%% Heptadecagon\r\nn = 17;\r\ny_correct = 183.4592171734470;\r\nassert(abs(totalLength(n)-y_correct)./y_correct\u003c1e-12)\r\n\r\n%% Icosikaitetragon\r\nn = 24;\r\ny_correct = 366.1692405183716;\r\nassert(abs(totalLength(n)-y_correct)./y_correct\u003c1e-12)\r\n\r\n%% Icosidodecagon\r\nn = 32;\r\ny_correct = 651.3749639995958;\r\nassert(abs(totalLength(n)-y_correct)./y_correct\u003c1e-12)\r\n\r\n%% Heptacontatetragon\r\nn = 74;\r\ny_correct = 3485.606258980444;\r\nassert(abs(totalLength(n)-y_correct)./y_correct\u003c1e-12)\r\n\r\n%% Hectogon\r\nn = 100;\r\ny_correct = 6365.674116287712;\r\nassert(abs(totalLength(n)-y_correct)./y_correct\u003c1e-12)\r\n\r\n%% ?-gon\r\nn = floor(totalLength(21));\r\ny_correct = 49910.46655373736;\r\nassert(abs(totalLength(n)-y_correct)./y_correct\u003c1e-12)\r\n\r\n%%\r\na = floor(totalLength(1:1000));\r\nassert(isequal(sum(a),212524005))\r\nassert(isequal(max(a),636619))\r\nassert(isequal(sum(a(isprime(a))),15303427))\r\nassert(isequal(a(mod(a,171)==0),[0 66006 119358 191178 225378 393300]))\r\n\r\n%%\r\nfiletext = fileread('totalLength.m');\r\nillegal = contains(filetext, 'assignin') || contains(filetext, 'assert') || contains(filetext, 'regexp'); \r\nassert(~illegal)","published":true,"deleted":false,"likes_count":0,"comments_count":7,"created_by":46909,"edited_by":46909,"edited_at":"2023-12-03T18:16:16.000Z","deleted_by":null,"deleted_at":null,"solvers_count":8,"test_suite_updated_at":"2023-12-03T18:16:16.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2023-12-02T17:23:24.000Z","updated_at":"2026-01-04T09:44:09.000Z","published_at":"2023-12-02T17:29:06.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a function to compute the total length of between all vertices of a regular polygon inscribed in a unit circle. For example, a square in a unit circle would have side length of \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"sqrt(2)\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\sqrt{2}\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and each of the two diagonals would have a length of 2. Therefore, for \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"n = 4\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en=4\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e the total length is \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"4(1+sqrt(2))\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e4(1+\\\\sqrt{2})\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. In the hexagon below, there are 6 lines of length 1 connecting adjacent points, 3 lines of length 2 connecting opposite points, and 6 lines of length \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"sqrt(3)\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\sqrt{3}\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e connecting points two away; therefore, for \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"n = 6\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en = 6\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, the total length is \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"6(2+sqrt(3))\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e6(2+\\\\sqrt{3})\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"328\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"438\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"middle\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"hexagon\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId1\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/image\",\"target\":\"/media/image1.png\",\"relationshipId\":\"rId1\"}]},{\"partUri\":\"/media/image1.png\",\"contentType\":\"image/png\",\"content\":\"data:image/png;base64,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\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":44492,"title":"Approximate the cosine function ","description":"Without using MATLAB trigonometric functions, calculate the cosine of an argument x to a precision of 0.0001\r\nHint: You may wish to consider the cosine Maclaurin series.","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 51.5px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 25.75px; transform-origin: 407px 25.75px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21.5px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.75px; text-align: left; transform-origin: 384px 10.75px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 262px 8px; transform-origin: 262px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWithout using MATLAB trigonometric functions, calculate the cosine of an argument\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 2px 8px; transform-origin: 2px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 4px 8px; transform-origin: 4px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; perspective-origin: 4px 8.5px; transform-origin: 4px 8.5px; \"\u003ex\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 52.5px 8px; transform-origin: 52.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e to a precision of\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 2px 8px; transform-origin: 2px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 24px 8px; transform-origin: 24px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; perspective-origin: 24px 8.5px; transform-origin: 24px 8.5px; \"\u003e0.0001\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 16px 8px; transform-origin: 16px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eHint:\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 93.5px 8px; transform-origin: 93.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e You may wish to consider the\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 2px 8px; transform-origin: 2px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://en.wikipedia.org/wiki/Taylor_series#Trigonometric_functions\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003ecosine Maclaurin series\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 2px 8px; transform-origin: 2px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = myCos(x)\r\n    y = 1 - 0.5*x^2;\r\nend","test_suite":"%%\r\nfiletext = fileread('myCos.m');\r\nassert(isempty(strfind(filetext, 'regexp')),'regexp hacks are forbidden')\r\n\r\n\r\n%%\r\nfiletext = fileread('myCos.m');\r\ntrigUsed = any(strfind(filetext, 'cos')) || any(strfind(filetext, 'sin')) ||...\r\n     any(strfind(filetext, 'sec')) || any(strfind(filetext, 'tan')) || any(strfind(filetext, 'cot'));\r\nassert(~trigUsed, 'Cannot use MATLAB trigonometric functions')\r\n\r\n%%\r\nx = 0;\r\nassert(abs(myCos(x)-cos(x)) \u003c 0.0001)\r\n\r\n%%\r\nx = pi;\r\nassert(abs(myCos(x)-cos(x)) \u003c 0.0001)\r\n\r\n%%\r\nx = pi/2;\r\nassert(abs(myCos(x)-cos(x)) \u003c 0.0001)\r\n\r\n%%\r\nx = 5*pi/3;\r\nassert(abs(myCos(x)-cos(x)) \u003c 0.0001)\r\n","published":true,"deleted":false,"likes_count":1,"comments_count":3,"created_by":140356,"edited_by":223089,"edited_at":"2022-10-17T13:07:34.000Z","deleted_by":null,"deleted_at":null,"solvers_count":343,"test_suite_updated_at":"2022-10-17T13:07:34.000Z","rescore_all_solutions":false,"group_id":61,"created_at":"2018-01-07T23:20:12.000Z","updated_at":"2026-02-11T20:08:56.000Z","published_at":"2018-01-07T23:20:12.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWithout using MATLAB trigonometric functions, calculate the cosine of an argument\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ex\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e to a precision of\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e0.0001\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eHint:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e You may wish to consider the\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://en.wikipedia.org/wiki/Taylor_series#Trigonometric_functions\\\"\u003e\u003cw:r\u003e\u003cw:t\u003ecosine Maclaurin series\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":60301,"title":"Compute the area of a lune","description":"Write a function to compute the area of the shaded moon-shaped region in the figure below—that is, the area of a smaller circle that does not overlap with a larger circle. The input will be the radius  of the smaller circle, the radius  of the larger circle, and the separation  between centers of the circles. \r\n","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 405.7px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 202.85px; transform-origin: 407px 202.85px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 31.5px; text-align: left; transform-origin: 384px 31.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 377.175px 8px; transform-origin: 377.175px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function to compute the area of the shaded moon-shaped region in the figure below—that is, the area of a smaller circle that does not overlap with a larger circle. The input will be the radius \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003ea\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 98.7917px 8px; transform-origin: 98.7917px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e of the smaller circle, the radius \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eb\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 41.225px 8px; transform-origin: 41.225px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e of the larger circle, and the separation \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003ec\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 98.4px 8px; transform-origin: 98.4px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e between centers of the circles. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 333.7px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 166.85px; text-align: left; transform-origin: 384px 166.85px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cimg class=\"imageNode\" width=\"438\" height=\"328\" style=\"vertical-align: baseline;width: 438px;height: 328px\" src=\"data:image/png;base64,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\" data-image-state=\"image-loaded\"\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = luneArea(a,b,c)\r\n%  a = radius of smaller circle\r\n%  b = radius of larger circle\r\n%  c = distance between the centers of the circles\r\n   y = (b-a)*(b+c)/2;\r\nend","test_suite":"%%\r\na = 1; \r\nb = 1.2;\r\nc = 0.9; \r\nA = luneArea(a,b,c);\r\nA_correct = 1.285341014608472;\r\nassert(abs(A-A_correct)/A_correct\u003c1e-13)\r\n\r\n%%\r\na = 4; \r\nb = 5;\r\nc = 3; \r\nA = luneArea(a,b,c);\r\nA_correct = 13.950360778678039;\r\nassert(abs(A-A_correct)/A_correct\u003c1e-13)\r\n\r\n%%\r\na = exp(1); \r\nb = pi;\r\nc = -psi(1); \r\nA = luneArea(a,b,c);\r\nA_correct = 0.443456401155954;\r\nassert(abs(A-A_correct)/A_correct\u003c1e-13)\r\n\r\n%%\r\na = 3; \r\nb = 4;\r\nc = 1.01; \r\nA = luneArea(a,b,c);\r\nA_correct = 0.0065019633283;\r\nassert(abs(A-A_correct)/A_correct\u003c8e-12)\r\n\r\n%%\r\na = 1/sqrt(2); \r\nb = 1;\r\nc = a; \r\nA = luneArea(a,b,c);\r\nA_correct = 1/2;\r\nassert(abs(A-A_correct)/A_correct\u003c1e-13)\r\n\r\n%% \r\na = 5*rand;\r\nb = a*sqrt(2);\r\nc = a; \r\nA = luneArea(a,b,c);\r\nA_correct = b^2/2;\r\nassert(abs(A-A_correct)/A_correct\u003c1e-13)","published":true,"deleted":false,"likes_count":1,"comments_count":2,"created_by":46909,"edited_by":46909,"edited_at":"2024-06-01T23:28:36.000Z","deleted_by":null,"deleted_at":null,"solvers_count":8,"test_suite_updated_at":"2024-06-01T23:28:36.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2024-05-13T12:25:08.000Z","updated_at":"2026-01-04T10:52:42.000Z","published_at":"2024-05-13T12:25:26.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a function to compute the area of the shaded moon-shaped region in the figure below—that is, the area of a smaller circle that does not overlap with a larger circle. The input will be the radius \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ea\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e of the smaller circle, the radius \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eb\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e of the larger circle, and the separation \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ec\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e between centers of the circles. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"328\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"438\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"baseline\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId1\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/image\",\"target\":\"/media/image1.png\",\"relationshipId\":\"rId1\"}]},{\"partUri\":\"/media/image1.png\",\"contentType\":\"image/png\",\"content\":\"data:image/png;base64,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\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":1257,"title":"PONG 001: Player  vs Wall, 4 Lives, Interactive download","description":"Variation of the Original Classic PONG game brought to Cody.\r\n\r\nAttempt to keep the ball alive against a Wall. The ball speeds up on every hit. When it is missed it restarts at a new location. The start locations and sequences are purely deterministic. Movement of the paddle are max up/down steps of -1 to 1 (effective delta 50) or no move. Partial paddle moves allowed.\r\n\r\nPaddle center is provided and paddle covers +/- 50 units.\r\nThe field is square at 1000 by 1000 with 3 walls and the lower left corner being (0,0)\r\n\r\nTo aid in development of your routine, a PONG_Interactive_001a.m file that creates a solver script and video has been posted at \u003chttps://sites.google.com/site/razapor/matlab_cody/PONG_Interactive_001a.m PONG_Interactive_001a.m\u003e. (Right click, 'save link as'). The routine creates a PONG_001_solver.m script from the interactive play. The script demonstrates Interactivity, figure/KeyPressFcn, listdlg, and VideoWriter.\r\n\r\n\r\n\u003chttps://sites.google.com/site/razapor/matlab_cody/PONG_001_video_63_185.mp4 PONG Interactive 63 Returns\u003e (MP4)\r\n\r\n\r\n\r\n*Inputs:* (paddle,ball)  \r\n \r\n   paddle = 500 ; Paddle Center on the Y-axis, Paddle is +/- 50 from center\r\n   ball=[500 500 40 60]; % x y vx vy  Posiiton and Velocity, Treated as a Point\r\n\r\n*Output:* Direction\r\n\r\n   1 Up, -1 is Down, 0-No move\r\n   Paddle moves 50*direction, half paddle step. abs(direction)\u003c=1 is allowed\r\n\r\n*Pass Criteria:* 10 hits, a score of 450 or better\r\n\r\n*Scoring:* 100 - 5 * Hits + 100 * Lives,  (500 - 5 * hits  for \u003c 100 hits)\r\n\r\n*Game Theory:* Position Paddle to minimize travel to next location. Vx=1.1*Vx and Vy=1.05*Vy after every return.\r\n\r\n*Near Future:* Paddle vs Paddle (Mirror). Followed by Angle varation based on Paddle/Ball Position","description_html":"\u003cp\u003eVariation of the Original Classic PONG game brought to Cody.\u003c/p\u003e\u003cp\u003eAttempt to keep the ball alive against a Wall. The ball speeds up on every hit. When it is missed it restarts at a new location. The start locations and sequences are purely deterministic. Movement of the paddle are max up/down steps of -1 to 1 (effective delta 50) or no move. Partial paddle moves allowed.\u003c/p\u003e\u003cp\u003ePaddle center is provided and paddle covers +/- 50 units.\r\nThe field is square at 1000 by 1000 with 3 walls and the lower left corner being (0,0)\u003c/p\u003e\u003cp\u003eTo aid in development of your routine, a PONG_Interactive_001a.m file that creates a solver script and video has been posted at \u003ca href=\"https://sites.google.com/site/razapor/matlab_cody/PONG_Interactive_001a.m\"\u003ePONG_Interactive_001a.m\u003c/a\u003e. (Right click, 'save link as'). The routine creates a PONG_001_solver.m script from the interactive play. The script demonstrates Interactivity, figure/KeyPressFcn, listdlg, and VideoWriter.\u003c/p\u003e\u003cp\u003e\u003ca href=\"https://sites.google.com/site/razapor/matlab_cody/PONG_001_video_63_185.mp4\"\u003ePONG Interactive 63 Returns\u003c/a\u003e (MP4)\u003c/p\u003e\u003cp\u003e\u003cb\u003eInputs:\u003c/b\u003e (paddle,ball)\u003c/p\u003e\u003cpre\u003e   paddle = 500 ; Paddle Center on the Y-axis, Paddle is +/- 50 from center\r\n   ball=[500 500 40 60]; % x y vx vy  Posiiton and Velocity, Treated as a Point\u003c/pre\u003e\u003cp\u003e\u003cb\u003eOutput:\u003c/b\u003e Direction\u003c/p\u003e\u003cpre\u003e   1 Up, -1 is Down, 0-No move\r\n   Paddle moves 50*direction, half paddle step. abs(direction)\u0026lt;=1 is allowed\u003c/pre\u003e\u003cp\u003e\u003cb\u003ePass Criteria:\u003c/b\u003e 10 hits, a score of 450 or better\u003c/p\u003e\u003cp\u003e\u003cb\u003eScoring:\u003c/b\u003e 100 - 5 * Hits + 100 * Lives,  (500 - 5 * hits  for \u0026lt; 100 hits)\u003c/p\u003e\u003cp\u003e\u003cb\u003eGame Theory:\u003c/b\u003e Position Paddle to minimize travel to next location. Vx=1.1*Vx and Vy=1.05*Vy after every return.\u003c/p\u003e\u003cp\u003e\u003cb\u003eNear Future:\u003c/b\u003e Paddle vs Paddle (Mirror). Followed by Angle varation based on Paddle/Ball Position\u003c/p\u003e","function_template":"function pdir = PONG_001_solver(paddle,ball)\r\n %  paddle=500; % position y % min max paddle [50 950]\r\n %  ball=[500 500 40 60]; % x y vx vy  Treated as a Point\r\n %\r\n % Output Paddle movement : pdir range [-1 1]\r\n %\r\n % Paddle Size is +/- 50 from paddle value\r\n % Predict ball location and move to within +/- 50\r\n % or Load PONG_001_solver.m from Interactive Play with file create\r\n \r\npdir = randi([-1 1]);\r\n \r\n \r\n","test_suite":"%%\r\nfeval(@assignin,'caller','score',500);\r\n\r\n pwidth=50; % Total size +/- 50 for 101 Paddle\r\n bwidth=10; % Radius of ball\r\n\r\n vup=10; % Sub-sampling ball movements for Interactive\r\n spfx=1.10; % Speed increase factor\r\n spfy=1.05; % to Avoid fixed Paddle solution\r\n negVmax=-200;\r\n posVmax=210;\r\n mov_step=50; % Paddle Quantized Movement  (1/2 Paddle)\r\n maxLives=4;\r\n maxHits=100;\r\n\r\n% Initial Start\r\n paddle=500; % position y % min max paddle [50 950]\r\n ball=[500 500 40 60]; % x y vx vy  Treated as a Point\r\n\r\nlives=0; % Lives\r\nhits=0;\r\nentry=0;\r\n\r\nwhile lives\u003cmaxLives \u0026\u0026 hits\u003cmaxHits\r\n\r\n [curdir]=PONG_001_solver(paddle,ball); % FUNCTION CALL\r\n\r\n if abs(curdir)\u003e1,curdir=0;end % Max 1 / -1 allowed\r\n curmov=mov_step*curdir;\r\n\r\n if entry==0\r\n  curdirvec=curdir;\r\n  entry=1;\r\n else\r\n  curdirvec=[curdirvec curdir]; % Saving moves for file create\r\n end\r\n\r\n% Paddle Move\r\n paddle=max(pwidth,min(1000-pwidth,paddle+curmov)); % [50 : 950] limits\r\n\r\n% Ball Move : Hopefully I got the Mirror solutions right\r\n\r\n  for j=1:vup\r\n    % ball=[500 500 1 1]; % x y vx vy  Treated as a Point\r\n\r\n    if ball(1)+ball(3)/vup\u003c=0 % Check if Point is Over\r\n\r\n    % Find x=0 crossing and check if paddle is within\r\n    % [paddle-pwidth-bwidth,paddle+pwidth+bwidth] pwidth=50; \r\n    % set speed scalar\r\n    \r\n      xc=ball(2)-ball(1)*ball(4)/ball(3);\r\n      if xc\u003e=1000\r\n       xc=1000-(xc-1000);\r\n      else\r\n       xc=abs(xc);\r\n      end\r\n      \r\n      paddlemax= paddle+pwidth+bwidth;\r\n      paddlemin= paddle-pwidth-bwidth;\r\n      \r\n      if xc\u003epaddlemax || xc\u003cpaddlemin % Swing and a Miss\r\n       lives=lives+1;\r\n       fprintf('Oops %i\\n',lives);\r\n       \r\n       if lives\u003e=maxLives,break;end\r\n       % draw ball\r\n       %paddle=500; % position y % min max paddle [50 950]\r\n\r\n       % Reset Ball Keep deterministic but different\r\n       ball=[500-100*lives 500 40+11*lives 35-3*lives];\r\n\r\n       break;\r\n      end\r\n      \r\n      \r\n      % Ball returned\r\n      hits=hits+1;\r\n      ball(1:2)=ball(1:2)+ball(3:4)/vup;\r\n      \r\n      ball(1)=-ball(1);\r\n      ball(3)=-spfx*ball(3);\r\n      \r\n      if ball(2)\u003c0\r\n       ball(2)=-ball(2);\r\n       ball(4)=-spfy*ball(4);\r\n      elseif ball(2)\u003e1000\r\n       ball(2)=2000-ball(2);\r\n       ball(4)=-spfy*ball(4);\r\n      else\r\n       ball(4)=spfy*ball(4);\r\n      end\r\n      \r\n      ball(3)=max(negVmax,min(posVmax,ball(3)));\r\n      ball(4)=max(negVmax,min(posVmax,ball(4)));\r\n      \r\n    else % Wall bounces\r\n     ball(1:2)=ball(1:2)+ball(3:4)/vup;\r\n     \r\n     if ball(1)\u003e=1000 % To the right\r\n      ball(1)=1000-(ball(1)-1000);\r\n      ball(3)=-ball(3);\r\n      if ball(2)\u003e=1000 % TR\r\n       ball(2)=1000-(ball(2)-1000);\r\n       ball(4)=-ball(4);\r\n      elseif ball(2)\u003c=0 % BR\r\n       ball(2)=-ball(2); % abs\r\n       ball(4)=-ball(4);\r\n      end\r\n     else % Middle\r\n      if ball(2)\u003e=1000 % TM\r\n       ball(2)=1000-(ball(2)-1000);\r\n       ball(4)=-ball(4);\r\n      elseif ball(2)\u003c=0 % BM\r\n       ball(2)=-ball(2); % abs\r\n       ball(4)=-ball(4);\r\n      end\r\n     end\r\n    \r\n     \r\n    end % Ball Pass / New Position\r\n\r\n  end % j vup\r\n\r\n\r\nend % while Alive and Hits \u003c Total Success\r\n\r\n%fprintf('%i ',curdirvec);fprintf('\\n'); % Moves\r\nfprintf('Hits %i\\n',hits)\r\nfprintf('Lives %i\\n',lives)\r\nscore= max(0,maxHits-5*hits+100*lives); % \r\n \r\nfprintf('Score %i\\n',score)\r\n% Passing Score is 10 hits to Score 450 or Less\r\n\r\nassert(score\u003c=450,sprintf('Score %i\\n',score))\r\n\r\n\r\nfeval( @assignin,'caller','score',floor(min( 500,score )) );","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":3097,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":16,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":33,"created_at":"2013-02-10T05:51:19.000Z","updated_at":"2026-02-07T15:54:36.000Z","published_at":"2013-02-10T06:57:18.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eVariation of the Original Classic PONG game brought to Cody.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eAttempt to keep the ball alive against a Wall. The ball speeds up on every hit. When it is missed it restarts at a new location. The start locations and sequences are purely deterministic. Movement of the paddle are max up/down steps of -1 to 1 (effective delta 50) or no move. Partial paddle moves allowed.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ePaddle center is provided and paddle covers +/- 50 units. The field is square at 1000 by 1000 with 3 walls and the lower left corner being (0,0)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eTo aid in development of your routine, a PONG_Interactive_001a.m file that creates a solver script and video has been posted at\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://sites.google.com/site/razapor/matlab_cody/PONG_Interactive_001a.m\\\"\u003e\u003cw:r\u003e\u003cw:t\u003ePONG_Interactive_001a.m\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e. (Right click, 'save link as'). The routine creates a PONG_001_solver.m script from the interactive play. The script demonstrates Interactivity, figure/KeyPressFcn, listdlg, and VideoWriter.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:hyperlink w:docLocation=\\\"https://sites.google.com/site/razapor/matlab_cody/PONG_001_video_63_185.mp4\\\"\u003e\u003cw:r\u003e\u003cw:t\u003ePONG Interactive 63 Returns\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e (MP4)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eInputs:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e (paddle,ball)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[   paddle = 500 ; Paddle Center on the Y-axis, Paddle is +/- 50 from center\\n   ball=[500 500 40 60]; % x y vx vy  Posiiton and Velocity, Treated as a Point]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eOutput:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e Direction\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[   1 Up, -1 is Down, 0-No move\\n   Paddle moves 50*direction, half paddle step. abs(direction)\u003c=1 is allowed]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ePass Criteria:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e 10 hits, a score of 450 or better\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eScoring:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e 100 - 5 * Hits + 100 * Lives, (500 - 5 * hits for \u0026lt; 100 hits)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eGame Theory:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e Position Paddle to minimize travel to next location. Vx=1.1*Vx and Vy=1.05*Vy after every return.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eNear Future:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e Paddle vs Paddle (Mirror). Followed by Angle varation based on Paddle/Ball Position\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":59501,"title":"Compute the sum of distances from a point to the sides of an equilateral triangle","description":"Write a function to compute the sum of the (shortest) distances from a point inside an equilateral triangle to the sides of the triangle. That is, for the triangle below, compute the sum . Input will consist of the point (x0,y0) and vectors x and y with the coordinates of the vertices of the triangle. \r\n","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 565.7px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 282.85px; transform-origin: 407px 282.85px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 31.5px; text-align: left; transform-origin: 384px 31.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 381.433px 8px; transform-origin: 381.433px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function to compute the sum of the (shortest) distances from a point inside an equilateral triangle to the sides of the triangle. That is, for the triangle below, compute the sum \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"58.5\" height=\"18\" alt=\"a+b+c\" style=\"width: 58.5px; height: 18px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 95.675px 8px; transform-origin: 95.675px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. Input will consist of the point (\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 7.7px 8px; transform-origin: 7.7px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003ex0\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.94167px 8px; transform-origin: 1.94167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e,\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 7.7px 8px; transform-origin: 7.7px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003ey0\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 42.3917px 8px; transform-origin: 42.3917px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e) and vectors \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.85px 8px; transform-origin: 3.85px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003ex\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 15.5583px 8px; transform-origin: 15.5583px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.85px 8px; transform-origin: 3.85px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003ey\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0.241667px 8px; transform-origin: 0.241667px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e with the coordinates of the vertices of the triangle. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 493.7px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 246.85px; text-align: left; transform-origin: 384px 246.85px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cimg class=\"imageNode\" width=\"495\" height=\"488\" style=\"vertical-align: baseline;width: 495px;height: 488px\" src=\"data:image/png;base64,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\" alt=\"equilateral triangle with distances from a point\" data-image-state=\"image-loaded\"\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function d = sumdist(x,y,x0,y0)\r\n%  x,y = coordinates of the triangle's vertices\r\n%  x0,y0 = coordinates of the point in the interior of the triangle\r\n  d = sum(hypot(x-x0,y-y0));\r\nend","test_suite":"%%\r\nx = [1 6.215999461960969 2.397622843553612];\r\ny = [2 3.397622843553612 7.215999461960969];\r\nx0 = 2.1;\r\ny0 = 3.2;\r\nd = sumdist(x,y,x0,y0);\r\nd_correct = 4.676537180435970;\r\nassert(abs(d-d_correct)/d_correct \u003c 1e-8)\r\n\r\n%%\r\nx = [1   4.284147809382832  3.404163056034262];\r\ny = [-2 -2.879984753348571  0.404163056034262];\r\nx0 = 3;\r\ny0 = -1;\r\nd = sumdist(x,y,x0,y0);\r\nd_correct = 2.944486372867091;\r\nassert(abs(d-d_correct)/d_correct \u003c 1e-8)\r\n\r\n%%\r\nx = [1   1.292541480647668  0.910019578262454];\r\ny = [-2 -1.727200655975001 -1.610251974085906];\r\nx0 = 1.1;\r\ny0 = -1.8;\r\nd = sumdist(x,y,x0,y0);\r\nd_correct = 0.346410161513776;\r\nassert(abs(d-d_correct)/d_correct \u003c 1e-8)\r\n\r\n%%\r\nx = [-4  0.854101966249685 -4.627170779605921];\r\ny = [-8 -4.473288486245162 -2.032868627790361];\r\nx0 = -2;\r\ny0 = -4;\r\nd = sumdist(x,y,x0,y0);\r\nd_correct = 5.196152422706631;\r\nassert(abs(d-d_correct)/d_correct \u003c 1e-8)\r\n\r\n%%\r\nxr = 100*rand; yr = 100*rand; s  = 100*rand;\r\nx = xr+s*[-4  0.854101966249685 -4.627170779605921];\r\ny = yr+s*[-8 -4.473288486245162 -2.032868627790361];\r\nx0 = mean(x);\r\ny0 = mean(y);\r\nd = sumdist(x,y,x0,y0);\r\nd_correct = 5.196152422706631*s;\r\nassert(abs(d-d_correct)/d_correct \u003c 1e-8)\r\n\r\n%%\r\nx = [0 0.819152044288992 -0.087155742747658];\r\ny = [0 0.573576436351046  0.996194698091746];\r\nx0 = 0.2;\r\ny0 = 0.4;\r\nd = sumdist(x,y,x0,y0);\r\nd_correct = 0.866025403784439;\r\nassert(abs(d-d_correct)/d_correct \u003c 1e-8)\r\n\r\n%%\r\nfiletext = fileread('sumdist.m');\r\nillegal = contains(filetext, 'assignin') || contains(filetext, 'assert') || contains(filetext,'regexp'); \r\nassert(~illegal)","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":46909,"edited_by":46909,"edited_at":"2023-12-28T05:22:29.000Z","deleted_by":null,"deleted_at":null,"solvers_count":6,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2023-12-28T05:22:00.000Z","updated_at":"2023-12-28T05:22:29.000Z","published_at":"2023-12-28T05:22:07.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a function to compute the sum of the (shortest) distances from a point inside an equilateral triangle to the sides of the triangle. That is, for the triangle below, compute the sum \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"a+b+c\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ea+b+c\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. Input will consist of the point (\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ex0\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e,\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ey0\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e) and vectors \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ex\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ey\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e with the coordinates of the vertices of the triangle. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"488\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"495\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"baseline\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"equilateral triangle with distances from a point\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId1\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/image\",\"target\":\"/media/image1.png\",\"relationshipId\":\"rId1\"}]},{\"partUri\":\"/media/image1.png\",\"contentType\":\"image/png\",\"content\":\"data:image/png;base64,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\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":57512,"title":"Easy Sequences 89: Double Summation of a Trigonometric Product","description":"Given and angle  in radians and a positive integer , evaluate the following product summation:\r\n                    \r\nwhich 'directly' translates to Matlab as:\r\n    \u003e\u003e PS = @(A,x) sum(arrayfun(@(n) sum(arrayfun(@(m) prod(arrayfun(@(k) 2*sin(k*pi/m+A),0:m-1)),1:n)),1:x));\r\nFor example  and :\r\n    \u003e\u003e x = 3; A = 1;\r\n    \u003e\u003e PS(A,x)\r\n    ans =\r\n        8.9683\r\nPlease present your answer rounded-off to nearest 4 decimal places.","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.440001px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none; white-space: normal; \"\u003e\u003cdiv style=\"block-size: 288px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 492.078125px 144px; transform-origin: 492.078125px 144px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eGiven and angle \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eA\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e in radians and a positive integer \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003ex\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e, evaluate the following product summation:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 46px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 23px; text-align: left; transform-origin: 384px 23px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e                    \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-17px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"236\" height=\"46\" style=\"width: 236px; height: 46px;\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003ewhich 'directly' translates to Matlab as:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgb(247, 247, 247); block-size: 20px; border-bottom-left-radius: 4px; border-bottom-right-radius: 4px; border-end-end-radius: 4px; border-end-start-radius: 4px; border-start-end-radius: 4px; border-start-start-radius: 4px; border-top-left-radius: 4px; border-top-right-radius: 4px; margin-block-end: 10px; margin-block-start: 10px; margin-bottom: 10px; margin-inline-end: 3px; margin-inline-start: 3px; margin-left: 3px; margin-right: 3px; margin-top: 10px; perspective-origin: 489.078125px 10px; transform-origin: 489.078125px 10px; margin-left: 3px; margin-top: 10px; margin-bottom: 10px; margin-right: 3px; \"\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e    \u0026gt;\u0026gt; PS = @(A,x) sum(arrayfun(@(n) sum(arrayfun(@(m) prod(arrayfun(@(k) 2*sin(k*pi/m+A),0:m-1)),1:n)),1:x));\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 10px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 10px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 10px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eFor example \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"36.5\" height=\"18\" style=\"width: 36.5px; height: 18px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"40\" height=\"18\" style=\"width: 40px; height: 18px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgb(247, 247, 247); block-size: 80px; border-bottom-left-radius: 4px; border-bottom-right-radius: 4px; border-end-end-radius: 4px; border-end-start-radius: 4px; border-start-end-radius: 4px; border-start-start-radius: 4px; border-top-left-radius: 4px; border-top-right-radius: 4px; margin-block-end: 10px; margin-block-start: 10px; margin-bottom: 10px; margin-inline-end: 3px; margin-inline-start: 3px; margin-left: 3px; margin-right: 3px; margin-top: 10px; perspective-origin: 489.078125px 40px; transform-origin: 489.078125px 40px; margin-left: 3px; margin-top: 10px; margin-bottom: 10px; margin-right: 3px; \"\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 489.078125px 10px; transform-origin: 489.078125px 10px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e    \u0026gt;\u0026gt; x = 3; A = 1;\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 489.078125px 10px; transform-origin: 489.078125px 10px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e    \u0026gt;\u0026gt; PS(A,x)\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 489.078125px 10px; transform-origin: 489.078125px 10px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e    ans =\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 489.078125px 10px; transform-origin: 489.078125px 10px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e        8.9683\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 10px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 10px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 10px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003ePlease present your answer rounded-off to nearest 4 decimal places.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function p = PS(A,x)\r\n    p = sum(arrayfun(@(n) sum(arrayfun(@(m) prod(arrayfun(@(k) 2*sin(k*pi/m+A),0:m-1)),1:n)),1:x));\r\nend","test_suite":"%%\r\nA = 1; x = 3;\r\np_correct = 8.9683;\r\nassert(isequal(PS(A,x),p_correct))\r\n%%\r\nA = 2:2:20; x = 3:3:30;\r\np_correct = [1.8697 -3.3674 -62.4997 11.5088 -4.8523 -71.5196 25.1022 -3.2420 -64.7730 49.3233];\r\nassert(isequal(arrayfun(@(i) PS(A(i),x(i)),1:10),p_correct))\r\n%%\r\np_correct = 4166.0746;\r\nassert(isequal(sum(arrayfun(@(i) PS(i,i),1:100)),p_correct))\r\n%%\r\nA = 100; x = 200;\r\np_correct = -739.8950;\r\nassert(isequal(PS(A,x),p_correct))\r\n%%\r\nA = 2000; x = 3000;\r\np_correct = 2041.1906;\r\nassert(isequal(PS(A,x),p_correct))\r\n%%\r\nA = 10000; x = 20000;\r\np_correct = -3131.6478;\r\nassert(isequal(PS(A,x),p_correct))\r\n%%\r\nA = 200000; x = 300000;\r\np_correct = -8386548.7261;\r\nassert(isequal(PS(A,x),p_correct))\r\n%%\r\nA = 1000000; x = 2000000;\r\np_correct = -11067350.2876;\r\nassert(isequal(PS(A,x),p_correct))\r\n%%\r\nA = 123456; xs = 200001:200100;\r\nps = arrayfun(@(x) PS(A,x),xs);\r\nss_correct = [-88558 -88558 -88580 12]; \r\nassert(isequal(floor([mean(ps) median(ps) mode(ps) std(ps)]),ss_correct))\r\n%%\r\nfiletext = fileread('PS.m');\r\nnot_allowed = contains(filetext, 'persistent') || contains(filetext, 'global') || contains(filetext, 'java') || contains(filetext, 'py') || contains(filetext, 'regexp') || contains(filetext, 'eval') || contains(filetext, 'assignin');\r\nassert(~not_allowed)","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":255988,"edited_by":255988,"edited_at":"2023-01-07T06:37:48.000Z","deleted_by":null,"deleted_at":null,"solvers_count":2,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2023-01-06T09:42:25.000Z","updated_at":"2025-11-22T20:00:54.000Z","published_at":"2023-01-07T06:37:48.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eGiven and angle \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eA\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e in radians and a positive integer \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ex\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e, evaluate the following product summation:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e                    \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ePS(A,x) = \\\\sum_{n=1}^{x} \\\\sum_{m=1}^{n} \\\\prod_{k=0}^{m-1} 2 \\\\sin \\\\left( \\\\frac_{k\\\\pi}^{m} +A \\\\right).\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ewhich 'directly' translates to Matlab as:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[    \u003e\u003e PS = @(A,x) sum(arrayfun(@(n) sum(arrayfun(@(m) prod(arrayfun(@(k) 2*sin(k*pi/m+A),0:m-1)),1:n)),1:x));]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFor example \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ex = 3\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eA = 1\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[    \u003e\u003e x = 3; A = 1;\\n    \u003e\u003e PS(A,x)\\n    ans =\\n        8.9683]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ePlease present your answer rounded-off to nearest 4 decimal places.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":57969,"title":"Compute flow in a partially full pipe","description":"Problem statement\r\nWhen does the maximum flow occur in a pipe? Intuition might suggest that it occurs when the pipe is flowing full—i.e., when the depth of flow  equals the diameter  of the pipe. \r\nWrite a function that takes the ratio  and produces the flow rate as a fraction of the value for a full pipe. For example, when the input is 1/2, the output should be 1/2, and when the input is 1, the output should be 1. Assume that Manning’s equation applies and Manning’s roughness coefficient is constant. \r\nSee Test 13 for the answer to the initial question.\r\nBackground\r\nSteady uniform flow in a channel is often computed with Manning’s equation, which results from a balance between the component of the fluid’s weight in the flow direction and friction on the walls of the channel. The shear stress on the channel walls is computed with an empirical relation. Manning’s equation for the flow  is\r\n\r\nwhere  is Manning’s roughness coefficient,  is the hydraulic radius,  is the slope of the channel,  is the cross-sectional area of the flow, and  is the wetted perimeter (i.e., the perimeter of the solid wall of the channel that is touching the water.) The coefficient  is 1 for SI units and 1.5 (or 1.49) for U.S. customary units. ","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 392.8px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 196.4px; transform-origin: 407px 196.4px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 63.0083px 8px; transform-origin: 63.0083px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eProblem statement\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 384px 8px; transform-origin: 384px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWhen does the maximum flow occur in a pipe? Intuition might suggest that it occurs when the pipe is flowing full—i.e., when the depth of flow \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eh\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 65.35px 8px; transform-origin: 65.35px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e equals the diameter \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eD\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 38.5px 8px; transform-origin: 38.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e of the pipe. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 31.5px; text-align: left; transform-origin: 384px 31.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 109.933px 8px; transform-origin: 109.933px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function that takes the ratio \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAADsAAAAlCAYAAAD8+ZFYAAADwElEQVRoQ+1ZuaoUQRR97wvEJTJ0AQ1EQU1EY7dYVDQwcwkFFdREXEARzFxAQUyeIiaCogYmiiAaaCAmKn6AC+gH6DnQdzhTU8utnp4WmTdwmZ7XVbfuuXXurdP9Zmem6DM7RVhn5sH2tNtXsc5l2Jee1vtnO7sWAN/Blk8D2PMN0D197SrX8dYsd2I17BfscQcBfoKP07C7GV/LcG+pc62XnnE5sJvhYDvspDg6hOsbHseZMTtw7xFsCex7Aewq3D8D2xCMe9r8Xiz37uH6Dux1yq9nZ0k5A7wO1+/HBMvGxM8Rpx8m/YWM3YlrZRcBH5UYmQj6Hml8HrCk2m7YZ9gKZ4C5YT9wc38QcG78Qdy83gz4ie9FicGs/7nm3tsm5iHAHrAMbiHsWsVupIJnQNzZVMCxeZZs3iNVc03tCe5vbZyMjC2BVQqF9GmzyQycDDlVMdmSzSl7YbmmZv3A3A+VXQnsccy62MwsNZRS/Kytb7Caurfz2Hx7zuU/EsgJXF+y3yWwRgsW/TZxwsB5FP2GeRsWa+8YrKbuNdnenvEGa1j3HqJyDqztBDFqhjQAD7UsRwziJqzm6NIavOCkv85ho9ro2Vnl/xZM+AijI56N52C3YaTVkMMElykQuDMeGqoLpaS3Z2iNu8Ha+cp2v7IBqjtjTksdksHT13qYlkIiL4M/h82mVHI2URPkprFxnxMIjKCti2qXHmoCCQQeeRhOVTET9oxUokIB4mpQRjs6JVjSb8B9XGvdkuI5bWoB1HZzbTSehBqDVN66jh5VI3QSBmpNIKdoLPu18pDztDnyt/e4IoO4MfyM9JJUHTDAw82kmPi3uvDUa6085LKabE9Cwzn8PdLQUmCt+cQW0rooKZo28pCBarI9MpVM4NOO7Wp0TgysqpZYrWi9ljokpR0T533CMeorHUsJDZOTFB+xYPUpI1YrVq9GYe7eGliod9vIQwZeKxGVBeza+2DR5+QY2NIjndUrM06h8QAWk4BMAsVHjTwk2PCRjmd8LHiW0xWYScOiwoqBNTAx3mu9ki6saQqFWDA8Ou7DBkLcOJr55pH3TGqPQ9kgP8icTbjeJSAZp+stZQiWFLKnHNZrKPJJzbMwBvUcdisBtI08JBMOOBLCB/KvsFcw17sn81lqMI61o0PYxJh9FSJtfXU2b1Jg28jDzkClHE0CrHXTWnn4X4K1d0y9vgD3ZGoSO9tGHnpiHXtM12B5ND2E1bw9HBuE10HXYHk0LYD19p85L1CO6xpszdq9j50H23vKe1rwL6q22CbizNfIAAAAAElFTkSuQmCC\" alt=\"h/D\" style=\"width: 29.5px; height: 18.5px;\" width=\"29.5\" height=\"18.5\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 251.258px 8px; transform-origin: 251.258px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and produces the flow rate as a fraction of the value for a full pipe. For example, when the input is 1/2, the output should be 1/2, and when the input is 1, the output should be 1. Assume that Manning’s equation applies and Manning’s roughness coefficient is constant. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 150.917px 8px; transform-origin: 150.917px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eSee Test 13 for the answer to the initial question.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 40.8333px 8px; transform-origin: 40.8333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eBackground\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 31.5px; text-align: left; transform-origin: 384px 31.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 369.8px 8px; transform-origin: 369.8px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eSteady uniform flow in a channel is often computed with Manning’s equation, which results from a balance between the component of the fluid’s weight in the flow direction and friction on the walls of the channel. The shear stress on the channel walls is computed with an empirical relation. Manning’s equation for the flow \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eQ\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 7px 8px; transform-origin: 7px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 34.8px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 17.4px; text-align: left; transform-origin: 384px 17.4px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"vertical-align:-15px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"Q = (C/n)R^(2/3)S0^(1/2)A\" style=\"width: 105.5px; height: 35px;\" width=\"105.5\" height=\"35\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 64px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 32px; text-align: left; transform-origin: 384px 32px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 21.0083px 8px; transform-origin: 21.0083px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003ewhere \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003en\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 112.55px 8px; transform-origin: 112.55px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is Manning’s roughness coefficient, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"R = A/P\" style=\"width: 59px; height: 18.5px;\" width=\"59\" height=\"18.5\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 73.5167px 8px; transform-origin: 73.5167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is the hydraulic radius, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"S0\" style=\"width: 15.5px; height: 20px;\" width=\"15.5\" height=\"20\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 87.125px 8px; transform-origin: 87.125px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is the slope of the channel, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eA\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 39.6667px 8px; transform-origin: 39.6667px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is the cross-sectional area of the flow, and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eP\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 278.1px 8px; transform-origin: 278.1px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is the wetted perimeter (i.e., the perimeter of the solid wall of the channel that is touching the water.) The coefficient \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eC\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 182.383px 8px; transform-origin: 182.383px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is 1 for SI units and 1.5 (or 1.49) for U.S. customary units. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function f = pipeFlow(hoverD)\r\n  f = hoverD.^2;\r\nend","test_suite":"%%\r\nhoverD = 1;\r\nf_correct = 1;\r\nassert(abs(pipeFlow(hoverD)-f_correct)\u003c1e-4)\r\n\r\n%%\r\nhoverD = 0.9;\r\nf_correct = 1.06580;\r\nassert(abs(pipeFlow(hoverD)-f_correct)\u003c1e-4)\r\n\r\n%%\r\nhoverD = 0.8;\r\nf_correct = 0.97747;\r\nassert(abs(pipeFlow(hoverD)-f_correct)\u003c1e-4)\r\n\r\n%%\r\nhoverD = 0.75;\r\nf_correct = 0.91188;\r\nassert(abs(pipeFlow(hoverD)-f_correct)\u003c1e-4)\r\n\r\n%%\r\nhoverD = 0.6;\r\nf_correct = 0.67184;\r\nassert(abs(pipeFlow(hoverD)-f_correct)\u003c1e-4)\r\n\r\n%%\r\nhoverD = 0.5;\r\nf_correct = 0.5;\r\nassert(abs(pipeFlow(hoverD)-f_correct)\u003c1e-4)\r\n\r\n%%\r\nhoverD = 0.4;\r\nf_correct = 0.33699;\r\nassert(abs(pipeFlow(hoverD)-f_correct)\u003c1e-4)\r\n\r\n%%\r\nhoverD = 0.3;\r\nf_correct = 0.19583;\r\nassert(abs(pipeFlow(hoverD)-f_correct)\u003c1e-4)\r\n\r\n%%\r\nhoverD = 0.2;\r\nf_correct = 0.08757;\r\nassert(abs(pipeFlow(hoverD)-f_correct)\u003c1e-4)\r\n\r\n%%\r\nhoverD = 0.1;\r\nf_correct = 0.02088;\r\nassert(abs(pipeFlow(hoverD)-f_correct)\u003c1e-4)\r\n\r\n%%\r\nhoverD = 0;\r\nf_correct = 0;\r\nassert(abs(pipeFlow(hoverD)-f_correct)\u003c1e-4)\r\n\r\n%%\r\nhoverD = (1:6)/7;\r\nf_correct = [0.04395 0.17812 0.38187 0.62268 0.85931 1.03672];\r\nassert(all(abs(pipeFlow(hoverD)-f_correct)\u003c1e-4))\r\n\r\n%%\r\ng = @(x) -pipeFlow(x); \r\nhoverD_max = fminsearch(g,0.9);\r\nhoverD_max_correct = 0.93817;\r\nassert(abs(hoverD_max-hoverD_max_correct)\u003c1e-4)\r\n\r\n%%\r\nfiletext = fileread('pipeFlow.m');\r\nillegal = contains(filetext, 'assignin') || contains(filetext, 'assert'); \r\nassert(~illegal)","published":true,"deleted":false,"likes_count":1,"comments_count":9,"created_by":46909,"edited_by":46909,"edited_at":"2023-04-08T16:02:01.000Z","deleted_by":null,"deleted_at":null,"solvers_count":5,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2023-04-08T12:50:01.000Z","updated_at":"2023-04-08T16:02:01.000Z","published_at":"2023-04-08T12:50:08.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eProblem statement\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWhen does the maximum flow occur in a pipe? Intuition might suggest that it occurs when the pipe is flowing full—i.e., when the depth of flow \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"h\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eh\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e equals the diameter \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"D\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eD\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e of the pipe. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a function that takes the ratio \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"h/D\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eh/D\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and produces the flow rate as a fraction of the value for a full pipe. For example, when the input is 1/2, the output should be 1/2, and when the input is 1, the output should be 1. Assume that Manning’s equation applies and Manning’s roughness coefficient is constant. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eSee Test 13 for the answer to the initial question.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eBackground\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eSteady uniform flow in a channel is often computed with Manning’s equation, which results from a balance between the component of the fluid’s weight in the flow direction and friction on the walls of the channel. The shear stress on the channel walls is computed with an empirical relation. Manning’s equation for the flow \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"Q\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eQ\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"Q = (C/n)R^(2/3)S0^(1/2)A\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eQ = \\\\frac{C}{n}R^{2/3}S_0^{1/2}A\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ewhere \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is Manning’s roughness coefficient, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"R = A/P\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eR=A/P\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is the hydraulic radius, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"S0\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eS_0\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is the slope of the channel, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"A\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eA\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is the cross-sectional area of the flow, and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"P\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eP\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is the wetted perimeter (i.e., the perimeter of the solid wall of the channel that is touching the water.) The coefficient \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"C\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eC\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is 1 for SI units and 1.5 (or 1.49) for U.S. customary units. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":60336,"title":"Determine whether a property description closes","description":"The arrival of summer makes me think back to the summers I spent working for my father’s engineering firm. For the first several summers I worked on land surveying crews, and a common job was to measure properties. The measurements would then be used in a metes and bounds description of the property, as in this example:\r\n…Commencing from the point of beginning; thence N0°0ʹ0ʺE 35 m; thence N60°0ʹ0ʺE 34.64 m; thence S0°0ʹ0ʺE 52.32 m; thence S90°0ʹ0ʺW 30 m to the point of beginning. \r\nThis text describes a polygon by giving orientations and lengths of the sides.* The orientations are specified as bearings, in which angles are given as degrees, minutes, and seconds. For example, N60°0ʹ0ʺE is 60° to the east of north. The direction WSW would be written as S67°30ʹ0ʺW.\r\nAn important element of measuring and describing a property is to verify that the property, as described, closes—that is, the last side ends at the point of beginning. States in the U.S. will specify the tolerance for the closure. \r\nWrite a function to determine whether a property description closes. The input will be a character string with the bearings and distances between the points. The function should return a logical variable tf with the result as well as the distance d of the end point from the point of beginning. Take the property to close when the distance between the beginning and end points is less than 0.01 m. \r\n*The description would also specify the location of the point of beginning and describe the property and boundaries, among other things.  ","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 382.35px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 191.175px; transform-origin: 407px 191.175px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 31.5px; text-align: left; transform-origin: 384px 31.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 374.658px 7.79167px; transform-origin: 374.658px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe arrival of summer makes me think back to the summers I spent working for my father’s engineering firm. For the first several summers I worked on land surveying crews, and a common job was to measure properties. The measurements would then be used in a metes and bounds description of the property, as in this example:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42.9px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21.45px; text-align: left; transform-origin: 384px 21.45px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 369.6px 7.79167px; transform-origin: 369.6px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; perspective-origin: 369.6px 8.25px; transform-origin: 369.6px 8.25px; \"\u003e…Commencing from the point of beginning; thence N0°0ʹ0ʺE 35 m; thence N60°0ʹ0ʺE 34.64 m; thence S0°0ʹ0ʺE 52.32 m; thence S90°0ʹ0ʺW 30 m to the point of beginning. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 31.5px; text-align: left; transform-origin: 384px 31.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 381.992px 7.79167px; transform-origin: 381.992px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThis text describes a polygon by giving orientations and lengths of the sides.* The orientations are specified as bearings, in which angles are given as degrees, minutes, and seconds. For example, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 157.608px 7.79167px; transform-origin: 157.608px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eN60°0ʹ0ʺE is 60° to the east of north. The direction WSW would be written as S67°30ʹ0ʺW.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 384px 7.79167px; transform-origin: 384px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eAn important element of measuring and describing a property is to verify that the property, as described, closes—that is, the last side ends at the point of beginning. States in the U.S. will specify the tolerance for the closure. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 84.45px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 42.225px; text-align: left; transform-origin: 384px 42.225px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 374.458px 7.79167px; transform-origin: 374.458px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function to determine whether a property description closes. The input will be a character string with the bearings and distances between the points. The function should return a logical variable \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 7.7px 7.79167px; transform-origin: 7.7px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; perspective-origin: 7.7px 8.25px; transform-origin: 7.7px 8.25px; \"\u003etf\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 119.408px 7.79167px; transform-origin: 119.408px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e with the result as well as the distance \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.85px 7.79167px; transform-origin: 3.85px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; perspective-origin: 3.85px 8.25px; transform-origin: 3.85px 8.25px; \"\u003ed\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 7.96667px 7.79167px; transform-origin: 7.96667px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e of the end point from the point of beginning. Take the property to close when the distance between the beginning and end points is less than 0.01 m. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 382.4px 7.79167px; transform-origin: 382.4px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e*The description would also specify the location of the point of beginning and describe the property and boundaries, among other things. \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.94167px 7.79167px; transform-origin: 1.94167px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function [tf,d] = isPropertyClosed(s)\r\n  tf = sum(str2num(s))==0;\r\nend","test_suite":"%%\r\nc = {'N0°0ʹ0ʺE 35 m' 'N60°0ʹ0ʺE 34.64 m' 'S0°0ʹ0ʺE 52.32 m' 'S90°0ʹ0ʺW 30 m'};\r\ns = strjoin(c,char(13));\r\n[tf,d] = isPropertyClosed(s);\r\nd_correct = 8.800129070465346e-04;\r\nassert(tf)\r\nassert(abs(d-d_correct)\u003c1e-6)\r\n\r\n%%\r\nc = {'N0°0ʹ0ʺE 35 m' 'N60°0ʹ0ʺE 34.64 m' 'S0°0ʹ0ʺE 52.1 m' 'S90°0ʹ0ʺW 30 m'};\r\ns = strjoin(c,char(13));\r\n[tf,d] = isPropertyClosed(s);\r\nd_correct = 0.220001760044587;\r\nassert(~tf)\r\nassert(abs(d-d_correct)\u003c1e-6)\r\n\r\n%%\r\nc = {'N52°17ʹ31ʺE 46.13 m' 'S52°17ʹ31ʺE 23.67 m' 'S52°17ʹ31ʺW 46.13 m' 'N52°17ʹ31ʺW 23.67 m'};\r\ns = strjoin(c,char(13));\r\n[tf,d] = isPropertyClosed(s);\r\nd_correct = 1.913194867290181e-14;\r\nassert(tf)\r\nassert(abs(d-d_correct)\u003c1e-6)\r\n    \r\n%%\r\nc = {'N52°17ʹ31ʺE 46.14 m' 'S52°17ʹ31ʺE 23.66 m' 'S52°17ʹ31ʺW 46.12 m' 'N52°17ʹ31ʺW 23.68 m'};\r\ns = strjoin(c,char(13));\r\n[tf,d] = isPropertyClosed(s);\r\nd_correct = 0.024465531079178;\r\nassert(~tf)\r\nassert(abs(d-d_correct)\u003c1e-6)\r\n\r\n%%\r\nc = {'N4°23ʹ55ʺW 52.15 m','N33°10ʹ42ʺE 31.06 m','N52°52ʹ34ʺE 41.40 m','S60°15ʹ18ʺE 24.19 m','S37°28ʹ34ʺE 37.80 m','S55°53ʹ7ʺE 37.44 m','S16°15ʹ36ʺE 50.00 m','S84°44ʹ15ʺW 76.32 m','N75°44ʹ7ʺW 60.88'};\r\ns = strjoin(c,char(13));\r\n[tf,d] = isPropertyClosed(s);\r\nd_correct = 0.018626452840054;\r\nassert(~tf)\r\nassert(abs(d-d_correct)\u003c1e-6)\r\n\r\n%%\r\nc = {'N4°23ʹ55ʺW 52.15 m','N33°10ʹ42ʺE 31.06 m','N52°51ʹ11ʺE 41.40 m','S60°15ʹ18ʺE 24.19 m','S37°28ʹ34ʺE 37.80 m','S55°53ʹ7ʺE 37.44 m','S16°15ʹ36ʺE 50.00 m','S84°44ʹ15ʺW 76.32 m','N75°44ʹ7ʺW 60.88'};\r\ns = strjoin(c,char(13));\r\n[tf,d] = isPropertyClosed(s);\r\nd_correct = 0.007209083851337;\r\nassert(tf)\r\nassert(abs(d-d_correct)\u003c1e-6)\r\n\r\n%%\r\nc = {'N4°32ʹ55ʺW 52.15 m','N33°10ʹ42ʺE 31.06 m','N52°51ʹ11ʺE 41.40 m','S60°15ʹ18ʺE 24.19 m','S37°28ʹ34ʺE 37.80 m','S55°53ʹ7ʺE 37.44 m','S16°15ʹ36ʺE 50.00 m','S84°44ʹ15ʺW 76.32 m','N75°44ʹ7ʺW 60.88'};\r\ns = strjoin(c,char(13));\r\n[tf,d] = isPropertyClosed(s);\r\nd_correct = 0.142364438065814;\r\nassert(~tf)\r\nassert(abs(d-d_correct)\u003c1e-6)\r\n\r\n%%\r\nc = {'N69°26ʹ38ʺW 42.72 m','N19°34ʹ23ʺW\t47.76 m','N47°51ʹ44ʺE 56.64 m','N47°2ʹ43ʺE 39.62 m','S80°32ʹ15ʺE 42.58 m','S25°16ʹ39ʺE 39.81 m','S28°23ʹ34ʺW 42.06 m','S24°40ʹ36ʺW 40.72 m','S77°47ʹ58ʺW 37.85 m'};\r\ns = strjoin(c,char(13));\r\n[tf,d] = isPropertyClosed(s);\r\nd_correct = 0.002087577619808;\r\nassert(tf)\r\nassert(abs(d-d_correct)\u003c1e-6)\r\n\r\n%%\r\nc = {'N69°26ʹ38ʺW 42.72 m','N19°34ʹ23ʺW\t47.76 m','N47°51ʹ44ʺE 56.4 m','N47°2ʹ43ʺE 39.62 m','S80°32ʹ15ʺE 42.58 m','S25°16ʹ39ʺE 39.81 m','S28°23ʹ34ʺW 42.06 m','S24°40ʹ36ʺW 40.72 m','S77°47ʹ58ʺW 37.85 m'};\r\ns = strjoin(c,char(13));\r\n[tf,d] = isPropertyClosed(s);\r\nd_correct = 0.238926560421110;\r\nassert(~tf)\r\nassert(abs(d-d_correct)\u003c1e-6)\r\n\r\n%%\r\nn = randi(10);\r\nm = n+randi(10);\r\nA = m^2-n^2; B = 2*m*n; C = m^2+n^2;\r\nth = acosd(A/C);\r\ndeg = floor(th);\r\nmnt = floor(60*(th-deg));\r\nscd = floor(3600*(th-deg-mnt/60));\r\nc = {['N0°0ʹ0ʺW ' num2str(A,5) ' m'],['S' num2str(deg,2) '°' num2str(mnt,2) 'ʹ' num2str(scd,2) 'ʺE ' num2str(C,5)\t' m'],['N90°0ʹ0ʺW ' num2str(B,5) ' m']};\r\ns = strjoin(c,char(13));\r\n[tf,d] = isPropertyClosed(s);\r\nassert(tf)\r\n\r\n%%\r\nfiletext = fileread('isPropertyClosed.m');\r\nillegal = contains(filetext, 'assignin') || contains(filetext, 'assert'); \r\nassert(~illegal)","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":46909,"edited_by":46909,"edited_at":"2024-06-04T15:37:54.000Z","deleted_by":null,"deleted_at":null,"solvers_count":5,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2024-05-19T01:52:51.000Z","updated_at":"2024-06-04T15:37:54.000Z","published_at":"2024-05-19T01:53:17.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe arrival of summer makes me think back to the summers I spent working for my father’s engineering firm. For the first several summers I worked on land surveying crews, and a common job was to measure properties. The measurements would then be used in a metes and bounds description of the property, as in this example:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e…Commencing from the point of beginning; thence N0°0ʹ0ʺE 35 m; thence N60°0ʹ0ʺE 34.64 m; thence S0°0ʹ0ʺE 52.32 m; thence S90°0ʹ0ʺW 30 m to the point of beginning. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThis text describes a polygon by giving orientations and lengths of the sides.* The orientations are specified as bearings, in which angles are given as degrees, minutes, and seconds. For example, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003eN60°0ʹ0ʺE is 60° to the east of north. The direction WSW would be written as S67°30ʹ0ʺW.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eAn important element of measuring and describing a property is to verify that the property, as described, closes—that is, the last side ends at the point of beginning. States in the U.S. will specify the tolerance for the closure. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a function to determine whether a property description closes. The input will be a character string with the bearings and distances between the points. The function should return a logical variable \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003etf\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e with the result as well as the distance \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ed\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e of the end point from the point of beginning. Take the property to close when the distance between the beginning and end points is less than 0.01 m. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e*The description would also specify the location of the point of beginning and describe the property and boundaries, among other things. \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":57785,"title":"Inscribe a circle in a triangle with a side of length equal to the circle’s circumference","description":"A circle of radius  is inscribed in a triangle with a side that has a length equal to the circle’s circumference. The center of the circle is at , and the special side is along the -axis. \r\nWrite a function to determine the coordinates of the third vertex. If the circle cannot be inscribed, return (NaN, NaN).\r\n         ","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 344.7px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 172.35px; transform-origin: 407px 172.35px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 43px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21.5px; text-align: left; transform-origin: 384px 21.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 53.675px 8px; transform-origin: 53.675px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eA circle of radius \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003er\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 318.433px 8px; transform-origin: 318.433px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is inscribed in a triangle with a side that has a length equal to the circle’s circumference. The center of the circle is at \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"(xc,r)\" style=\"width: 38.5px; height: 20px;\" width=\"38.5\" height=\"20\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 105.417px 8px; transform-origin: 105.417px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, and the special side is along the \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003ex\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 18.6667px 8px; transform-origin: 18.6667px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e-axis. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 321.917px 8px; transform-origin: 321.917px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function to determine the coordinates of the third vertex. If the circle cannot be inscribed, return (\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 11.55px 8px; transform-origin: 11.55px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003eNaN\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.88333px 8px; transform-origin: 3.88333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 11.55px 8px; transform-origin: 11.55px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003eNaN\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 4.275px 8px; transform-origin: 4.275px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e).\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 262.7px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 131.35px; text-align: left; transform-origin: 384px 131.35px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cimg class=\"imageNode\" style=\"vertical-align: baseline;width: 510px;height: 257px\" src=\"data:image/png;base64,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\" data-image-state=\"image-loaded\" width=\"510\" height=\"257\"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 17.475px 8px; transform-origin: 17.475px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e         \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function [x,y] = Barker_circle(xc,r)\r\n  x = xc+r; y = hypot(xc,r);\r\nend","test_suite":"%%\r\nxc = 4;\r\nr = 15;\r\n[x,y] = Barker_circle(xc,r);\r\nx_correct = 4.909246587607476;\r\ny_correct = 33.409674703528040;\r\nassert(abs(x-x_correct)\u003c1e-10)\r\nassert(abs(y-y_correct)\u003c1e-10)\r\n\r\n%%\r\nxc = -8*tand(71);\r\nr = 8;\r\n[x,y] = Barker_circle(xc,r);\r\nx_correct = -130.0150820572266;\r\ny_correct = 52.767782896424826;\r\nassert(abs(x-x_correct)\u003c1e-10)\r\nassert(abs(y-y_correct)\u003c1e-10)\r\n\r\n%%\r\nxc = 1.5;\r\nr = 1;\r\n[x,y] = Barker_circle(xc,r);\r\nx_correct = 1.953199287786186;\r\ny_correct = 2.302132858524124;\r\nassert(abs(x-x_correct)\u003c1e-10)\r\nassert(abs(y-y_correct)\u003c1e-10)\r\n\r\n%%\r\nxc = -6;\r\nr = 3;\r\n[x,y] = Barker_circle(xc,r);\r\nx_correct = -8.464265885195013;\r\ny_correct = 7.232132942597507;\r\nassert(abs(x-x_correct)\u003c1e-10)\r\nassert(abs(y-y_correct)\u003c1e-10)\r\n\r\n%%\r\nxc = -3;\r\nr = 1;\r\n[x,y] = Barker_circle(xc,r);\r\nassert(isnan(x) \u0026 isnan(y))\r\n\r\n%%\r\nxc = sqrt(2)/2+sqrt(3)/3+sqrt(5)/5+sqrt(7)/7+sqrt(11)/11+sqrt(13)/13+sqrt(17)/17;\r\nr = 1;\r\n[x,y] = Barker_circle(xc,r);\r\nx_correct = 23.968050071481240;\r\ny_correct = 9.177341136326962;\r\nassert(abs(x-x_correct)\u003c1e-10)\r\nassert(abs(y-y_correct)\u003c1e-10)\r\n\r\n%%\r\np = primes(20);\r\nxc = -sum(sqrt(p)./p);\r\nr = 1;\r\n[x,y] = Barker_circle(xc,r);\r\nassert(isnan(x) \u0026 isnan(y))\r\n\r\n%%\r\nxc = 0;\r\nr = 30*rand;\r\n[x,y] = Barker_circle(xc,r);\r\nx_correct = 0;\r\ny_correct = 2.225489199919036*r;\r\nassert(abs(x-x_correct)\u003c1e-10)\r\nassert(abs(y-y_correct)\u003c1e-10)\r\n\r\n%%\r\nxc = 10*rand;\r\nr = 7;\r\n[x1,y1] = Barker_circle(xc,r);\r\n[x2,y2] = Barker_circle(-xc,r);\r\nassert(abs(x1+x2)\u003c1e-10)\r\nassert(abs(y2-y1)\u003c1e-10)\r\n\r\n%%\r\np = primes(4e6);\r\nxc = sum(1./p(1:264833));\r\nr = 1;\r\n[x,y] = Barker_circle(xc,r);\r\nassert(~isnan(x) \u0026 ~isnan(y))\r\n\r\n%%\r\np = primes(4e6);\r\nxc = sum(1./p(1:264834));\r\nr = 1;\r\n[x,y] = Barker_circle(xc,r);\r\nassert(isnan(x) \u0026 isnan(y))\r\n\r\n%%\r\nfiletext = fileread('Barker_circle.m');\r\nillegal = contains(filetext, 'assignin') || contains(filetext, 'assert'); \r\nassert(~illegal)\r\n","published":true,"deleted":false,"likes_count":2,"comments_count":1,"created_by":46909,"edited_by":46909,"edited_at":"2023-03-14T02:42:07.000Z","deleted_by":null,"deleted_at":null,"solvers_count":6,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2023-03-14T02:41:59.000Z","updated_at":"2023-03-14T02:42:08.000Z","published_at":"2023-03-14T02:42:08.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eA circle of radius \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"r\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003er\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is inscribed in a triangle with a side that has a length equal to the circle’s circumference. The center of the circle is at \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"(xc,r)\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e(x_c,r)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, and the special side is along the \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"x\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ex\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e-axis. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a function to determine the coordinates of the third vertex. If the circle cannot be inscribed, return (\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eNaN\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eNaN\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e).\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"257\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"510\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"baseline\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId1\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e         \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/image\",\"target\":\"/media/image1.png\",\"relationshipId\":\"rId1\"}]},{\"partUri\":\"/media/image1.png\",\"contentType\":\"image/png\",\"content\":\"data:image/png;base64,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\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":61082,"title":"Slicing the area of a circle","description":"Given the area, A, of a square, consider a circle having the area, πA, and the radius, r.\r\nFor a given slicing number n\u003e1, find the (n+1)×2 matrix, M = [A1/π a1; A2/π a2; ...; An/π an; A_r L], where\r\nin the first row (i=1), A1 stands for the area of one slice (like a pizza slice), and a1 stands for the logical 1 if A1 is smaller than or reaches the square's area A or a1 stands for the logical 0 if A1 surpasses A;\r\nin the second row (i=2), A2 stands for the area of two slices and a2 has the same previous false-true meaning relative to the areas A2 and A;\r\nand so on, until last slice of the circle;\r\nin the last row (i=n+1), A_r is the area of the rectangle, with dimensions L×r, which contains the maximum possible number of slices, such that have the true meaning of their sum has the area smaller or equal than the square's area, in their adjacent arrangement.\r\nHint: Compare with Problem 61081.\r\ninput: (A,n)\r\noutput:  M = [A1/π a1; A2/π a2; ...; An/π an; A_r L]","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(33, 33, 33); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none; white-space: normal; \"\u003e\u003cdiv style=\"block-size: 325.5px; display: block; min-width: 0px; padding-block-start: 0px; padding-inline-start: 2px; padding-left: 2px; padding-top: 0px; perspective-origin: 408px 162.75px; transform-origin: 408px 162.75px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eGiven the area, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eA\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, of a square, consider a circle having the area, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eπA,\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and the radius, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003er\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eFor a given slicing number \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003en\u0026gt;1\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, find the \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e(n+1)\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e×\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e2\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e matrix, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eM = [A1/π a1; A2/π a2; ...; An/π an; A_r L]\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, where\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cul style=\"block-size: 163.5px; font-family: Helvetica, Arial, sans-serif; list-style-type: square; margin-block-end: 20px; margin-block-start: 10px; margin-bottom: 20px; margin-top: 10px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 391px 81.75px; transform-origin: 391px 81.75px; margin-top: 10px; margin-bottom: 20px; \"\u003e\u003cli style=\"block-size: 40.875px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 20.4375px; text-align: left; transform-origin: 363px 20.4375px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003ein the first row \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e(i=1)\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eA1\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e stands for the area of one slice (like a pizza slice), and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003ea1\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e stands for the logical \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e1\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e if \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eA1\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is smaller than or reaches the square's area \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eA\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e or \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003ea1\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e stands for the logical \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e0\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e if \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eA1\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e surpasses \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eA\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e;\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 40.875px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 20.4375px; text-align: left; transform-origin: 363px 20.4375px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003ein the second row \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e(i=2)\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eA2\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e stands for the area of two slices and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003ea2\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e has the same previous false-true meaning relative to the areas \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eA2\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eA\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e;\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4375px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 10.2125px; text-align: left; transform-origin: 363px 10.2188px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eand so on, until last slice of the circle;\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 61.3125px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 30.65px; text-align: left; transform-origin: 363px 30.6562px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003ein the last row \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e(i=n+1),\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eA_r\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is the area of the rectangle, with dimensions \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eL\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e×\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003er\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, which contains the maximum possible number of slices, such that have the true meaning of their sum has the area smaller or equal than the square's area, in their adjacent arrangement.\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ul\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eHint: Compare with \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/61081-slicing-the-area-of-a-regular-polygon\"\u003e\u003cspan style=\"border-block-end-color: rgb(0, 91, 130); border-block-start-color: rgb(0, 91, 130); border-bottom-color: rgb(0, 91, 130); border-inline-end-color: rgb(0, 91, 130); border-inline-start-color: rgb(0, 91, 130); border-left-color: rgb(0, 91, 130); border-right-color: rgb(0, 91, 130); border-top-color: rgb(0, 91, 130); caret-color: rgb(0, 91, 130); color: rgb(0, 91, 130); column-rule-color: rgb(0, 91, 130); outline-color: rgb(0, 91, 130); text-decoration-color: rgb(0, 91, 130); text-emphasis-color: rgb(0, 91, 130); \"\u003e\u003cspan style=\"\"\u003eProblem 61081\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003einput:\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e(A,n)\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003eoutput: \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eM = [A1/π a1; A2/π a2; ...; An/π an; A_r L]\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function M = slicing_circle(A,n)\r\n  M = x;\r\nend","test_suite":"%%\r\nA = 8;\r\nn = 4;\r\ny_correct = [2 1; 4 0; 6 0; 8 0; 8*sqrt(2) 4];\r\nY = slicing_circle(A,n);\r\ntolerance = 1e-13;\r\nassert(all(Y(1:n) == y_correct(1:n)) \u0026 ...\r\n    abs(Y(end)-y_correct(end)) \u003c tolerance \u0026 all(Y(1:end,2) == y_correct(1:end,2)))\r\n\r\n%%\r\nA = 36;\r\nn = 6;\r\ny_correct = [6 1; 12 0; 18 0; 24 0; 30 0; 36 0; 36 6];\r\ntolerance = 1e-13;\r\nY = slicing_circle(A,n);\r\nassert(all(Y(1:n) == y_correct(1:n)) \u0026 all(Y(1:n,2) == y_correct(1:n,2)) \u0026 ...\r\n    all(abs(Y(end,:)-y_correct(end,:)) \u003c tolerance))\r\n\r\n\r\n%%\r\nA = 36;\r\nn = 12;\r\ny_correct = [3 1; 6 1; 9 1; 12 0; 15 0; 18 0; 21 0; 24 0; 27 0; 30 0; 33 0; 36 0; ...\r\n    37.92731310242232  6.32121885040372];\r\ntolerance = 1e-13;\r\nY = slicing_circle(A,n);\r\nassert(all(Y(1:n) == y_correct(1:n)) \u0026 all(Y(1:n,2) == y_correct(1:n,2)) \u0026 ...\r\n    all(abs(Y(end,:)-y_correct(end,:)) \u003c tolerance))\r\n\r\n%%\r\nfiletext = fileread('slicing_circle.m');\r\nillegal = contains(filetext, 'assignin') || contains(filetext, 'regexp') || ...\r\n          contains(filetext, 'str2num'); \r\nassert(~illegal)\r\n\r\n%%\r\nA = 70;\r\nn = 7;\r\ny_correct = [10 1; 20 1; 30 0; 40 0; 50 0; 60 0; 70 0; ...\r\n    94.4539467929851 11.28940594715244];\r\ntolerance = 1e-13;\r\nY = slicing_circle(A,n);\r\nassert(all(Y(1:n) == y_correct(1:n)) \u0026 all(Y(1:n,2) == y_correct(1:n,2)) \u0026 ...\r\n    all(abs(Y(end,:)-y_correct(end,:)) \u003c tolerance))\r\n\r\n%%\r\nA = 70;\r\nn = 10;\r\ny_correct = [7 1; 14 1; 21 1; 28 0; 35 0; 42 0; 49 0; 56 0; 63 0; 70 0; ...\r\n    88.7511366850995 10.6077897676978];\r\ntolerance = 1e-13;\r\nY = slicing_circle(A,n);\r\nassert(all(Y(1:n) == y_correct(1:n)) \u0026  all(Y(1:n,2) == y_correct(1:n,2))  \u0026  ...\r\n    all(abs(Y(end,:)-y_correct(end,:)) \u003c tolerance))","published":true,"deleted":false,"likes_count":0,"comments_count":10,"created_by":4993982,"edited_by":4993982,"edited_at":"2025-11-27T14:44:37.000Z","deleted_by":null,"deleted_at":null,"solvers_count":5,"test_suite_updated_at":"2025-11-27T14:44:37.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2025-11-20T14:17:04.000Z","updated_at":"2025-12-17T10:09:27.000Z","published_at":"2025-11-21T15:27:17.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGiven the area, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eA\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, of a square, consider a circle having the area, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eπA,\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e and the radius, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003er\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFor a given slicing number \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003en\u0026gt;1\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, find the \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e(n+1)\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e×\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e2\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e matrix, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eM = [A1/π a1; A2/π a2; ...; An/π an; A_r L]\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, where\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ein the first row \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e(i=1)\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eA1\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e stands for the area of one slice (like a pizza slice), and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ea1\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e stands for the logical \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e1\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e if \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eA1\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e is smaller than or reaches the square's area \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eA\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e or \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ea1\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e stands for the logical \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e0\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e if \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eA1\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e surpasses \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eA\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e;\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ein the second row \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e(i=2)\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eA2\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e stands for the area of two slices and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ea2\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e has the same previous false-true meaning relative to the areas \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eA2\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eA\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e;\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eand so on, until last slice of the circle;\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ein the last row \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e(i=n+1),\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eA_r\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e is the area of the rectangle, with dimensions \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eL\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e×\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003er\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, which contains the maximum possible number of slices, such that have the true meaning of their sum has the area smaller or equal than the square's area, in their adjacent arrangement.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eHint: Compare with \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/61081-slicing-the-area-of-a-regular-polygon\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eProblem 61081\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003einput:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e(A,n)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eoutput: \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eM = [A1/π a1; A2/π a2; ...; An/π an; A_r L]\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":45374,"title":" Hanging cable - 02","description":"previous problem -\r\n\r\n\u003chttps://www.mathworks.com/matlabcentral/cody/problems/45373-hanging-cable-01\u003e\r\n\r\n The height of the poles is h\r\n the length of the cable is l\r\n \r\n\r\nbut in this case, the two poles are of different heights.\r\n\r\n\u003chttps://ibb.co/2P4P14Q\u003e\r\n\r\nThe image is collected from Wikipedia.","description_html":"\u003cp\u003eprevious problem -\u003c/p\u003e\u003cp\u003e\u003ca href = \"https://www.mathworks.com/matlabcentral/cody/problems/45373-hanging-cable-01\"\u003ehttps://www.mathworks.com/matlabcentral/cody/problems/45373-hanging-cable-01\u003c/a\u003e\u003c/p\u003e\u003cpre\u003e The height of the poles is h\r\n the length of the cable is l\u003c/pre\u003e\u003cp\u003ebut in this case, the two poles are of different heights.\u003c/p\u003e\u003cp\u003e\u003ca href = \"https://ibb.co/2P4P14Q\"\u003ehttps://ibb.co/2P4P14Q\u003c/a\u003e\u003c/p\u003e\u003cp\u003eThe image is collected from Wikipedia.\u003c/p\u003e","function_template":"function d = cable_03(h,l)","test_suite":"%%\r\nassert(abs(cable_03([50,70],140)-55.4172)\u003c0.0001)\r\n%%\r\nassert(abs(cable_03([80,70],160)-35.4678)\u003c0.0001)\r\n%%\r\nassert(isequal(cable_03([80,70],150),0))\r\n%%\r\nassert(abs(cable_03([50 100],1000)-984.5341)\u003c0.0001)\r\n%%\r\nassert(abs(cable_03([500 100],1000)-721.5116)\u003c0.0001)\r\n","published":true,"deleted":false,"likes_count":1,"comments_count":2,"created_by":363598,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":9,"test_suite_updated_at":"2020-03-22T18:22:00.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2020-03-22T10:15:37.000Z","updated_at":"2020-03-22T18:22:00.000Z","published_at":"2020-03-22T11:05:56.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eprevious problem -\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/45373-hanging-cable-01\\\"\u003e\u003cw:r\u003e\u003cw:t\u003e\u0026lt;https://www.mathworks.com/matlabcentral/cody/problems/45373-hanging-cable-01\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e\u0026gt;\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[ The height of the poles is h\\n the length of the cable is l]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ebut in this case, the two poles are of different heights.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:hyperlink w:docLocation=\\\"https://ibb.co/2P4P14Q\\\"\u003e\u003cw:r\u003e\u003cw:t\u003e\u0026lt;https://ibb.co/2P4P14Q\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e\u0026gt;\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe image is collected from Wikipedia.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"}],"term":"tag:\"trigonometry\"","current_player_id":null,"fields":[{"name":"page","type":"integer","callback":null,"default":1,"directive":null,"facet":null,"facet_method":"and","operator":null,"param":null,"static":null,"prepend":true},{"name":"per_page","type":"integer","callback":null,"default":50,"directive":null,"facet":null,"facet_method":"and","operator":null,"param":null,"static":null,"prepend":true},{"name":"sort","type":"string","callback":null,"default":null,"directive":null,"facet":null,"facet_method":"and","operator":null,"param":null,"static":null,"prepend":true},{"name":"body","type":"text","callback":null,"default":"*:*","directive":null,"facet":null,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":false},{"name":"group","type":"string","callback":null,"default":null,"directive":"group","facet":true,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true},{"name":"difficulty_rating_bin","type":"string","callback":null,"default":null,"directive":"difficulty_rating_bin","facet":true,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true},{"name":"id","type":"integer","callback":null,"default":null,"directive":"id","facet":null,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true},{"name":"tag","type":"string","callback":null,"default":null,"directive":"tag","facet":null,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true},{"name":"product","type":"string","callback":null,"default":null,"directive":"product","facet":null,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true},{"name":"created_at","type":"timeframe","callback":{},"default":null,"directive":"created_at","facet":null,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true},{"name":"profile_id","type":"integer","callback":null,"default":null,"directive":"author_id","facet":null,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true},{"name":"created_by","type":"string","callback":null,"default":null,"directive":"author","facet":null,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true},{"name":"player_id","type":"integer","callback":null,"default":null,"directive":"solver_id","facet":null,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true},{"name":"player","type":"string","callback":null,"default":null,"directive":"solver","facet":null,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true},{"name":"solvers_count","type":"integer","callback":null,"default":null,"directive":"solvers_count","facet":null,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true},{"name":"comments_count","type":"integer","callback":null,"default":null,"directive":"comments_count","facet":null,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true},{"name":"likes_count","type":"integer","callback":null,"default":null,"directive":"likes_count","facet":null,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true},{"name":"leader_id","type":"integer","callback":null,"default":null,"directive":"leader_id","facet":null,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true},{"name":"leading_solution","type":"integer","callback":null,"default":null,"directive":"leading_solution","facet":null,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true}],"filters":[{"name":"asset_type","type":"string","callback":null,"default":null,"directive":null,"facet":null,"facet_method":"and","operator":null,"param":null,"static":"\"cody:problem\"","prepend":true},{"name":"profile_id","type":"integer","callback":{},"default":null,"directive":null,"facet":null,"facet_method":"and","operator":null,"param":"author_id","static":null,"prepend":true}],"query":{"params":{"per_page":50,"term":"tag:\"trigonometry\"","current_player":null,"sort":"map(difficulty_value,0,0,999) asc"},"parser":"MathWorks::Search::Solr::QueryParser","directives":{"term":{"directives":{"tag":[["tag:\"trigonometry\"","","\"","trigonometry","\""]]}}},"facets":{"#\u003cMathWorks::Search::Field:0x00007f74ba5bea60\u003e":null,"#\u003cMathWorks::Search::Field:0x00007f74ba5be9c0\u003e":null},"filters":{"#\u003cMathWorks::Search::Field:0x00007f74ba5be100\u003e":"\"cody:problem\""},"fields":{"#\u003cMathWorks::Search::Field:0x00007f74ba5bece0\u003e":1,"#\u003cMathWorks::Search::Field:0x00007f74ba5bec40\u003e":50,"#\u003cMathWorks::Search::Field:0x00007f74ba5beba0\u003e":"map(difficulty_value,0,0,999) asc","#\u003cMathWorks::Search::Field:0x00007f74ba5beb00\u003e":"tag:\"trigonometry\""},"user_query":{"#\u003cMathWorks::Search::Field:0x00007f74ba5beb00\u003e":"tag:\"trigonometry\""},"queried_facets":{}},"query_backend":{"connection":{"configuration":{"index_url":"http://index-op-v2/solr/","query_url":"http://search-op-v2/solr/","direct_access_index_urls":["http://index-op-v2/solr/"],"direct_access_query_urls":["http://search-op-v2/solr/"],"timeout":10,"vhost":"search","exchange":"search.topic","heartbeat":30,"pre_index_mode":false,"host":"rabbitmq-eks","port":5672,"username":"search","password":"J3bGPZzQ7asjJcCk","virtual_host":"search","indexer":"amqp","http_logging":"true","core":"cody"},"query_connection":{"uri":"http://search-op-v2/solr/cody/","proxy":null,"connection":{"parallel_manager":null,"headers":{"User-Agent":"Faraday v1.0.1"},"params":{},"options":{"params_encoder":"Faraday::FlatParamsEncoder","proxy":null,"bind":null,"timeout":null,"open_timeout":null,"read_timeout":null,"write_timeout":null,"boundary":null,"oauth":null,"context":null,"on_data":null},"ssl":{"verify":true,"ca_file":null,"ca_path":null,"verify_mode":null,"cert_store":null,"client_cert":null,"client_key":null,"certificate":null,"private_key":null,"verify_depth":null,"version":null,"min_version":null,"max_version":null},"default_parallel_manager":null,"builder":{"adapter":{"name":"Faraday::Adapter::NetHttp","args":[],"block":null},"handlers":[{"name":"Faraday::Response::RaiseError","args":[],"block":null}],"app":{"app":{"ssl_cert_store":{"verify_callback":null,"error":null,"error_string":null,"chain":null,"time":null},"app":{},"connection_options":{},"config_block":null}}},"url_prefix":"http://search-op-v2/solr/cody/","manual_proxy":false,"proxy":null},"update_format":"RSolr::JSON::Generator","update_path":"update","options":{"url":"http://search-op-v2/solr/cody"}}},"query":{"params":{"per_page":50,"term":"tag:\"trigonometry\"","current_player":null,"sort":"map(difficulty_value,0,0,999) asc"},"parser":"MathWorks::Search::Solr::QueryParser","directives":{"term":{"directives":{"tag":[["tag:\"trigonometry\"","","\"","trigonometry","\""]]}}},"facets":{"#\u003cMathWorks::Search::Field:0x00007f74ba5bea60\u003e":null,"#\u003cMathWorks::Search::Field:0x00007f74ba5be9c0\u003e":null},"filters":{"#\u003cMathWorks::Search::Field:0x00007f74ba5be100\u003e":"\"cody:problem\""},"fields":{"#\u003cMathWorks::Search::Field:0x00007f74ba5bece0\u003e":1,"#\u003cMathWorks::Search::Field:0x00007f74ba5bec40\u003e":50,"#\u003cMathWorks::Search::Field:0x00007f74ba5beba0\u003e":"map(difficulty_value,0,0,999) asc","#\u003cMathWorks::Search::Field:0x00007f74ba5beb00\u003e":"tag:\"trigonometry\""},"user_query":{"#\u003cMathWorks::Search::Field:0x00007f74ba5beb00\u003e":"tag:\"trigonometry\""},"queried_facets":{}},"options":{"fields":["id","difficulty_rating"]},"join":" "},"results":[{"id":44880,"difficulty_rating":"easy"},{"id":2772,"difficulty_rating":"easy"},{"id":44271,"difficulty_rating":"easy"},{"id":2518,"difficulty_rating":"easy"},{"id":43563,"difficulty_rating":"easy"},{"id":44282,"difficulty_rating":"easy"},{"id":43564,"difficulty_rating":"easy-medium"},{"id":45345,"difficulty_rating":"easy-medium"},{"id":401,"difficulty_rating":"easy-medium"},{"id":336,"difficulty_rating":"easy-medium"},{"id":837,"difficulty_rating":"easy-medium"},{"id":44070,"difficulty_rating":"easy-medium"},{"id":44936,"difficulty_rating":"easy-medium"},{"id":2495,"difficulty_rating":"easy-medium"},{"id":61081,"difficulty_rating":"easy-medium"},{"id":60311,"difficulty_rating":"easy-medium"},{"id":1460,"difficulty_rating":"easy-medium"},{"id":42306,"difficulty_rating":"easy-medium"},{"id":59249,"difficulty_rating":"easy-medium"},{"id":44492,"difficulty_rating":"medium"},{"id":60301,"difficulty_rating":"medium"},{"id":1257,"difficulty_rating":"medium"},{"id":59501,"difficulty_rating":"medium"},{"id":57512,"difficulty_rating":"medium"},{"id":57969,"difficulty_rating":"medium"},{"id":60336,"difficulty_rating":"medium"},{"id":57785,"difficulty_rating":"medium"},{"id":61082,"difficulty_rating":"medium-hard"},{"id":45374,"difficulty_rating":"medium-hard"}]}}