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Solved
Scaling vertically functions
Given a real function by the 1×n array, x, of inputs and the 1×n array, y, of outputs, consider shifting vertically its graph by...
15 hours ago
Solved
Translating even-degree polynomial by its vertex to the origin
Let p be an even-degree polynomial such that has a unique vertex (single global extremum). Consider its translation by shifting ...
16 hours ago
Solved
Translating parabola by its vertex to the origin
Given a quadratic polynomial, p(x) = ax^2 + bx + c (a ~= 0), represented by the vector [a b c], consider the translation of the ...
17 hours ago
Solved
Shifting vertically a function's graph
Given a real function, f, by n input-output pairs, consider a translation in the up-down direction given by an amount k. For a ...
17 hours ago
Solved
Spiral Mandala
Generate a clockwise spiral pattern using 1s in an N×N matrix to create an intricate mandala effect. e.g. N = 5; y_correct...
11 days ago
Solved
Starburst Mandala
Create a mandala starburst using diagonal and orthogonal symmetry in a matrix.
11 days ago
Solved
Hourglass Mandala
Generate an hourglass shape using matrix geometry and symmetry. e.g. N = 5; 1 1 1 1 1; 0 1 1 1 0; ...
11 days ago
Solved
Vertical Mirror Mandala
Create a symmetric left-right mirrored pattern in an N×N matrix to emulate mandala reflection symmetry. e.g. N = 5; ...
11 days ago
Solved
Plus Cross Mandala
Create a symmetrical plus (+) shaped pattern centered in an N×N matrix.
11 days ago
Solved
Diagonal Cross Mandala
Generate an N×N matrix with diagonals highlighted to form an artistic X-shaped mandala pattern. e.g. N = 5; 1 0 0...
12 days ago
Solved
Concentric Squares Mandala
Generate concentric square rings of alternating 1s and 0s to form a layered mandala-style matrix. e.g. N = 5; 1 1 1 1 1;...
12 days ago
Solved
Circular Ring Approximation Mandala
Generate a matrix that approximates a circular ring using distance-based thresholding , a visually rich mandala-inspired challen...
12 days ago
Solved
Hollow Diamond Pattern
Create an N×N matrix that forms a hollow diamond shape using 1s, leaving the interior empty. This challenge emphasizes boundary ...
12 days ago
Solved
Filled Diamond Pattern
Create an N×N binary matrix that forms a filled diamond shape centered in the matrix. The diamond expands symmetrically toward t...
12 days ago
Solved
Simulate full-stop emergency braking scenario.
Emergency braking events demand rapid deceleration to bring the vehicle safely to rest. Given initial vehicle speed and constant...
13 days ago
Solved
Compute optimal regenerative and friction brake torque blending.
Electric and hybrid vehicles combine regenerative braking with traditional friction braking to maximize energy recovery while en...
13 days ago
Solved
Estimate brake disc temperature rise during braking.
During braking, kinetic energy is converted into thermal energy, causing brake discs to heat up. Excessive temperature rise can ...
13 days ago
Solved
Compute optimal front–rear brake force distribution.
Modern braking systems dynamically distribute braking forces between front and rear axles to maintain stability, reduce stopping...
13 days ago
Solved
Compute wheel slip ratio during braking.
During braking, a difference develops between the vehicle’s forward speed and the rotational speed of its wheels. This differenc...
13 days ago
Solved
Estimate dynamic load transfer to front axle during braking.
During braking, load shifts from the rear axle to the front axle. Given mass, deceleration, center of gravity height, and wheelb...
14 days ago
Solved
Estimate brake line pressure required for a given force.
Hydraulic braking systems amplify pedal input to generate braking force. Given braking force and piston area, compute the hydrau...
14 days ago
Solved
Compute the required brake torque at wheel to stop the car
Brake torque defines how effectively braking force translates into wheel deceleration. Given braking force and wheel radius, det...
14 days ago
Solved
Compute braking force using vehicle mass and acceleration.
Compute braking force required to stop a vehicle of mass 'm' and with acceleration 'a' Remember: F = m × a.
14 days ago
Solved
Compute vehicle stopping distance using initial speed and constant deceleration.
Given vehicle speed v (m/s) and constant deceleration a (m/s²), compute stopping distance Remember: d = v² / (2a)
14 days ago
Solved
Slicing a 4-pointed star polygon
Given the area, A, of a 4-pointed star polygon formed by the rectangle, with dimensions L×2L, and four triangles, with height h ...
2 months ago
Solved
Covering a 4-pointed star polygon by a circle sector
Given the area, A, of a 4-pointed star polygon formed by the rectangle, with dimensions L×2L, and four triangles, with height h ...
2 months ago
Solved
Covering a four-pointed star polygon by circles
Given the area, A, of a star polygon formed by the rectangle, with dimensions L×2L, and four triangles, with height h from their...
2 months ago
Solved
Covering a four-pointed star polygon by rectangles
Given the area, A, of a star polygon formed by the rectangle, with dimensions L×2L, and four triangles, with height h from their...
2 months ago
Solved
Covering rectangle area of a four-pointed star polygon
Given the four-pointed star polygon formed by the rectangle, with dimensions l1xl2, and four triangles, with height, h, from the...
2 months ago
Solved
Height of a four-pointed star polygon
Given the area A, of a rectangle with dimensions l1xl2, where the side lengths are integers and form the smallest possible perim...
2 months ago
