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Breaking straight lines
Let P be a point in Oxy plane and let p be a 1×2 array representing an one-degree or zero-degree polynomials, if its first entry...
2일 전
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Scaling vertically parabola by evaluating its area over an interval
Let p be a quadratic polynomial, with its axis of symmetry being the y-axis. Considering the vertical shift of its vertex to the...
3일 전
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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...
4일 전
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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 ...
4일 전
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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 ...
4일 전
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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 ...
4일 전
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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...
14일 전
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Starburst Mandala
Create a mandala starburst using diagonal and orthogonal symmetry in a matrix.
14일 전
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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; ...
14일 전
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Vertical Mirror Mandala
Create a symmetric left-right mirrored pattern in an N×N matrix to emulate mandala reflection symmetry. e.g. N = 5; ...
14일 전
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Plus Cross Mandala
Create a symmetrical plus (+) shaped pattern centered in an N×N matrix.
14일 전
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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...
15일 전
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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;...
15일 전
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Circular Ring Approximation Mandala
Generate a matrix that approximates a circular ring using distance-based thresholding , a visually rich mandala-inspired challen...
15일 전
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Hollow Diamond Pattern
Create an N×N matrix that forms a hollow diamond shape using 1s, leaving the interior empty. This challenge emphasizes boundary ...
15일 전
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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...
15일 전
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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...
16일 전
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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...
16일 전
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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 ...
16일 전
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Compute optimal front–rear brake force distribution.
Modern braking systems dynamically distribute braking forces between front and rear axles to maintain stability, reduce stopping...
16일 전
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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...
16일 전
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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...
17일 전
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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...
17일 전
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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...
17일 전
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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.
17일 전
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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)
17일 전
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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 ...
2개월 전
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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 ...
2개월 전
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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...
2개월 전
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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...
2개월 전
