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Feeds
Risolto
Euler primes
Historical context The great swiss mathematician Leonhard Euler found the formula to give some prime numbers. Problem...
3 giorni fa
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Rotating 2d curve around a vertical axis
Let p be an even-degree polynomial such that has a unique vertex (single global extremum). Consider the counterclockwise rotatio...
4 giorni fa
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Rotating the plane region bounded by two polynomials
Let p and q be n-degree and m-degree polynomials with n >= m >= 1. Consider clockwise rotate the plane region bounded by these t...
4 giorni fa
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Odd Run Sums
Given a row vector x of integers, find every maximal run of consecutive odd numbers and return a row vector containing the sum o...
8 giorni fa
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Comparing to scale all terms versus one term of even-degree polynomial by the same scale factor
Let p be an even-degree polynomial with positive leading coefficient. Consider the scale factor, k, that vertically transforms ...
8 giorni fa
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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...
8 giorni fa
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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...
8 giorni fa
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Shifting vertically even-degree polynomial's graph by its mean over an interval
Let p be an even-degree polynomial with positive leading coefficient. Consider its vertical translation by shifting its graph by...
8 giorni fa
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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 ...
8 giorni fa
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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 ...
8 giorni fa
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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 ...
8 giorni fa
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Is it Possible? ( Easy )
In the first part of series, we simplify the problem. Given two jugs with capacities A and B, and a target amount T, determine i...
11 giorni fa
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Power of Moving Vehicle
Engineers at Tesla calculate how much power is required to maintain vehicle motion.
11 giorni fa
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Spring Energy Storage
Engineers at Bosch design suspension systems using springs. They calculate the energy stored when the spring compresses.
11 giorni fa
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Machine Efficiency Test
Engineers at Siemens test how efficiently a motor converts electrical energy into mechanical work.
11 giorni fa
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Falling Object Velocity
Scientists at ISRO drop test equipment from a height to study motion under gravity. They must calculate the velocity just befor...
11 giorni fa
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Pushing a Heavy Machine
At a factory operated by Bharat Heavy Electricals Limited in Haridwar, engineers must move a heavy generator across the floor. ...
11 giorni fa
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Roller Coaster Height Energy
At Imagicaa Theme Park, engineers calculate potential energy at the top of a roller coaster.
11 giorni fa
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Kinetic Energy of a Moving Car
Engineers at Mahindra & Mahindra test how much kinetic energy a car gains when accelerating.
11 giorni fa
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Work Done in Lifting an Object
Engineers at Larsen & Toubro are testing a crane used to lift heavy construction materials at a building site in Mumbai. They n...
11 giorni fa
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Maximum Power Transfer
Engineers at Texas Instruments design circuits for maximum efficiency. Internal resistance = 4 Ω Find load resistance for maxi...
11 giorni fa
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Kirchhoff’s Loop Law
Engineers at ISRO design spacecraft circuits. Battery = 10 V Total resistance = 2 Ω Find current in loop.
11 giorni fa
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Power Loss in Transmission Lines
Electricity transmitted by Power Grid Corporation of India experiences power loss due to resistance. Current = 10 A Resistance...
11 giorni fa
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Car Battery Internal Resistance
Engineers at Tata Motors test a car battery with: EMF = 12 V Internal resistance = 1 Ω External resistance = 5 Ω Find curren...
11 giorni fa
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Parallel Circuit in Home Wiring
Home appliances connected in parallel in a house in Gurgaon have resistances of 6 Ω and 3 Ω. Find equivalent resistance.
11 giorni fa
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Series Circuit in Street Lights
Street lights installed by the Delhi Electricity Distribution Company use three resistors of 2 Ω, 3 Ω, and 5 Ω in series. Find ...
11 giorni fa
