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A) Prove the following theorem by considering two distinct cases. For any integer n, n 2 + n is even. B) If x = r 2 - s 2 and y = 2rs for any integers r and s, then x 2 +
application of mathematics in engineering
a restrained steel bar is heated from 20 degrees to 194 degrees and not permitted to expand. the bar is 10mm diameter, determine the thermal stress in the bar
A stone weighing 50 newton is tied to one end of a cord 0.90 meter long. the stone is then whirled in a vertical circle. if the breaking strength of the cord in tension is 60 newto
The data in this exam are a set of 6 integers a through f, based on your social security number. Write the LAST 6 digits of your social security or ID number in the spaces below, t
You notice at the gym that it appears more women tend to work out together, whereas more men tend to work out alone. To examine whether this difference is significant, you collect
From this point on it is assumed that any problem amenable to solution with the aid of the Discrete Fourier Transform (or DFT) will in fact be treated computationally with a fast r
Prove that the Lagrangian coef?cient polynomials for p n (x) satisfy ∑ n k=0 l k (x) = 1. Hint: It is only a 3-line proof. Consider the interpolating polynomial for a constan
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Find the equilibrium points (real and imaginary parts, to 3 decimal places) if unit positive line charges are placed at a+ic, b+id, and -3-2i. Designate one of these numbers as "m
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