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A) Prove the following theorem by considering two distinct cases. For any integer n, n2 + n is even.
B) If x = r2 - s2 and y = 2rs for any integers r and s, then x2 + y2 = z2 for some nonnegative integer z. State the hypothesis of this sentence and the conclusion. Give a direct proof of the statement
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A scientist calculates the temperature of melting platinum using a new type of thermometer. The temperature of the metal is called to be exactly 1768.3 centigrade. The measurements
If x and y are two independent random variables then their joint density function is given by The density function f z of the sum of these two variables is given by the c
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There are many situations which call for the replacement of an integral by a sum, or vice versa. In the former case the highest accuracy is sometimes required. This means that in t
In the x,y plane, divide up the x-axis by placing marks at x=a, x=b, and x = -2. Suppose φ is harmonic in the upper half plane and on the segments of the x-axis defined by your mar
A company manufactures an assembly consisting of a frame, a shaft, and a ball bearing. The company manufactures the shafts and frames but purchases the ball bearings from a ball be
The vertical motion of a general aviation airplane subjected to a sharp-edged wind gust is described by the equation Δw(t) = A g (1-e -t/τ ) assume A g = 30 where Δ w is in
if the sides of a triangle ABC vary in such a way that it''s circum-radius remains constant. prove that, da/cos A+db/cos B+dc/cos C =0
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
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