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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
procedure of tracing a closed loop
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 solution of diffusion equation by using separation of variables
model an equation to determine the amount of oil in a reservior
given sample A : HAS SIZE 6,MEAN 8,VARIANCE 16 AND SAMPLE B:has size 10,mean 20 and variance 36 .calculate pooled sample variance
The integral has an exact answer, viz., sinc(pfT). As T®¥ the sinc function tends to zero. Divide the region from -T/2 to T/2 into N equal parts and sum the rectangles on b
1. Joe and Sam each invested $20,000 in the stock market. Joe's investment increased in value by 5% per year for 10 years. Sam's investment decreased in value by 5% for 5 years and
A function f(t) is defined as f(t) = p - t for 0 Write down the even extension of f(t) for -p Determine the Fourier cosine series, and hence, calculate the Fourier series approx
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what are the uses of laplace transformation?
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