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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
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
If V is the initial speed of the ball at angle of elevation a , if the origin of the coordinate system is chosen to coincide with the propulsion device, then the initial conditi
State each of the following arguments in abstract form. Recognize the premises and the conclusion of the argument. Then test whether the argument is valid or invalid. Describe how
An electronic module is mounted on a machine and is modelled as a single degree of freedom spring, mass, and damper. During normal operation, the module of mass m kg is subject to
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
Below are the conditions specified by the institution: a) If the temperature sensor shows 30 degree Celsius or higher, the air-conditioner will be turned ON regardless of the othe
A company's full profit per unit production is given by the function y = -5x 2 +17x-12 where x is the number of items produced (in hundreds) and the y is the profit per unit (in
a) Use divided differences to ?nd the polynomial (in nested form) that interpolates the data b) Add the data point x = 6, y = -20 and hence estimate y for x = 2.
y''(x)=2*10^-6*y(x)(100000-y(x))
integral dx/root of sinx using beta and gamma functions
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