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A) For a given integer n, if n 2 is divisible by 4, then n2 4 is divisible by 16. State the hypothesis of this sentence and the conclusion. Give a direct proof of the statement.
(b) Use the law of contrapositive to show that for any given integers a and b, if ab is odd then either a is odd or b is odd. Describe the hypothesis of this statement and the conclusion
Draw concentric circles of radii a and b, each centered at z=id (on the imaginary axis). Suppose φ(x,y) is a harmonic function inside the washer defined by these circles. The circl
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1. (i) How many digits does the number 101000 have when written to base 7 ? (ii) Use the prime number theorem to estimate the proportion of prime numbers among the positive inte
Verify how long $400 must be left to store at 12 % p.a. compounded monthly for it to amount to triple the soted value of another $400 deposited at the similar time at 8.8% p.a. com
if u=x^2-2y^2, v=2x^2-y^2 and x=rcosp ad y=rsinp, find the value of the jacobian d(u,v)/d(r,p)
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
The following are 8 data points that shows the relationship between the number of fishermen and the amount of fish they can catch a day. (Let the number of fishermen be X and the a
a.) Give a short sequence of machine instructions for the task " Add the contents of memory location A to those of memory location B, and place the answer in location C ". You have
i need a quote in analytical methods for engineers (Algebraic methods)
prove that A=3i+j-2k, B=-i+3j+4k ,C=4i-2j-6k and find the length of the triangle
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