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The division algorithm says that when a is divided by b, a unique quotient and remainder is obtained. For a fixed integer b where b ≥ 2, consider the function f : Z → Z given by f(a) = r where r is the unique remainder obtained when a is divided by b.
(a) What is the range of f? Based on your answer, is f onto?
(b) Determine whether f a 1-1 function.
Solve the subsequent IVP. cos(x) y' + sin(x) y = 2 cos 3 (x) sin(x) - 1 y(p/4) = 3√2, 0 Solution : Rewrite the differential equation to determine the coefficient of t
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Find the sum of first 40 positive integers divisible by 6 also find the sum of first 20 positive integers divisible by 5 or 6. Ans: No's which are divisible by 6 are
Ask question A triangle has two sides that measure 23 ft and 30 ft. Which could be the measure of the third side? A. 5 ft B. 7 ft C. 10 ft D. 53 ft #Minimum 100 words accepted
The curve (y+1) 2 =x 2 passes by the points (1, 0) and (- 1, 0). Does Rolle's Theorem clarify the conclusion that dy dx vanishes for some value of x in the interval -1≤x≤1?
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Steps for Integration Strategy 1. Simplify the integrand, if possible This step is vital in the integration process. Several integrals can be taken from impossible or ve
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how many numbers must be selected from the set A={1, 3, 5, 7, 9, 11, 13, 15}to guarantee that at least one pair of these numbers add up to16? Explain and justify your answer
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