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Let a, b, c 2 Z+.
(a) Prove that if a|b, then ac|bc for all c.
(b) If a|bc, can you conclude that either a|b or a|c? Justify your answer with a proof or a counter example.
(c) Prove that gcd(a, a + b) = gcd(a, b).
Given, y = f(x) = 2 x 3 - 3x 2 + 4x +5 a) Use the Power function to find derivative of the function. b) Find the value of the derivative at x = 4.
prove the the centre of a circle is twice of reference angle
How to Converting Fractions to Decimals explain with example? To convert fractions to decimals, divide the numerator by the denominator. The quotient is the decimal. Ex
approximate the following problem as a mixed integer program. maximize z=e-x1+x1+(x2+1)2 subject to x12+x2 =0
Ask queThe low temperature in Anchorage, Alaska today was -4°F. The low temperature in Los Angeles, California was 63°F. What is the difference in the two low temperatures?stion #M
A bank pays on its savings an interest rate of 6% per year but compounds interest monthly (i.e., estimates the interest each month and adds it to the balance). You plan to deposit
When 6 boys were admitted & 6 girls left the percentage of boys increased from 60% to 75%. Find the original no. of boys and girls in the class. Ans: Let the no. of Boys be x
200000+500
Fermat's Theorem If f(x) has a relative extrema at x = c and f′(c) exists then x = c is a critical point of f(x). Actually, this will be a critical point that f′(c) =0.
1. Suppose n ≡ 7 (mod 8). Show that n ≠ x 2 + y 2 + z 2 for any x, y, z ε Z. 2. Prove ∀n ε Z, that n is divisible by 9 if and only if the sum of its digits is divisible by 9.
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