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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).
We have seen that if y is a function of x, then for each given value of x, we can determine uniquely the value of y as per the functional relationship. For some f
Charlie needs to know the area of his property, that measures 120 ft through 150 ft. Which formula will he use? The area of a rectangle is length × width.
what is the main different between mean and median
Find the acute angle theta that satisfies the given equation. Give theta in both degrees and radians. You should do these problems without a calculator. Sin= sqroot3/2
1. (‡) Prove asymptotic bounds for the following recursion relations. Tighter bounds will receive more marks. You may use the Master Theorem if it applies. 1. C(n) = 3C(n/2) + n
An aeroplane is flying at a specific height of 5 km, and at a velocity of 450 km/hr. A camera on the ground is pointed towards the plane, at an angle θ from the horizontal. As the
Write a script to determine the volume of a pyramid, which is 1/3 * base * height, where the base is length * width. On time the user to enter values for the length, width, and th
Not understanding the concept of curves
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The Fisher's index The index of Fisher acts as a compromise between Paasche' index and Laspeyre's index. This is calculated as a geometric mean of the two indexes.
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