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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).
If a+b+c = 3a , then cotB/2 cotC/2 is equal to
Let D(subscript12) = ({x,y : x^2 = e ; y^6 = e ; xy =(y^-1) x}) a) Which of the following subsets are subgroups of D(subscript12) ? Justify your answer. i) {x,y,xy,y^2,y^3,e}
From a fixed point directly in front of the center of a bull's eye, Kim aims two arrows at the bull's eye. The first arrow nicks one point on the edge of the bull's eye; the second
Evaluating a Function You evaluate a function by "plugging in a number". For example, to evaluate the function f(x) = 3x 2 + x -5 at x = 10, you plug in a 10 everywhere you
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How t determine locus of a goven point
Estimation of difference among two means We know that the standard error of a sample is given by the value of the standard deviation (σ) divided by the square root of the numbe
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show that the subtangent at any point on parabola y2 =4ax is twice the abscissa at that point.
IS SQUARE A UNIQUE RHOMBUS?
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