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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).
1. The polynomial G(x) = -0.006x4 + 0.140x3 - 0.53x2 + 1.79x measures the concentration of a dye in the bloodstream x seconds after it is injected. Does the concentration increase
I am here to tell you, Alex has a cold.
please give the answer 1/9+1/3 with working out
A circle touches the sides of a quadrilateral ABCD at P, Q, R and S respectively. Show that the angles subtended at the centre by a pair of opposite sides are supplementary.
Write a Matlab function MyIVP that solves an initial-value problem (IVP) for a system of ordinary differential equations (ODEs) of the form x ?(t) = f (t, x(t)), where f : R × Rn ?
Ut=Uxx+A exp(-bx) u(x,0)=A/b^2(1-exp(-bx)) u(0,t)=0 u(1,t)=-A/b^2 exp(-b)
what is an isosceles triangle? ..
Finding the Slope of a Line, Given Two Points on it ? Find the slope of the line passing through the pairs of points (-5, -2) and (2, 4). One way to find the slope is
1. Find the third and fourth derivatives of the function Y=5x 7 +3x-6-17x -3 2. Find the Tangent to the curve Y= 5x 3 +2x-1 At the point where x = 2.
If the vertices of a triangle are (1, k), (4, -3), (-9, 7) and its area is 15 sq units, find the value(s) of k..
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