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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.
Find the circumference of a circle whose area is 16 times the area of the circle with diameter 7cm (Ans: 88cm) Ans: Π R 2 = 16 Π r 2 R 2 = 16 r 2
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Vertical Tangent for Parametric Equations Vertical tangents will take place where the derivative is not defined and thus we'll get vertical tangents at values of t for that we
The graph C n , n ≥ 3 contains n vertices and n edges creating a cycle. For what value of n is C n a bipartite graph? Draw the bipartite graph of C n to give explanation for yo
A bag contains 5 red balls and some blue balls. If the probability of drawing a blue ball is double that of a red ball , determine the number of blue balls in the bag.
PROBLEMS RELATED TO APPLYING OPERATIONS : Some of us were testing Class 4 children with addition and subtraction problems. We gave them sums that were written horizontally and th
what''s the beneit of study mathematics ?
Consider the function f: N → N, where N is the set of natural numbers, defined by f(n) = n 2 +n+1. Show that the function f is one-one but not onto. Ans: To prove that f is one
A right triangle whose sides are 15 cm and 20 cm is made to revolve about its hypotenuse. Find the volume and surface area of the double cone so formed. (Ans : 3768cu.cm,1318.8
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