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Find the initial number of balls, Balls are arranged in rows to form an equ...

Balls are arranged in rows to form an equilateral triangle .The first row consists of one ball, the second two balls and so on.   If 669 more balls are added, then all the balls ca

Types of relation, Relations in a Set: Let consider R be a relation fro...

Relations in a Set: Let consider R be a relation from A to B. If B = A, then R is known as a relation in A. Thus relation in a set A is a subset of A ΧA. Identity Relation:

Prove the equality of axiom choice, (1) Prove that Zorn's lemma is equivale...

(1) Prove that Zorn's lemma is equivalent to axiom of choice. (2) Use Zorn's Lemma to prove the existence of E.

Real constant and difference equation, Derive for the filter from z=a and p...

Derive for the filter from z=a and poles at z=b andz=c, where a, b, c are the real constants the corresponding difference equation. For what values of parameters a, b, and c the fi

Determine the minimum cost , A company is taking bids on four construction ...

A company is taking bids on four construction jobs. Three Contractors have placed bids on the jobs. Their bids (in thousands of dollars) are given in the file. (A blank indicates n

Triangles, if P is a point in the interior of a triangles ABC,prove that AB...

if P is a point in the interior of a triangles ABC,prove that AB>BC+CA

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