Prove the following statements by mathematical induction: - (a) Vn € N, - Σ (21 (2i − 1)² = n(2n + 1)(2n − 1) . 3 i=1 n (b) For all integers n ≥ 3, n²2 2n + 1. Note: the set of natural numbers N does not include 0. Please show as much detailed work / steps as possible - thank you!

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A: We can solve this as follows:

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A: Since we are given with the multiple number of question and our guideline is solve first question…

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A: Let's complete the given table.

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A: A toy rocket is launched vertically from 5 feet above ground level with an initial velocity of 112…

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A: Follow the procedure given below.

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A: To find the solutions of y=-(x+2)2+1, y=2x+5

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A: A detailed solution is given below

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Q: ·N·

A: We can answer the question as below.

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A: We have to determine an equation in factored form for a polynomial function with zeros: x=-3 order 2…

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A: Let's solve for x.

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A: In this question, we want to solve the given equation.

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A: In the graph there are two parabolas one is upwards and the other is downwards.

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A: We will use given definition to find the solution.

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A: Solve for the no of white roses

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A: I have used sumation formula of geometric series.

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A: The given equations are; 5x+4y=44 10x+8y=88.

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A: To find the unit vectors with given conditions. Note that, u is said to be a unit vector if u=1.