2nd Edition

ISBN: 9781259985607

Author: David Sobecki Professor, Brian A. Mercer

Publisher: McGraw-Hill Education

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Have you ever seen a bridge in the shape of a parabola? Where is its maximum on the bridge? The maximum of that bridge is the highest point on that bridge. The process of finding the maximum of the bridge here is called the maximization.

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Textbook Question

Chapter 4.7, Problem 7A

The equation of the parabola representing the ball’s height is f ( x ) = − 18 ( x − 1.8 ) 2 + 60 , where f ( x ) is the height in feet and x is the number of seconds after it was kicked. Find the exact height after the number of seconds you found in Question 6. How accurate were your answers to Question 6?

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Chapter 4.7, Problem 6A

Chapter 4.7, Problem 8A

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7. [10 marks] Let G = (V,E) be a 3-connected graph. We prove that for every x, y, z Є V, there is a cycle in G on which x, y, and z all lie. (a) First prove that there are two internally disjoint xy-paths Po and P₁. (b) If z is on either Po or P₁, then combining Po and P₁ produces a cycle on which x, y, and z all lie. So assume that z is not on Po and not on P₁. Now prove that there are three paths Qo, Q1, and Q2 such that: ⚫each Qi starts at z; • each Qi ends at a vertex w; that is on Po or on P₁, where wo, w₁, and w₂ are distinct; the paths Qo, Q1, Q2 are disjoint from each other (except at the start vertex 2) and are disjoint from the paths Po and P₁ (except at the end vertices wo, W1, and w₂). (c) Use paths Po, P₁, Qo, Q1, and Q2 to prove that there is a cycle on which x, y, and z all lie. (To do this, notice that two of the w; must be on the same Pj.)

6. [10 marks] Let T be a tree with n ≥ 2 vertices and leaves. Let BL(T) denote the block graph of T. (a) How many vertices does BL(T) have? (b) How many edges does BL(T) have? Prove that your answers are correct.

Chapter 4 Solutions

Pathways To Math Literacy (looseleaf)

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Solution Summary: The author calculates the time taken by the football after it reaches a height of 45 feet by using the provided parabolic equation.

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