Precalculus (6th Edition) Blitzer

Published by Pearson
ISBN 10: 0-13446-914-3
ISBN 13: 978-0-13446-914-0

Chapter 2 - Section 2.8 - Modeling Using Variation - Exercise Set - Page 424: 23


The ball is dropped from $80\text{ inches}$ such that it bounces 56 inches.

Work Step by Step

Consider that the height by which the ball bounces is B and the height from which the ball is dropped is D. It is provided that the variable B varies directly as D, that is $B\ =\ kD$. Thus, $\begin{align} & 8.4=12k \\ & k=\frac{8.4}{12} \\ & k=\frac{7}{10} \end{align}$ Substitute B = 56 and $k=\frac{7}{10}$ in $B\ =\ kD$. $\begin{align} & B=kD \\ & 56=\frac{7}{10}D \\ & D=\frac{56\times 10}{7} \\ & D=80 \end{align}$ Thus, if the ball is dropped from 80 inches, it bounces 56 inches.
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