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 423: 6



Work Step by Step

To find out the solution we need to follow the four-step procedure: Step (1). As $a$ varies directly as $b$ and inversely as ${{c}^{2}}$ varies, we have $a=k\frac{b}{{{c}^{2}}}$ Here $k$ is a constant. Step (2). Substitute $b=9$ , $c=6$ and $a=7$ in $a=k\frac{b}{{{c}^{2}}}$ to find the value of k. $\begin{align} & 7=k\frac{9}{{{6}^{2}}} \\ & k=\frac{7\times 36}{9} \\ & k=28 \\ \end{align}$ Step (3). Substitute $k=28$ in the equation $a=k\frac{b}{{{c}^{2}}}$ $a=\left( 28 \right)\frac{b}{{{c}^{2}}}$ Step (4). Substitute $b=4\,\text{ and }\,c=8$ to get: $\begin{align} & a=28\times \frac{4}{{{8}^{2}}} \\ & a=\frac{28\times 4}{64} \\ & a=\frac{7}{4} \\ \end{align}$
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