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: 9



Work Step by Step

To find out the solution we need to follow the four-step procedure: Step (1). As $y$ varies directly as $a$ , $b$ and inversely as $\sqrt{c}$ , we have $y=k\frac{ab}{\sqrt{c}}$ Here $k$ is a constant. Step (2). Substitute $a=3$ , $b=2$ , $c=25$ and $y=12$ in $y=k\frac{ab}{\sqrt{c}}$ $\begin{align} & 12=k\frac{3\times 2}{\sqrt{25}} \\ & k=\frac{12\times 5}{6} \\ & k=10 \\ \end{align}$ Step (3). Substitute the value of $k$ into the main equation. $y=\left( 10 \right)\frac{ab}{\sqrt{c}}$ Step (4). Substitute the values $a=5,b=3,\,\text{ and }\,c=9$ in the above equation. That is., $\begin{align} & y=10\times \frac{5\times 3}{\sqrt{9}} \\ & y=\frac{150}{3} \\ & y=50 \\ \end{align}$
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