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: 5

Answer

$y=\frac{5}{6}$  

Work Step by Step

To find out the solution we need to follow the four-step procedure, Step (1): As $y$ varies directly as $x$ and inversely as ${{z}^{2}}$ varies, we have $y=k\frac{x}{{{z}^{2}}}$ Here $k$ is a constant. Step (2): Substitute $x=50$ , $y=20$ and $z=5$ in the equation $y=k\frac{x}{{{z}^{2}}}$ to find the value of k. $\begin{align} & 20=k\frac{50}{{{5}^{2}}} \\ & k=\frac{20\times 25}{50} \\ & k=10 \\ \end{align}$ Step (3): Substitute $k=10$ in the equation $y=k\frac{x}{{{z}^{2}}}$ $y=\left( 10 \right)\frac{x}{{{z}^{2}}}$ Step (4): Substitute $x=3\,\text{ and }\,z=6$ in the above equation to get: $\begin{align} & y=10\times \frac{3}{{{6}^{2}}} \\ & y=\frac{30}{36} \\ & y=\frac{15}{18} \\ & y=\frac{5}{6} \end{align}$
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