College Algebra (10th Edition)

Published by Pearson
ISBN 10: 0321979478
ISBN 13: 978-0-32197-947-6

Chapter 2 - Section 2.5 - Variation - 2.5 Assess Your Understanding - Page 192: 28

Answer

$\approx 21.33$ inches.

Work Step by Step

$y$ varies $\bf{inversely}$ with $x,$ or $y$ is inversely proportional to $x,$ if there is a nonzero constant $k$ such that $\displaystyle \ \ y=\frac{k}{x}$ --- Here, y= rate of vibration, x = length of the string, and $y=\displaystyle \frac{k}{x}$ Given that, for x=48, y=256, we calculate k: $256=\displaystyle \frac{k}{48}\qquad/\times 48$ $k=12,288$ So, $y=\displaystyle \frac{12,288}{x}$. When y=576, we find x from: $576=\displaystyle \frac{12,288}{x}\qquad/\times\frac{x}{576}$ $x=\displaystyle \frac{12,288}{576}\approx 21.33$ inches.
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