College Algebra 7th Edition

Published by Brooks Cole
ISBN 10: 1305115546
ISBN 13: 978-1-30511-554-5

Chapter 1, Equations and Graphs - Section 1.10 - Modeling Variation - 1.10 Exercises - Page 164: 32


(a) $z=k \frac{x^{2}}{y^{4}}$ (b) $\frac{9}{16}$

Work Step by Step

(a) Since $z$ is directly proportional to the square of $x$ and inversely proportional to the fourth power of $y$, we have: $z=k \frac{x^{2}}{y^{4}}$ (b) We are given that $x$ is tripled and $y$ is doubled, so we have: $z=k \frac{(3x)^{2}}{(2y)^{4}}=k\frac{9}{16}\frac{x^{2}}{y^{4}}$ Therefore, $z$ changes by a factor of $\frac{9}{16}$.
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