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: 34


(a) $z= \frac{k}{x^{2}y^{3}}$ (b) $\frac{1}{72}$

Work Step by Step

(a) Since $z$ is inversely proportional to the square of $x$ and the cube of $y$, we have: $z= \frac{k}{x^{2}y^{3}}$ (b) We know that $x$ is tripled and $y$ is doubled, so we have: $z= \frac{k}{(3x)^{2}(2y)^{3}}=\frac{1}{72}\frac{k}{x^{2}y^{3}}$ Therefore, $z$ changes by a factor of $\frac{1}{72}$.
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