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: 31


(a) $z=k \frac{x^{3}}{y^{2}}$ (b) $\frac{27}{4}$

Work Step by Step

(a) Since $z$ is directly proportional to the cube of $x$ and inversely proportional to the square of $y$, we have: $z=k \frac{x^{3}}{y^{2}}$ (b) We are given that $x$ is tripled and $y$ is doubled, so we have: $z=k \frac{(3x)^{3}}{(2y)^{2}}=k\frac{27}{4}\frac{x^{3}}{y^{2}}$ Therefore, $z$ changes by a factor of $\frac{27}{4}$.
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