Precalculus (6th Edition)

Published by Pearson
ISBN 10: 013421742X
ISBN 13: 978-0-13421-742-0

Chapter 3 - Polynomial and Rational Functions - 3.6 Variation - 3.6 Exercises - Page 387: 15

Answer

$a=0.144=18/125$

Work Step by Step

Because $a$ is directly proportional to $m$ and $n^2$, and inversely proportional to $y^3$, we can expressed $a$ by this equation: $a=\frac{kmn^2}{y^3}$ Then, replace $a$, $m$, $n$, $y$ with the value given would yield us the constant k. $9=\frac{k*4*9^2}{3^3}$ $9=\frac{k*4*3^4}{3^3}$ $9=k*4*3=12k$ $k=3/4$ Now, we are able to use this $k$ value to find the missing $a$ with a different set of $m$, $n$, $y$ given. $a=\frac{3/4*6*2^2}{5^3}=\frac{3*6*4}{4*125}=72/500=0.144$
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