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: 10

Answer

$m=36$

Work Step by Step

$m$ varies jointly as $z$ and $p$ therefore $m=kzp$ $m=10$ when $z=2$ and $p=7.5$. Substitute these values into $m=kxy$ to obtain: $m=kpz \\10=k(7.5)(2) \\10=15k \\\frac{10}{15}=\frac{15k}{15} \\\frac{2}{3}=k$ Thus, the equation for $m$ is $m=\frac{2}{3}pz$. To find the value of $m$ when $z=6$ and $p=9$, substitute 6 to z and 9 to p in the equation above to obtain: $\require{cancel} \\m=\frac{2}{3}pz \\m=\frac{2}{3}(9)(6) \\m=\frac{2}{\cancel{3}}(\cancel{9}3)(6) \\m=2(3)(6) \\m=36$
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