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: 9

Answer

$m=60$

Work Step by Step

$m$ varies jointly as $x$ and $y$ therefore $m=kxy$ $m=10$ when $x=2$ and $y=14$. Substitute these values into $m=kxy$ to obtain: $m=kxy \\10=k(2)(14) \\10=28k \\\frac{10}{28}=\frac{28k}{28} \\\frac{5}{14}=k$ Thus, the equation for $m$ is $m=\frac{5}{14}xy$. the values of $x$ and To find the value of $m$ when $x=21$ and $y=8$, substitute 21 to x and 8 to y in the equation above to obtain: $\require{cancel} \\m=\frac{5}{14}xy \\m=\frac{5}{14}(21)(8) \\m=\frac{5}{\cancel{14}2}(\cancel{21}3)(8) \\m=\frac{5}{2}(3)(8) \\m=\frac{5}{\cancel{2}}(3)(\cancel{8}4) \\m=60$
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