College Algebra (11th Edition)

Published by Pearson
ISBN 10: 0321671791
ISBN 13: 978-0-32167-179-0

Chapter 3 - Review Exercises - Page 380: 91

Answer

$f=27$

Work Step by Step

$\bf{\text{Solution Outline:}}$ Use $ f=kg^2h $ and solve for the value of $k$ with the given $ f,g $ and $ h $ values. Then use the equation of variation to solve for the value of the unknown variable. $\bf{\text{Solution Details:}}$ Since $f$ varies jointly as $g^2$ and $h,$ then $ f=kg^2h .$ Substituting the given values, $ f=50,g=5, $ and $ h=4 ,$ then the value of $k$ is \begin{array}{l}\require{cancel} f=kg^2h \\\\ 50=k(5)^2(4) \\\\ 50=k(25)(4) \\\\ 50=k(100) \\\\ \dfrac{50}{100}=k \\\\ k=\dfrac{\cancel{50}}{\cancel{50}\cdot2} \\\\ k=\dfrac{1}{2} .\end{array} Hence, the equation of variation is given by \begin{array}{l}\require{cancel} f=kg^2h \\\\ f=\dfrac{1}{2}g^2h .\end{array} If $g=3$ and $h=6,$ then \begin{array}{l}\require{cancel} f=\dfrac{1}{2}g^2h \\\\ f=\dfrac{1}{2}(3)^2(6) \\\\ f=\dfrac{1}{2}(9)(6) \\\\ f=\dfrac{1}{\cancel2}(9)(\cancel2\cdot3) \\\\ f=9(3) \\\\ f=27 .\end{array}
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