Elementary and Intermediate Algebra: Concepts & Applications (6th Edition)

Published by Pearson
ISBN 10: 0-32184-874-8
ISBN 13: 978-0-32184-874-1

Chapter 7 - Functions and Graphs - 7.5 Formulas, Applications, and Variation - 7.5 Exercise Set: 76

Answer

$\color{blue}{y=\dfrac{6x}{wz^2}}$

Work Step by Step

RECALL: (1) When $y$ varies directly as $x$, the equation of the variation is $y=kx$ . (2) When $y$ varies inversely as $x$, the equation of the variation is $y=\frac{k}{x}$. (3) When $y$ varies jointly as $x$ and $z$, the equation of the variation is $y=kxz$. $y$ varies directly as $x$ and inversely as $w$ and the square of $z$. Thus, the equation of the variation is $y=\dfrac{kx}{wz^2}$. To find the value of $k$, substitute the given values to obtain: $$y=\dfrac{kx}{wz^2} \\4.5=\dfrac{k\cdot15}{5\cdot2^2} \\4.5=\dfrac{15k}{5\cdot 4} \\4.5=\dfrac{15k}{20} \\\frac{20}{15} \cdot 4.5=\frac{15k}{20} \cdot \frac{20}{15} \\6=k$$ Thus, the equation of the variation is: $\color{blue}{y=\dfrac{6x}{wz^2}}$.
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