# Chapter 7 - Functions and Graphs - 7.5 Formulas, Applications, and Variation - 7.5 Exercise Set - Page 488: 75

$\color{blue}{y=\dfrac{4wx^2}{z}}$

#### 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 jointly as $w$ and the square of $x$ and inversely as $z$. Thus, the equation of the variation is $y=\dfrac{kwx^2}{z}$. To find the value of $k$, substitute the given values to obtain: $$y=\dfrac{kwx^2}{z} \\49=\dfrac{k\cdot3\cdot 7^2}{12} \\49=\dfrac{3k\cdot 49}{12} \\49=\dfrac{147k}{12} \\\frac{12}{147} \cdot 49=\frac{147k}{12} \cdot \frac{12}{147} \\4=k$$ Thus, the equation of the variation is: $\color{blue}{y=\dfrac{4wx^2}{z}}$.

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