# Chapter 6 - Section 6.6 - Variation - 6.6 Exercises - Page 418: 39

$z=\dfrac{5}{8}=0.625$

#### Work Step by Step

Recall: If $y$ varies inversely as $x$, then the inverse variation's equation is $y=\frac{k}{x}$ where $k$ is the constant of variation. Since $z$ varies inversely as $w$, then the equation of the direct variation, with $k$ as the constant of variation, is: $$z=\frac{k}{w}$$ When $w=0.5$, $z=10$. Substitute these into the equation above to obtain: \begin{align*} z&=\frac{k}{w}\\\\ 10&=\frac{k}{0.5}\\\\ 10(0.5)&=k\\\\ 5&=k\\\\ \end{align*} Thus, the equation for the inverse variation is: $$z=\frac{5}{0.5}$$ To find the value of $z$ when $w=8$, substitute $8$ to $w$ in the equation above to obtain: \begin{align*} z&=\frac{5}{8}=0.625\\\\ \end{align*}

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