Answer
$\displaystyle \frac{7}{4}$
Work Step by Step
Solving Variation Problems (see p. 424)
1. $\ \ $Write an equation that models the given English statement.
2. $\ \ $Substitute the given pair of values into the equation in step 1 and find the value of k, the constant of variation.
3. $\ \ $Substitute the value of k into the equation in step 1.
4. $\ \ $Use the equation from step 3 to answer the problem's question.
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1.
$a$ varies directly as $b$ or $a$ is directly proportional to $a$.
$a=kb$
$a$ varies inversely as $c^{2}$ or $a$ is inversely proportional to $c^{2}$.
$y=\displaystyle \frac{k}{c^{2}}$
Combined: $a=\displaystyle \frac{kb}{c^{2}}$
2.
$7=\displaystyle \frac{k(9)}{6^{2}} $
$7=\displaystyle \frac{9k}{36} $
$7=\displaystyle \frac{k}{4}\qquad /\times 4$
$k=28$
3.
$a=\displaystyle \frac{28b}{c^{2}}$
4.
$y=\displaystyle \frac{28(4)}{8^{2}}=\frac{28(4)}{64}=\frac{7}{4}$
