Answer
216
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.
$y$ varies directly as $m:\qquad y=km$
$y$ varies directly as $n^{2}:\qquad y=kn^{2}$
$y$ varies inversely as $ p:\displaystyle \qquad y=\frac{k}{p},$
Combined (jointly): $\displaystyle \qquad y=\frac{kmn^{2}}{p}.$
2.
$15=\displaystyle \frac{k(2)(1^{2})}{6}$
$15=\displaystyle \frac{k}{3}\qquad/\times 3$
$k=45$
3.
$ y=\displaystyle \frac{45mn^{2}}{p}$
4.
$ y=\displaystyle \frac{45(3)(4^{2})}{10}=\frac{9(3)(16)}{2}=9(3)(8)=216$
