Solve the problem.
-If $y$ varies directly as $x ^ { 2 }$ and inversely as $m$, and $y = 6$ when $x = 8$ and $m = 4$, find $y$ when $x = 9$ and $m = 7 .$
A) $4.06$
B) $4.34$
C) $3.05$
D) $3.86$

Question

Quizplus · Accepted Answer

Given that $y$ varies directly as $x^2$ and inversely as $m$, we can write the equation as $y = k \frac{x^2}{m}$, where $k$ is the constant of variation. To find $k$, we use the given values $y = 6$, $x = 8$, and $m = 4$, which gives us $6 = k \frac{8^2}{4}$. Solving for $k$ gives $k = 3$. To find $y$ when $x = 9$ and $m = 7$, we substitute these values into the equation with $k = 3$, resulting in $y = 3 \frac{9^2}{7}$, which simplifies to $y = 3 \frac{81}{7} = 4.34$.

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