Translate the given formula to an English phrase using the word "varies".
-If $\mathrm { y }$ varies directly as $\mathrm { x } ^ { 2 }$ and inversely as $\mathrm { m }$, and $\mathrm { y } = 9$ when $\mathrm { x } = 2$ and $\mathrm { m } = 5$, find $\mathrm { y }$ when $\mathrm { x } = 8$ and $\mathrm { m } = 10$.
A) 18
B) $0.25$
C) 72
D) $1.13$

Question

Quizplus · Accepted Answer

The formula for direct and inverse variation is $y = k\frac{x^2}{m}$, where $k$ is the constant of variation. Given $y = 9$, $x = 2$, and $m = 5$, we can find $k$ by substituting these values: $9 = k\frac{2^2}{5}$, solving for $k$ gives $k = 22.5$. To find $y$ when $x = 8$ and $m = 10$, substitute these values into the formula with $k = 22.5$: $y = 22.5\frac{8^2}{10} = 72$.

Translate the Given Formula to an English Phrase Using the Word