Translate the given formula to an English phrase using the word "varies".
-Suppose $\mathrm { z }$ varies directly as $\mathrm { x }$ and inversely as the square of $\mathrm { y }$. If $\mathrm { x }$ is doubled and $\mathrm { y }$ is tripled, what happens to $\mathrm { z }$ ?
A) $\mathrm { z }$ is six times as large as before
B) $\mathrm { z }$ is multiplied by $\frac { 1 } { 18 }$
C) $\mathrm { z }$ is multiplied by $\frac { 2 } { 9 }$
D) $\mathrm { z }$ is one-sixth as large as before

Question

Quizplus · Accepted Answer

Since $z$ varies directly as $x$, doubling $x$ would double $z$. However, since $z$ also varies inversely as the square of $y$, tripling $y$ would divide $z$ by $3^2 = 9$. Combining these effects, $z$ is multiplied by $\frac{2}{9}$.

Translate the Given Formula to an English Phrase Using the Word