Suppose z varies directly as the square of x and inversely as y. If x is halved and y is tripled, what happens to z?
A) z is one-sixth as large as before
B) z is six times as large as before
C) z is multiplied by $\frac { 3 } { 2 }$
D) z is one-twelfth as large as before

Question

Quizplus · Accepted Answer

Since z varies directly as the square of x, halving x would make z one-fourth as large (because $(\frac{1}{2})^2 = \frac{1}{4}$). Since z varies inversely as y, tripling y would make z one-third as large. Combining these effects, z becomes $\frac{1}{4} \times \frac{1}{3} = \frac{1}{12}$ as large as before.

Suppose Z Varies Directly as the Square of X and Inversely