Question

Let r vary directly with s and inversely with t. Which equation represents this equation? Assume that a is a constant.

$r = ast$
$r = \frac{as}{t}$
$r = \frac{at}{s}$
$r = \frac{a}{st}$

Answer 1

$\bf \qquad \qquad \textit{combined variation} \\\\ \begin{array}{llll} \textit{\underline{y} varies directly with \underline{x}}\\ \textit{and inversely with \underline{z}} \end{array}\implies y=\cfrac{kx}{z}\impliedby \begin{array}{llll} k=constant\ of\\ \qquad variation \end{array}\\\\ -------------------------------\\\\ \stackrel{\textit{\underline{r} varies directly with \underline{s} and inversely with \underline{t}}}{r=\cfrac{ks}{t}\qquad \textit{ and since a = k}\qquad r=\cfrac{as}{t}}$