Question

Z varies inversely with the product of x and y. When x=2 and y =4 z=0.5 what is the value of x=4 and y=9

Answer 1

$\bf \qquad \qquad \textit{inverse proportional variation}\\\\ \textit{\underline{y} varies inversely with \underline{x}}\qquad \qquad y=\cfrac{k}{x}\impliedby \begin{array}{llll} k=constant\ of\\ \qquad variation \end{array}\\\\ -------------------------------$

$\bf \textit{\underline{z} varies inversely with the product of \underline{x} and \underline{y}}\implies z=\cfrac{k}{xy} \\\\\\ \textit{we also know that } \begin{cases} x=2\\ y=4\\ z=0.5 \end{cases}\implies 0.5=\cfrac{k}{(2)(4)}\implies 0.5=\cfrac{k}{8} \\\\\\ 4=k\qquad \qquad \boxed{z=\cfrac{4}{xy}} \\\\\\ \textit{when x = 4 and y = 9, what is \underline{z}?}\qquad z=\cfrac{4}{(4)(9)}$