Question

Write an equation for the following: y varies indirectly with x and z. Find k when x=3, y=24 and z=15.

Answer 1

`\qquad \qquad \stackrel{indirect~\hfill }{\textit{inverse proportional variation}} \\\\ \textit{\underline{y} varies inversely with \underline{x} and \underline{z}} ~\hspace{6em} \stackrel{\textit{constant of variation}}{y=\cfrac{\stackrel{\downarrow }{k}}{xz}~\hfill } \\\\ \textit{\underline{x} varies inversely with }\underline{z^5} ~\hspace{5.5em} \stackrel{\textit{constant of variation}}{x=\cfrac{\stackrel{\downarrow }{k}}{z^5}~\hfill } \\\\[-0.35em] ~\dotfill\\\\`

`y = \cfrac{k}{xz}\qquad \textit{we also know} \begin{cases} x=3\\ y=24\\ z=15 \end{cases}\implies 24=\cfrac{k}{(3)(15)} \\\\\\ 24(3)(15)=k\implies 1080=k~\hspace{10em}\boxed{y=\cfrac{1080}{xz}}`