[tex]\qquad \qquad \textit{inverse proportional variation} \\\\ \textit{\underline{y} varies inversely with \underline{x}} ~\hspace{6em} \stackrel{\textit{constant of variation}}{y=\cfrac{\stackrel{\downarrow }{k}}{x}~\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] \rule{34em}{0.25pt}[/tex]
[tex]\stackrel{\begin{array}{llll} \textit{"y" varies}\\ inversely\\ as~ x^2 \end{array}}{y=\cfrac{k}{x^2}}\qquad \textit{we also know that} \begin{cases} y=8\\ x=4 \end{cases}\implies 8=\cfrac{k}{(4)^2}[/tex]
[tex]8=\cfrac{k}{16}\implies 128=k~\hfill \boxed{y=\cfrac{128}{x^2}} \\\\\\ when~y=\frac{25}{36}\textit{ what is "x"?}\qquad \cfrac{25}{36}=\cfrac{128}{x^2}\implies 25x^2=4608 \\\\\\ x^2=\cfrac{4608}{25}\implies x = \sqrt{\cfrac{4608}{25}}\implies x=\cfrac{\sqrt{4608}}{\sqrt{25}}\implies x=\cfrac{48\sqrt{2}}{5}[/tex]
