[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 } \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{\underline{y} is inversely proportional to the square root of \underline{x}}}{y = \cfrac{k}{\sqrt{x}}}~\hfill \stackrel{\textit{we also know that}}{ \begin{cases} y = 61\\ x = 9 \end{cases}}[/tex]
[tex]61=\cfrac{k}{\sqrt{9}}\implies 61=\cfrac{k}{3}\implies 183=k~\hfill \boxed{y = \cfrac{183}{\sqrt{x}}} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{when x = 81, what is "y"?}}{ y = \cfrac{183}{\sqrt{81}}\implies y=\cfrac{183}{9}}\implies y = \cfrac{61}{3}\implies y = 20.\overline{3}\implies y = \stackrel{\textit{rounded up}}{20.33}[/tex]
