Mathematics, 22.11.2021 14:00 reneewilliams20
If y is inversely proportional to the square root of x and y=61 when x=9, find y if x=81. (Round off your answer to the nearest hundredth.)
Answers: 3
![\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}}](/tpl/images/2566/3792/14597.png)
![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}](/tpl/images/2566/3792/b9139.png)
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If y is inversely proportional to the square root of x and y=61 when x=9, find y if x=81. (Round off...
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