Question

F

Answer 1

$\qquad \qquad \textit{inverse proportional variation} \\\\ \textit{\underline{y} varies inversely with \underline{x}} ~\hspace{6em} \stackrel{\textit{constant of variation}}{y=\cfrac{\stackrel{\downarrow }{k}}{x}~\hfill } \\\\ \textit{\underline{x} varies inversely with }\underline{z^5} ~\hspace{5.5em} \stackrel{\textit{constant of variation}}{x=\cfrac{\stackrel{\downarrow }{k}}{z^5}~\hfill } \\\\[-0.35em] \rule{34em}{0.25pt}$

$\stackrel{\textit{"F" inversely proportional to }\sqrt{g}}{F=\cfrac{k}{\sqrt{g}}}\qquad \textit{we also know that} \begin{cases} F=18\\ g=9 \end{cases} \\\\\\ 18=\cfrac{k}{\sqrt{9}}\implies 18=\cfrac{k}{3}\implies 54=k~\hfill\boxed{ F=\cfrac{54}{\sqrt{g}}} \\\\\\ \textit{when g = 36, what is "F"?}\qquad F=\cfrac{54}{\sqrt{36}}\implies F=\cfrac{54}{6}\implies F=9$