Question

If p is inversely proportional to the square of q and p is 28 when q is 3, determine p and q is equal to 2

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] ~\dotfill`

`\stackrel{\textit{P varies inversely with }Q^2}{P = \cfrac{k}{Q^2}}\hspace{5em}\textit{we also know that} \begin{cases} Q=3\\ P=28 \end{cases} \\\\\\ 28=\cfrac{k}{3^2}\implies 28=\cfrac{k}{9}\implies 252 = k\hspace{5em}\boxed{P=\cfrac{252}{Q^2}} \\\\\\ \textit{when Q = 2, what is`