Question

P is inversely proportional to the cube of (q-2) p=6 when q=3 find the value of p when q is 5

Answer 1

`\bf \begin{array}{llllll} \textit{something}&&\textit{varies inversely to}&\textit{something else}\\ \quad \\ \textit{something}&=&\cfrac{{{\textit{some value}}}}{}&\cfrac{}{\textit{something else}}\\ \quad \\ y&=&\cfrac{{{\textit{k}}}}{}&\cfrac{}{x} \\ &&y=\cfrac{{{ k}}}{x} \end{array}\\\\ -----------------------------\\\\ \textit{p is inversely proportional to the cube of (q-2)}\implies p=\cfrac{k}{(q-2)^3} \\\\\\ now \quad \begin{cases} p=6\\ q=3 \end{cases}\implies 6=\cfrac{k}{(3-2)^3}`

solve for "k", to find k or the "constant of variation"

then plug k's value back to
`\bf p=\cfrac{k}{(q-2)^3}`

now.... what is "p" when q = 5? well, just set "q" to 5 on the right-hand-side, and simplify, to see what "p" is