Question

If y varies inversely as x, and y=39 when x=3 find y when x=11
?

Answer 1

`\bf \qquad \qquad \textit{inverse proportional variation} \\\\ \textit{\underline{y} varies inversely with \underline{x}}\qquad \qquad y=\cfrac{k}{x}\impliedby \begin{array}{llll} k=constant\ of\\ \qquad variation \end{array}\\\\ -------------------------------\\\\ \textit{we also know that } \begin{cases} y=39\\ x=3 \end{cases}\implies 39=\cfrac{k}{3}\implies 39(3)=k \\\\\\ 117=k\qquad therefore\qquad \boxed{y=\cfrac{117}{x}} \\\\\\ \textit{when x = 11, what is \underline{y}?}\qquad y=\cfrac{117}{11}`