Question

If y varies inversely as x, and y=20 as x=3, find y for the x value 4

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}\\\\ -------------------------------\\\\ \begin{cases} y=20\\ x=3 \end{cases}\implies 20=\cfrac{k}{3}\implies 20\cdot 3=k\implies 60=k \\\\\\ thus\qquad \boxed{y=\cfrac{60}{x}}\\\\ -------------------------------\\\\ now\qquad x=4\qquad y=\cfrac{60}{4}`