Question

suppose y varies jointly with s and the square of e. when s=2 and e=3, then y=54. find y if s=7 and e=11

Answer 1

`\bf \qquad \qquad \textit{direct proportional variation}\\\\ \textit{\underline{y} varies directly with \underline{x}}\qquad \qquad y=kx\impliedby \begin{array}{llll} k=constant\ of\\ \qquad variation \end{array}\\\\ -------------------------------`


`\bf \textit{y varies jointly with s and the square of e}\qquad y=kse^2 \\\\\\ \textit{we also know that } \begin{cases} s=2\\ e=3\\ y=54 \end{cases}\implies 54=k(2)(3)^2 \\\\\\ 54=18k\implies \cfrac{54}{18}=k\implies 3=k\qquad \qquad \boxed{y=3se^2} \\\\\\ \textit{when s = 7 and e = 11, what is \underline{y}?}\qquad y=3(7)(11)^2`