Question

w varies jointly as x and y and inversely as the square of z. If w=280 when x=30, y=12, and z=3, find w when x=20, y=10 and z=2

Answer 1

`\bf \qquad \qquad \textit{double proportional variation}\\\\ \begin{array}{llll} \textit{\underline{y} varies directly with \underline{x}}\\ \textit{and inversely with \underline{z}} \end{array}\implies y=\cfrac{kx}{z}\impliedby \begin{array}{llll} k=constant\ of\\ \qquad variation \end{array}\\\\ -------------------------------`


`\bf \begin{array}{llll} \textit{`


`\bf 280=\cfrac{360k}{9}\implies \cfrac{280\cdot 9}{360}=k\implies 7=k \\\\\\ therefore\qquad \boxed{w=\cfrac{7xy}{z^2}} \\\\\\ if~ \begin{cases} x=20\\ y=10\\ z=2 \end{cases}~\textit{what is \underline{w}?}\qquad w=\cfrac{7(20)(10)}{2^2}`