Respuesta :
[tex]\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}\\\\
-------------------------------[/tex]
[tex]\bf \begin{array}{llll} \textit{"\underline{w} varies jointly as \underline{x} and \underline{y}}\\ \textit{and inversely as the square of \underline{z}"} \end{array}\implies w=\cfrac{kxy}{z^2} \\\\\\ \textit{we also know that } \begin{cases} w=280\\ x=30\\ y=12\\ z=3 \end{cases}\implies 280=\cfrac{k(30)(12)}{3^2}[/tex]
[tex]\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}[/tex]
[tex]\bf \begin{array}{llll} \textit{"\underline{w} varies jointly as \underline{x} and \underline{y}}\\ \textit{and inversely as the square of \underline{z}"} \end{array}\implies w=\cfrac{kxy}{z^2} \\\\\\ \textit{we also know that } \begin{cases} w=280\\ x=30\\ y=12\\ z=3 \end{cases}\implies 280=\cfrac{k(30)(12)}{3^2}[/tex]
[tex]\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}[/tex]
