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 \stackrel{\textit{\underline{y} varies directly with the square of \underline{x} and inversely with \underline{z}}}{y=\cfrac{kx^2}{z}} \\\\\\ \textit{we also know that } \begin{cases} x=9\\ z=27\\ y=6 \end{cases}\implies 6=\cfrac{k9^2}{27} \\\\\\ \cfrac{27\cdot 6}{9^2}=k\implies 2=k[/tex]
[tex]\bf \stackrel{\textit{\underline{y} varies directly with the square of \underline{x} and inversely with \underline{z}}}{y=\cfrac{kx^2}{z}} \\\\\\ \textit{we also know that } \begin{cases} x=9\\ z=27\\ y=6 \end{cases}\implies 6=\cfrac{k9^2}{27} \\\\\\ \cfrac{27\cdot 6}{9^2}=k\implies 2=k[/tex]
