[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{y varies directly with}\\
\textit{the square root of x and inversely with z}
\end{array}\qquad y=\cfrac{k\sqrt{x}}{z}
\\\\\\
\textit{we also know that }
\begin{cases}
x=4\\
z=3\\
y=10
\end{cases}\implies 10=\cfrac{k\sqrt{4}}{3}\implies 30=k2
\\\\\\
\cfrac{30}{2}=k\implies 15=k\qquad \qquad \boxed{y=\cfrac{15\sqrt{x}}{z}}
\\\\\\
\textit{when x = 49 and z = 3, what is \underline{y}?}\qquad \qquad y=\cfrac{15\sqrt{49}}{3}[/tex]
[tex]\bf y=\cfrac{15\cdot 7}{3}\implies y=\cfrac{15}{3}\cdot 7\implies y=5\cdot 7\implies y=35[/tex]
