Respuesta :
[tex]\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}\\\\
-------------------------------\\\\[/tex]
[tex]\bf \textit{\underline{y} varies jointly as \underline{x} and \underline{z}}\implies y=kxz \\\\\\ \textit{we also know that } \begin{cases} y=80\\ x=5\\ z=4 \end{cases}\implies 80=k(5)(4)\implies 80=20k \\\\\\ \cfrac{80}{20}=k\implies 4=k\qquad thus\qquad \boxed{y=4xz}\\\\ -------------------------------\\\\ if~\begin{cases} x=4\\ z=6 \end{cases}~\textit{what is \underline{y}?}\qquad y=4(4)(6)[/tex]
[tex]\bf \textit{\underline{y} varies jointly as \underline{x} and \underline{z}}\implies y=kxz \\\\\\ \textit{we also know that } \begin{cases} y=80\\ x=5\\ z=4 \end{cases}\implies 80=k(5)(4)\implies 80=20k \\\\\\ \cfrac{80}{20}=k\implies 4=k\qquad thus\qquad \boxed{y=4xz}\\\\ -------------------------------\\\\ if~\begin{cases} x=4\\ z=6 \end{cases}~\textit{what is \underline{y}?}\qquad y=4(4)(6)[/tex]
