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Olin [163]
3 years ago
11

If y varies directly as (x+3) and inversely as (x-3) and y=21 when x=4, what is the equation for y in terms of x?

Mathematics
1 answer:
igor_vitrenko [27]3 years ago
6 0
\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 \textit{\underline{y} varies directly as (x+3) and inversely as (x-3)}\implies y=\cfrac{k(x+3)}{x-3}
\\\\\\
\textit{we also know that }
\begin{cases}
y=21\\
x=4
\end{cases}\implies 21=\cfrac{k(4+3)}{4-3}\implies 21=\cfrac{k(7)}{1}
\\\\\\
\cfrac{21}{7}=k\implies 3=k\qquad thus\qquad \qquad \boxed{y=\cfrac{3(x+3)}{x-3}}
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