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4 years ago

The time required for an outlet pipe to an empty a tank is inversely proportional to the cross-sectional area of the pipe. A pip

e with the cross-sectional area of 113.0 square inches requires 6.4 hours to empty a certain tank if the pipe was replaced with one with a cross-sectional area of 50.25 square inches, how long would it take to empty the same tank

Mathematics

1 answer:

NNADVOKAT [17]4 years ago

5 0

$\bf \qquad \qquad \textit{inverse proportional variation}
\\\\
\textit{\underline{y} varies inversely with \underline{x}}\qquad \qquad y=\cfrac{k}{x}\impliedby 
\begin{array}{llll}
k=constant\ of\\
\qquad variation
\end{array}\\\\
-------------------------------$

$\bf \stackrel{\textit{\underline{t}ime to empty a tank is inversely proportional to \underline{c}ross-sectional area}}{t=\cfrac{k}{c}}
\\\\\\
\textit{we also know that }
\begin{cases}
c=113.0\\
t=6.4
\end{cases}\implies 6.4=\cfrac{k}{113}\implies 723.2=k
\\\\\\
therefore\qquad \boxed{t=\cfrac{723.2}{c}}
\\\\\\
\textit{when c = 50.25, what is \underline{t}?}\qquad t=\cfrac{723.2}{50.25}\implies t\approx 14.3920398$

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