r varies directly as s and inversely as t cubed. If r= 607.5 when s= 12 and r= 2, find r when s=42 and c= 6
Question
Answer:
[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}\\\\
-------------------------------\\\\
\textit{\underline{r} varies directly as \underline{s} and inversely as \underline{t} cubed}\qquad r=\cfrac{ks}{t^3}[/tex][tex]\bf \textit{we also know that } \begin{cases} r=607.5\\ s=12\\ t=2 \end{cases}\implies 607.5=\cfrac{k12}{2^3} \\\\\\ 607.5=\cfrac{12k}{8}\implies 607.5=\cfrac{3k}{2}\implies \cfrac{607.5\cdot 2}{3}=k\implies 405=k \\\\\\ therefore\qquad \boxed{r=\cfrac{405s}{t^3}} \\\\\\ \textit{now, when s = 42 and t = 6, what is \underline{r}?}\qquad r=\cfrac{405(42)}{6^3}[/tex]
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11 months ago
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