Solve the problem.
-$R$ varies directly as $x ^ { 2 }$ and inversely as $t$ when $R = 30$ when $x = 6$ and $t = 12$. Find $R$ when $x = 7$ and $t = 9$.
A) $R = \frac { 9 } { 490 }$
B) $R = \frac { 490 } { 9 }$
C) $R = \frac { 3 } { 140 }$
D) $R = \frac { 140 } { 3 }$

Question

Quizplus · Accepted Answer

Given $R$ varies directly as $x^2$ and inversely as $t$, we use the formula $R = k\frac{x^2}{t}$ where $k$ is the constant of proportionality. Substituting the given values, $30 = k\frac{6^2}{12}$, we find $k = 10$. Then, for $x = 7$ and $t = 9$, $R = 10\frac{7^2}{9} = \frac{490}{9}$.

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