Determine the constant of variation for the stated condition.
-f varies jointly as $\mathrm { q } ^ { 2 }$ and $h$, and $\mathrm { f } = - 54$ when $\mathrm { q } = 3$ and $\mathrm { h } = 3$. Find $\mathrm { f }$ when $\mathrm { q } = 4$ and $\mathrm { h } = 5$.
A) $f = - 160$
B) $f = - 40$
C) $f = - 32$
D) $\mathrm { f } = - 10$

Question

Quizplus · Accepted Answer

The formula for joint variation is $f = kq^2h$, where $k$ is the constant of variation. Substituting the given values, $f = -54$, $q = 3$, and $h = 3$, we get $-54 = k(3)^2(3)$. Solving for $k$, we find $k = -2$. To find $f$ when $q = 4$ and $h = 5$, substitute these values and $k = -2$ into the formula: $f = -2(4)^2(5) = -160$.

Determine the Constant of Variation for the Stated Condition q2\mathrm { q } ^ { 2 }q2

Determine the Constant of Variation for the Stated Condition $\mathrm { q } ^ { 2 }$