If $\mathrm { f }$ varies jointly as $\mathrm { q } ^ { 2 }$ and $h$, and $\mathrm { f } = 24$ when $\mathrm { q } = 2$ and $\mathrm { h } = 3$, find $\mathrm { h }$ when $\mathrm { f } = 160$ and $\mathrm { q } = 4$.
A) $h = 2$
B) $h = 3$
C) $h = 5$
D) $h = 4$

Question

Quizplus · Accepted Answer

The formula for joint variation is $f = kq^2h$, where $k$ is the constant of variation. Given $f = 24$, $q = 2$, and $h = 3$, we can find $k$ by substituting these values into the formula: $24 = k(2)^2(3)$, which simplifies to $24 = 4k(3)$, and further to $k = 2$. To find $h$ when $f = 160$ and $q = 4$, substitute these values and the found $k$ into the formula: $160 = 2(4)^2h$, which simplifies to $160 = 32h$, and further to $h = 5$.

If f\mathrm { f }f Varies Jointly As q2\mathrm { q } ^ { 2 }q2

If $\mathrm { f }$ Varies Jointly As $\mathrm { q } ^ { 2 }$