Write the variation, and find the quantity indicated. $F$ varies jointly as $q_{1}$ and $q_{2}$ and inversely as the square of $d$. If $F=15$ when $q_{1}=9$, $\mathrm{q}_{2}=3$, and $\mathrm{d}=3$, find $\mathrm{F}$ when $\mathrm{q}_{1}=4, \mathrm{q}_{2}=8$, and $\mathrm{d}=4$. The variation is $\mathrm{F}=\square$. (Type $\mathrm{k}$ for the variation constant. Do not substitute in values.)

Step 1 ：Given that $F$ varies jointly as $q_{1}$ and $q_{2}$ and inversely as the square of $d$, we can write the variation as $F=k\frac{q_{1}q_{2}}{d^{2}}$, where $k$ is the variation constant.

Step 2 ：Substitute the given values into the equation to find the value of $k$. We have $F=15$, $q_{1}=9$, $q_{2}=3$, and $d=3$. So, $15=k\frac{9*3}{3^{2}}$ which gives $k=5.0$.

Step 3 ：Substitute $q_{1}=4$, $q_{2}=8$, and $d=4$ into the equation to find the value of $F$. So, $F=5.0\frac{4*8}{4^{2}}$ which gives $F=10.0$.

Step 4 ：Final Answer: The variation is $F=k\frac{q_{1}q_{2}}{d^{2}}$ and when $q_{1}=4, q_{2}=8$, and $d=4$, $F=\boxed{10}$.