Answer:
[tex]r=3.83\times10^8m[/tex]Explanation: We need to find the distance between the moon and earth provided the force between them and their masses. the equation used to solve this problem is as follows:
[tex]\begin{gathered} F=\frac{m_1m_2}{r^2}G\Rightarrow(1) \\ G=6.674\times10^{-11}m^3kg^{-1}s^{-2}_{} \end{gathered}[/tex]Using the known values, and plugging in the equation (1) results in:
[tex]\begin{gathered} m_1=7.34\times10^{22}\operatorname{kg} \\ m_2=5.98\times10^{24}\operatorname{kg} \\ F=2.00\times10^{20}N \\ \end{gathered}[/tex]The final step is as follows:
[tex]\begin{gathered} (2.00\times10^{20}N)=\frac{(7.34\times10^{22}\operatorname{kg})\cdot(5.98\times10^{24}\operatorname{kg})}{r^2}\cdot(6.674\times10^{-11}m^3kg^{-1}s^{-2}_{}) \\ \text{ Rearranging} \\ r^2=\frac{(7.34\times10^{22}\operatorname{kg})\cdot(5.98\times10^{24}\operatorname{kg})\cdot(6.674\times10^{-11}m^3kg^{-1}s^{-2}_{})}{(2.00\times10^{20}N)} \\ r^2=1.4647\times10^{17}m^2 \\ r=\sqrt[]{1.4647\times10^{17}m^2}=3.83\times10^8m \\ r=3.83\times10^8m \end{gathered}[/tex]Therefore the distance between the moon and the earth is:
[tex]r=3.83\times10^8m[/tex]