Let's write the equation
[tex] F=\dfrac{p_1-p_2}{r} [/tex]
plugging the known values:
[tex] p_1=100,\ p_2=0,\ F=5 [/tex]
So, the equation becomes
[tex] 5 = \dfrac{100-0}{r} \iff 5 = \dfrac{100}{r} [/tex]
To solve for [tex] r [/tex], Let's multiply both sides by r:
[tex] 5r = 100 [/tex]
And divide both sides by 5:
[tex] r = \dfrac{100}{5}=20 [/tex]
As for the table below, this is the equation solved for each variable: depending on what you need, use the appropriate formula, and plug the known values for the other variables:
First row: solving for [tex] r [/tex]
Start from
[tex] F=\dfrac{p_1-p_2}{r} [/tex]
Multiply both sides by r and divide both sides by F:
[tex] r=\dfrac{p_1-p_2}{F} [/tex]
Second row: solving for [tex] F [/tex]
This is the form we are already given:
[tex] F=\dfrac{p_1-p_2}{r} [/tex]
Third row: solving for [tex] p_1 [/tex]
Start from
[tex] F=\dfrac{p_1-p_2}{r} [/tex]
Multiply both sides by r:
[tex] rF=p_1-p_2 [/tex]
Add [tex]p_2[/tex] to both sides:
[tex] rF+p_2=p_1[/tex]
Fourth row: solving for [tex] p_2 [/tex]
Start from
[tex] F=\dfrac{p_1-p_2}{r} [/tex]
Multiply both sides by r:
[tex] rF=p_1-p_2 [/tex]
Subtract [tex]p_1[/tex] from both sides:
[tex] rF-p_1=-p_2[/tex]
Change sign to both sides:
[tex] p_1-rF=p_2[/tex]
