Question

1. $c = 2pi r$ solve for $r$
2. $v=pi r^{2}h$
3. $i = prt$ solve for $r$
4. $e = mc^{2}$
5. $p=\frac{100a}{t}$ solve for $a$
6. $v=\frac{1}{3}pi r^{2}h$
7. $y = mx + b$ solve for $m$
8. $a = 2(b - c)$
9. $w = 3x+7y$ solve for $y$
10. $a=\frac{1}{2}h(b_{1}+b_{2})$

Explanation:

Step1: Isolate the variable in 3.

Divide both sides of $C = 2\pi r$ by $2\pi$.
$r=\frac{C}{2\pi}$

Step2: Isolate the variable in 4.

First, divide both sides of $V=\pi r^{2}h$ by $\pi h$. Then take the square - root of both sides.
$r^{2}=\frac{V}{\pi h}$, $r = \pm\sqrt{\frac{V}{\pi h}}$ (we usually consider the positive value for radius in geometric contexts)

Step3: Isolate the variable in 5.

Divide both sides of $I = prt$ by $pt$.
$r=\frac{I}{pt}$

Step4: Isolate the variable in 6.

Divide both sides of $E = mc^{2}$ by $c^{2}$.
$m=\frac{E}{c^{2}}$

Step5: Isolate the variable in 7.

Multiply both sides of $P=\frac{100a}{t}$ by $t$ and then divide by 100.
$100a = Pt$, $a=\frac{Pt}{100}$

Step6: Isolate the variable in 8.

First, multiply both sides of $V=\frac{1}{3}\pi r^{2}h$ by 3 to get $3V=\pi r^{2}h$. Then divide by $\pi h$ and take the square - root.
$r^{2}=\frac{3V}{\pi h}$, $r=\pm\sqrt{\frac{3V}{\pi h}}$ (usually take positive for radius)

Step7: Isolate the variable in 9.

Subtract $b$ from both sides of $y = mx + b$ and then divide by $x$ ($x
eq0$).
$mx=y - b$, $m=\frac{y - b}{x}$

Step8: Isolate the variable in 10.

Divide both sides of $a = 2(b - c)$ by 2.
$b - c=\frac{a}{2}$, then $b=\frac{a}{2}+c$

Step9: Isolate the variable in 11.

Subtract $3x$ from both sides of $w = 3x+7y$ and then divide by 7.
$7y=w - 3x$, $y=\frac{w - 3x}{7}$

Step10: Isolate the variable in 12.

First, multiply both sides of $A=\frac{1}{2}h(b_{1}+b_{2})$ by 2 to get $2A = h(b_{1}+b_{2})$. Then divide by $h$ and subtract $b_{1}$.
$b_{1}+b_{2}=\frac{2A}{h}$, $b_{2}=\frac{2A}{h}-b_{1}$

Answer:

1. $r=\frac{C}{2\pi}$
2. $r = \pm\sqrt{\frac{V}{\pi h}}$
3. $r=\frac{I}{pt}$
4. $m=\frac{E}{c^{2}}$
5. $a=\frac{Pt}{100}$
6. $r=\pm\sqrt{\frac{3V}{\pi h}}$
7. $m=\frac{y - b}{x}$
8. $b=\frac{a}{2}+c$
9. $y=\frac{w - 3x}{7}$
10. $b_{2}=\frac{2A}{h}-b_{1}$