Solve 1/2mv^2=1/2*(2.1*10^3)(2.9*10^3)^2

$$\frac { 1 } { 2 } m v ^ { 2 } = \frac { 1 } { 2 } \cdot ( 2.1 \times 10 ^ { 3 } ) ( 2.9 \times 10 ^ { 3 } ) ^ { 2 }$$

Solve for m

$$m=\frac{17661000000}{v^{2}}$$

$$v\neq 0$$

Steps for Solving Linear Equation

Cancel out \frac{1}{2} on both sides.

$$mv^{2}=2.1\times 10^{3}\times \left(2.9\times 10^{3}\right)^{2}$$

Calculate 10 to the power of 3 and get 1000.

$$mv^{2}=2.1\times 1000\times \left(2.9\times 10^{3}\right)^{2}$$

Multiply 2.1 and 1000 to get 2100.

$$mv^{2}=2100\times \left(2.9\times 10^{3}\right)^{2}$$

Calculate 10 to the power of 3 and get 1000.

$$mv^{2}=2100\times \left(2.9\times 1000\right)^{2}$$

Multiply 2.9 and 1000 to get 2900.

$$mv^{2}=2100\times 2900^{2}$$

Calculate 2900 to the power of 2 and get 8410000.

$$mv^{2}=2100\times 8410000$$

Multiply 2100 and 8410000 to get 17661000000.

$$mv^{2}=17661000000$$

The equation is in standard form.

$$v^{2}m=17661000000$$

Divide both sides by v^{2}.

$$\frac{v^{2}m}{v^{2}}=\frac{17661000000}{v^{2}}$$

Dividing by v^{2} undoes the multiplication by v^{2}.

$$m=\frac{17661000000}{v^{2}}$$

Solve for v (complex solution)

$$v=-29000\sqrt{21}m^{-0.5}$$

$$v=29000\sqrt{21}m^{-0.5}\text{, }m\neq 0$$

Solve for v

$$v=29000\sqrt{\frac{21}{m}}$$

$$v=-29000\sqrt{\frac{21}{m}}\text{, }m>0$$