Precalculus Examples

$v = \frac{π}{12} h^{3}$ , $v = 75 t$

Step 1

Combine $\frac{π}{12}$ and $h^{3}$ .

$v = \frac{π h^{3}}{12}$

$v = 75 t$

Step 2

Solve the equation for $t$ .

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Rewrite the equation as $75 t = \frac{π h^{3}}{12}$ .

$75 t = \frac{π h^{3}}{12}$

$v = \frac{π h^{3}}{12}$

Divide each term in $75 t = \frac{π h^{3}}{12}$ by $75$ and simplify.

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Divide each term in $75 t = \frac{π h^{3}}{12}$ by $75$ .

$\frac{75 t}{75} = \frac{\frac{π h^{3}}{12}}{75}$

$v = \frac{π h^{3}}{12}$

Simplify the left side.

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Cancel the common factor of $75$ .

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Cancel the common factor.

$\frac{75 t}{75} = \frac{\frac{π h^{3}}{12}}{75}$

$v = \frac{π h^{3}}{12}$

Divide $t$ by $1$ .

$t = \frac{\frac{π h^{3}}{12}}{75}$

$v = \frac{π h^{3}}{12}$

$t = \frac{\frac{π h^{3}}{12}}{75}$

$v = \frac{π h^{3}}{12}$

$t = \frac{\frac{π h^{3}}{12}}{75}$

$v = \frac{π h^{3}}{12}$

Simplify the right side.

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Multiply the numerator by the reciprocal of the denominator.

$t = \frac{π h^{3}}{12} \cdot \frac{1}{75}$

$v = \frac{π h^{3}}{12}$

Combine.

$t = \frac{π h^{3} \cdot 1}{12 \cdot 75}$

$v = \frac{π h^{3}}{12}$

Multiply.

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Multiply $π$ by $1$ .

$t = \frac{h^{3} \cdot π}{12 \cdot 75}$

$v = \frac{π h^{3}}{12}$

Multiply $12$ by $75$ .

$t = \frac{h^{3} π}{900}$

$v = \frac{π h^{3}}{12}$

$t = \frac{h^{3} π}{900}$

$v = \frac{π h^{3}}{12}$

$t = \frac{h^{3} π}{900}$

$v = \frac{π h^{3}}{12}$

$t = \frac{h^{3} π}{900}$

$v = \frac{π h^{3}}{12}$

$t = \frac{h^{3} π}{900}$

$v = \frac{π h^{3}}{12}$

Step 3

Solve the equation for $π$ .

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Simplify $\frac{π}{12} h^{3}$ .

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Rewrite.

$\frac{π h^{3}}{12} = 0 + 0 + \frac{π}{12} h^{3}$

$t = \frac{h^{3} π}{900}$

Simplify by adding zeros.

$\frac{π h^{3}}{12} = \frac{π}{12} h^{3}$

$t = \frac{h^{3} π}{900}$

Combine $\frac{π}{12}$ and $h^{3}$ .

$\frac{π h^{3}}{12} = \frac{π h^{3}}{12}$

$t = \frac{h^{3} π}{900}$

$\frac{π h^{3}}{12} = \frac{π h^{3}}{12}$

$t = \frac{h^{3} π}{900}$

Since the expression on each side of the equation has the same denominator, the numerators must be equal.

$π h^{3} = π h^{3}$

$t = \frac{h^{3} π}{900}$

Move all terms not containing $`$ to the right side of the equation.

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Subtract $π h^{3}$ from both sides of the equation.

$0 = π h^{3} - π h^{3}$

$t = \frac{h^{3} π}{900}$

Subtract $π h^{3}$ from $π h^{3}$ .

$0 = 0$

$t = \frac{h^{3} π}{900}$

$0 = 0$

$t = \frac{h^{3} π}{900}$

Since $0 = 0$ , the equation will always be true.

Always true

$t = \frac{h^{3} π}{900}$

Always true

$t = \frac{h^{3} π}{900}$