Finite Math Examples

$h = - 16 t^{2} \cdot (160 t) + 50$

Step 1

Rewrite the equation as $- 16 t^{2} \cdot (160 t) + 50 = h$ .

$- 16 t^{2} \cdot (160 t) + 50 = h$

Step 2

Simplify each term.

Tap for more steps...

Step 2.1

Rewrite using the commutative property of multiplication.

$- 16 \cdot 160 t^{2} t + 50 = h$

Step 2.2

Multiply $t^{2}$ by $t$ by adding the exponents.

Tap for more steps...

Step 2.2.1

Move $t$ .

$- 16 \cdot 160 (t \cdot t^{2}) + 50 = h$

Step 2.2.2

Multiply $t$ by $t^{2}$ .

Tap for more steps...

Step 2.2.2.1

Raise $t$ to the power of $1$ .

$- 16 \cdot 160 (t^{1} t^{2}) + 50 = h$

Step 2.2.2.2

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$- 16 \cdot 160 t^{1 + 2} + 50 = h$

Step 2.2.3

Add $1$ and $2$ .

$- 16 \cdot 160 t^{3} + 50 = h$

Step 2.3

Multiply $- 16$ by $160$ .

$- 2560 t^{3} + 50 = h$

Step 3

Subtract $50$ from both sides of the equation.

$- 2560 t^{3} = h - 50$

Step 4

Divide each term in $- 2560 t^{3} = h - 50$ by $- 2560$ and simplify.

Tap for more steps...

Step 4.1

Divide each term in $- 2560 t^{3} = h - 50$ by $- 2560$ .

$\frac{- 2560 t^{3}}{- 2560} = \frac{h}{- 2560} + \frac{- 50}{- 2560}$

Step 4.2

Simplify the left side.

Tap for more steps...

Step 4.2.1

Cancel the common factor of $- 2560$ .

Tap for more steps...

Step 4.2.1.1

Cancel the common factor.

$\frac{- 2560 t^{3}}{- 2560} = \frac{h}{- 2560} + \frac{- 50}{- 2560}$

Step 4.2.1.2

Divide $t^{3}$ by $1$ .

$t^{3} = \frac{h}{- 2560} + \frac{- 50}{- 2560}$

Step 4.3

Simplify the right side.

Tap for more steps...

Step 4.3.1

Simplify each term.

Tap for more steps...

Step 4.3.1.1

Move the negative in front of the fraction.

$t^{3} = - \frac{h}{2560} + \frac{- 50}{- 2560}$

Step 4.3.1.2

Cancel the common factor of $- 50$ and $- 2560$ .

Tap for more steps...

Step 4.3.1.2.1

Factor $- 10$ out of $- 50$ .

$t^{3} = - \frac{h}{2560} + \frac{- 10 (5)}{- 2560}$

Step 4.3.1.2.2

Cancel the common factors.

Tap for more steps...

Step 4.3.1.2.2.1

Factor $- 10$ out of $- 2560$ .

$t^{3} = - \frac{h}{2560} + \frac{- 10 \cdot 5}{- 10 \cdot 256}$

Step 4.3.1.2.2.2

Cancel the common factor.

$t^{3} = - \frac{h}{2560} + \frac{- 10 \cdot 5}{- 10 \cdot 256}$

Step 4.3.1.2.2.3

Rewrite the expression.

$t^{3} = - \frac{h}{2560} + \frac{5}{256}$

Step 5

Take the specified root of both sides of the equation to eliminate the exponent on the left side.

$t = \sqrt[3]{- \frac{h}{2560} + \frac{5}{256}}$

Step 6

Simplify $\sqrt[3]{- \frac{h}{2560} + \frac{5}{256}}$ .

Tap for more steps...

Step 6.1

To write $\frac{5}{256}$ as a fraction with a common denominator, multiply by $\frac{10}{10}$ .

$t = \sqrt[3]{- \frac{h}{2560} + \frac{5}{256} \cdot \frac{10}{10}}$

Step 6.2

Write each expression with a common denominator of $2560$ , by multiplying each by an appropriate factor of $1$ .

Tap for more steps...

Step 6.2.1

Multiply $\frac{5}{256}$ by $\frac{10}{10}$ .

$t = \sqrt[3]{- \frac{h}{2560} + \frac{5 \cdot 10}{256 \cdot 10}}$

Step 6.2.2

Multiply $256$ by $10$ .

$t = \sqrt[3]{- \frac{h}{2560} + \frac{5 \cdot 10}{2560}}$

Step 6.3

Combine the numerators over the common denominator.

$t = \sqrt[3]{\frac{- h + 5 \cdot 10}{2560}}$

Step 6.4

Multiply $5$ by $10$ .

$t = \sqrt[3]{\frac{- h + 50}{2560}}$

Step 6.5

Rewrite $\frac{- h + 50}{2560}$ as ${(\frac{1}{8})}^{3} \frac{- h + 50}{5}$ .

Tap for more steps...

Step 6.5.1

Factor the perfect power $1^{3}$ out of $- h + 50$ .

$t = \sqrt[3]{\frac{1^{3} (- h + 50)}{2560}}$

Step 6.5.2

Factor the perfect power $8^{3}$ out of $2560$ .

$t = \sqrt[3]{\frac{1^{3} (- h + 50)}{8^{3} \cdot 5}}$

Step 6.5.3

Rearrange the fraction $\frac{1^{3} (- h + 50)}{8^{3} \cdot 5}$ .

$t = \sqrt[3]{{(\frac{1}{8})}^{3} \frac{- h + 50}{5}}$

Step 6.6

Pull terms out from under the radical.

$t = \frac{1}{8} \sqrt[3]{\frac{- h + 50}{5}}$

Step 6.7

Rewrite $\sqrt[3]{\frac{- h + 50}{5}}$ as $\frac{\sqrt[3]{- h + 50}}{\sqrt[3]{5}}$ .

$t = \frac{1}{8} \cdot \frac{\sqrt[3]{- h + 50}}{\sqrt[3]{5}}$

Step 6.8

Multiply $\frac{\sqrt[3]{- h + 50}}{\sqrt[3]{5}}$ by $\frac{{\sqrt[3]{5}}^{2}}{{\sqrt[3]{5}}^{2}}$ .

$t = \frac{1}{8} (\frac{\sqrt[3]{- h + 50}}{\sqrt[3]{5}} \cdot \frac{{\sqrt[3]{5}}^{2}}{{\sqrt[3]{5}}^{2}})$

Step 6.9

Combine fractions.

Tap for more steps...

Step 6.9.1

Combine and simplify the denominator.

Tap for more steps...

Step 6.9.1.1

Multiply $\frac{\sqrt[3]{- h + 50}}{\sqrt[3]{5}}$ by $\frac{{\sqrt[3]{5}}^{2}}{{\sqrt[3]{5}}^{2}}$ .

$t = \frac{1}{8} \cdot \frac{\sqrt[3]{- h + 50} {\sqrt[3]{5}}^{2}}{\sqrt[3]{5} {\sqrt[3]{5}}^{2}}$

Step 6.9.1.2

Raise $\sqrt[3]{5}$ to the power of $1$ .

$t = \frac{1}{8} \cdot \frac{\sqrt[3]{- h + 50} {\sqrt[3]{5}}^{2}}{{\sqrt[3]{5}}^{1} {\sqrt[3]{5}}^{2}}$

Step 6.9.1.3

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$t = \frac{1}{8} \cdot \frac{\sqrt[3]{- h + 50} {\sqrt[3]{5}}^{2}}{{\sqrt[3]{5}}^{1 + 2}}$

Step 6.9.1.4

Add $1$ and $2$ .

$t = \frac{1}{8} \cdot \frac{\sqrt[3]{- h + 50} {\sqrt[3]{5}}^{2}}{{\sqrt[3]{5}}^{3}}$

Step 6.9.1.5

Rewrite ${\sqrt[3]{5}}^{3}$ as $5$ .

Tap for more steps...

Step 6.9.1.5.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt[3]{5}$ as $5^{\frac{1}{3}}$ .

$t = \frac{1}{8} \cdot \frac{\sqrt[3]{- h + 50} {\sqrt[3]{5}}^{2}}{{(5^{\frac{1}{3}})}^{3}}$

Step 6.9.1.5.2

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$t = \frac{1}{8} \cdot \frac{\sqrt[3]{- h + 50} {\sqrt[3]{5}}^{2}}{5^{\frac{1}{3} \cdot 3}}$

Step 6.9.1.5.3

Combine $\frac{1}{3}$ and $3$ .

$t = \frac{1}{8} \cdot \frac{\sqrt[3]{- h + 50} {\sqrt[3]{5}}^{2}}{5^{\frac{3}{3}}}$

Step 6.9.1.5.4

Cancel the common factor of $3$ .

Tap for more steps...

Step 6.9.1.5.4.1

Cancel the common factor.

$t = \frac{1}{8} \cdot \frac{\sqrt[3]{- h + 50} {\sqrt[3]{5}}^{2}}{5^{\frac{3}{3}}}$

Step 6.9.1.5.4.2

Rewrite the expression.

$t = \frac{1}{8} \cdot \frac{\sqrt[3]{- h + 50} {\sqrt[3]{5}}^{2}}{5^{1}}$

Step 6.9.1.5.5

Evaluate the exponent.

$t = \frac{1}{8} \cdot \frac{\sqrt[3]{- h + 50} {\sqrt[3]{5}}^{2}}{5}$

Step 6.9.2

Combine.

$t = \frac{1 (\sqrt[3]{- h + 50} {\sqrt[3]{5}}^{2})}{8 \cdot 5}$

Step 6.9.3

Multiply.

Tap for more steps...

Step 6.9.3.1

Multiply $\sqrt[3]{- h + 50}$ by $1$ .

$t = \frac{\sqrt[3]{- h + 50} {\sqrt[3]{5}}^{2}}{8 \cdot 5}$

Step 6.9.3.2

Multiply $8$ by $5$ .

$t = \frac{\sqrt[3]{- h + 50} {\sqrt[3]{5}}^{2}}{40}$

Step 6.10

Simplify the numerator.

Tap for more steps...

Step 6.10.1

Rewrite ${\sqrt[3]{5}}^{2}$ as $\sqrt[3]{5^{2}}$ .

$t = \frac{\sqrt[3]{- h + 50} \sqrt[3]{5^{2}}}{40}$

Step 6.10.2

Raise $5$ to the power of $2$ .

$t = \frac{\sqrt[3]{- h + 50} \sqrt[3]{25}}{40}$

Step 6.11

Simplify with factoring out.

Tap for more steps...

Step 6.11.1

Combine using the product rule for radicals.

$t = \frac{\sqrt[3]{(- h + 50) \cdot 25}}{40}$

Step 6.11.2

Reorder factors in $\frac{\sqrt[3]{(- h + 50) \cdot 25}}{40}$ .

$t = \frac{\sqrt[3]{25 (- h + 50)}}{40}$