Finite Math Examples

$m (60) = 100 \cdot (- e^{- \frac{60}{100}})$

Step 1

Simplify.

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Step 1.1

Cancel the common factor of $60$ and $100$ .

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Step 1.1.1

Factor $20$ out of $60$ .

$m (60) = 100 \cdot (- 1 e^{- \frac{20 (3)}{100}})$

Step 1.1.2

Cancel the common factors.

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Step 1.1.2.1

Factor $20$ out of $100$ .

$m (60) = 100 \cdot (- 1 e^{- \frac{20 \cdot 3}{20 \cdot 5}})$

Step 1.1.2.2

Cancel the common factor.

$m (60) = 100 \cdot (- 1 e^{- \frac{20 \cdot 3}{20 \cdot 5}})$

Step 1.1.2.3

Rewrite the expression.

$m (60) = 100 \cdot (- 1 e^{- \frac{3}{5}})$

Step 1.2

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$m (60) = 100 \cdot (- 1 \frac{1}{e^{\frac{3}{5}}})$

Step 1.3

Rewrite $- 1 \frac{1}{e^{\frac{3}{5}}}$ as $- \frac{1}{e^{\frac{3}{5}}}$ .

$m (60) = 100 \cdot (- \frac{1}{e^{\frac{3}{5}}})$

Step 1.4

Multiply $100 (- \frac{1}{e^{\frac{3}{5}}})$ .

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Step 1.4.1

Multiply $- 1$ by $100$ .

$m (60) = - 100 \frac{1}{e^{\frac{3}{5}}}$

Step 1.4.2

Combine $- 100$ and $\frac{1}{e^{\frac{3}{5}}}$ .

$m (60) = \frac{- 100}{e^{\frac{3}{5}}}$

Step 1.5

Move the negative in front of the fraction.

$m (60) = - \frac{100}{e^{\frac{3}{5}}}$

Step 2

Divide each term in $m (60) = - \frac{100}{e^{\frac{3}{5}}}$ by $60$ and simplify.

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Step 2.1

Divide each term in $m (60) = - \frac{100}{e^{\frac{3}{5}}}$ by $60$ .

$\frac{m (60)}{60} = \frac{- \frac{100}{e^{\frac{3}{5}}}}{60}$

Step 2.2

Simplify the left side.

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Step 2.2.1

Cancel the common factor of $60$ .

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Step 2.2.1.1

Cancel the common factor.

$\frac{m \cdot 60}{60} = \frac{- \frac{100}{e^{\frac{3}{5}}}}{60}$

Step 2.2.1.2

Divide $m$ by $1$ .

$m = \frac{- \frac{100}{e^{\frac{3}{5}}}}{60}$

Step 2.3

Simplify the right side.

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Step 2.3.1

Multiply the numerator by the reciprocal of the denominator.

$m = - \frac{100}{e^{\frac{3}{5}}} \cdot \frac{1}{60}$

Step 2.3.2

Cancel the common factor of $20$ .

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Step 2.3.2.1

Move the leading negative in $- \frac{100}{e^{\frac{3}{5}}}$ into the numerator.

$m = \frac{- 100}{e^{\frac{3}{5}}} \cdot \frac{1}{60}$

Step 2.3.2.2

Factor $20$ out of $- 100$ .

$m = \frac{20 (- 5)}{e^{\frac{3}{5}}} \cdot \frac{1}{60}$

Step 2.3.2.3

Factor $20$ out of $60$ .

$m = \frac{20 \cdot - 5}{e^{\frac{3}{5}}} \cdot \frac{1}{20 \cdot 3}$

Step 2.3.2.4

Cancel the common factor.

$m = \frac{20 \cdot - 5}{e^{\frac{3}{5}}} \cdot \frac{1}{20 \cdot 3}$

Step 2.3.2.5

Rewrite the expression.

$m = \frac{- 5}{e^{\frac{3}{5}}} \cdot \frac{1}{3}$

Step 2.3.3

Multiply $\frac{- 5}{e^{\frac{3}{5}}}$ by $\frac{1}{3}$ .

$m = \frac{- 5}{e^{\frac{3}{5}} \cdot 3}$

Step 2.3.4

Simplify the expression.

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Step 2.3.4.1

Move $3$ to the left of $e^{\frac{3}{5}}$ .

$m = \frac{- 5}{3 \cdot e^{\frac{3}{5}}}$

Step 2.3.4.2

Move the negative in front of the fraction.

$m = - \frac{5}{3 e^{\frac{3}{5}}}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$m = - \frac{5}{3 e^{\frac{3}{5}}}$

Decimal Form:

$m = - 0.91468606 \dots$