Trigonometry Examples

P (80) = \frac{90}{1 + 271 e^{- 0.122 \cdot 80}}

$P (80) = \frac{90}{1 + 271 e^{- 0.122 \cdot 80}}$

Step 1

Simplify.

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Step 1.1

Multiply

- 0.122

$- 0.122$ by

80

$80$ .

P (80) = \frac{90}{1 + 271 e^{- 9.76}}

$P (80) = \frac{90}{1 + 271 e^{- 9.76}}$

Step 1.2

Rewrite the expression using the negative exponent rule

b^{- n} = \frac{1}{b^{n}}

$b^{- n} = \frac{1}{b^{n}}$ .

P (80) = \frac{90}{1 + 271 \frac{1}{e^{9.76}}}

$P (80) = \frac{90}{1 + 271 \frac{1}{e^{9.76}}}$

Step 1.3

Combine

271

$271$ and

\frac{1}{e^{9.76}}

$\frac{1}{e^{9.76}}$ .

P (80) = \frac{90}{1 + \frac{271}{e^{9.76}}}

$P (80) = \frac{90}{1 + \frac{271}{e^{9.76}}}$

Step 1.4

Simplify the denominator.

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Step 1.4.1

Write

1

$1$ as a fraction with a common denominator.

P (80) = \frac{90}{\frac{e^{9.76}}{e^{9.76}} + \frac{271}{e^{9.76}}}

$P (80) = \frac{90}{\frac{e^{9.76}}{e^{9.76}} + \frac{271}{e^{9.76}}}$

Step 1.4.2

Combine the numerators over the common denominator.

P (80) = \frac{90}{\frac{e^{9.76} + 271}{e^{9.76}}}

$P (80) = \frac{90}{\frac{e^{9.76} + 271}{e^{9.76}}}$

P (80) = \frac{90}{\frac{e^{9.76} + 271}{e^{9.76}}}

$P (80) = \frac{90}{\frac{e^{9.76} + 271}{e^{9.76}}}$

Step 1.5

Multiply the numerator by the reciprocal of the denominator.

P (80) = 90 \frac{e^{9.76}}{e^{9.76} + 271}

$P (80) = 90 \frac{e^{9.76}}{e^{9.76} + 271}$

Step 1.6

Combine

90

$90$ and

\frac{e^{9.76}}{e^{9.76} + 271}

$\frac{e^{9.76}}{e^{9.76} + 271}$ .

P (80) = \frac{90 e^{9.76}}{e^{9.76} + 271}

$P (80) = \frac{90 e^{9.76}}{e^{9.76} + 271}$

P (80) = \frac{90 e^{9.76}}{e^{9.76} + 271}

$P (80) = \frac{90 e^{9.76}}{e^{9.76} + 271}$

Step 2

Divide each term in

P (80) = \frac{90 e^{9.76}}{e^{9.76} + 271}

$P (80) = \frac{90 e^{9.76}}{e^{9.76} + 271}$ by

80

$80$ and simplify.

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Step 2.1

Divide each term in

P (80) = \frac{90 e^{9.76}}{e^{9.76} + 271}

$P (80) = \frac{90 e^{9.76}}{e^{9.76} + 271}$ by

80

$80$ .

\frac{P (80)}{80} = \frac{\frac{90 e^{9.76}}{e^{9.76} + 271}}{80}

$\frac{P (80)}{80} = \frac{\frac{90 e^{9.76}}{e^{9.76} + 271}}{80}$

Step 2.2

Simplify the left side.

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Step 2.2.1

Cancel the common factor of

80

$80$ .

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Step 2.2.1.1

Cancel the common factor.

\frac{P \cdot 80}{80} = \frac{\frac{90 e^{9.76}}{e^{9.76} + 271}}{80}

$\frac{P \cdot 80}{80} = \frac{\frac{90 e^{9.76}}{e^{9.76} + 271}}{80}$

Step 2.2.1.2

Divide

P

$P$ by

1

$1$ .

P = \frac{\frac{90 e^{9.76}}{e^{9.76} + 271}}{80}

$P = \frac{\frac{90 e^{9.76}}{e^{9.76} + 271}}{80}$

P = \frac{\frac{90 e^{9.76}}{e^{9.76} + 271}}{80}

$P = \frac{\frac{90 e^{9.76}}{e^{9.76} + 271}}{80}$

P = \frac{\frac{90 e^{9.76}}{e^{9.76} + 271}}{80}

$P = \frac{\frac{90 e^{9.76}}{e^{9.76} + 271}}{80}$

Step 2.3

Simplify the right side.

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Step 2.3.1

Multiply the numerator by the reciprocal of the denominator.

P = \frac{90 e^{9.76}}{e^{9.76} + 271} \cdot \frac{1}{80}

$P = \frac{90 e^{9.76}}{e^{9.76} + 271} \cdot \frac{1}{80}$

Step 2.3.2

Cancel the common factor of

10

$10$ .

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Step 2.3.2.1

Factor

10

$10$ out of

90 e^{9.76}

$90 e^{9.76}$ .

P = \frac{10 (9 e^{9.76})}{e^{9.76} + 271} \cdot \frac{1}{80}

$P = \frac{10 (9 e^{9.76})}{e^{9.76} + 271} \cdot \frac{1}{80}$

Step 2.3.2.2

Factor

10

$10$ out of

80

$80$ .

P = \frac{10 (9 e^{9.76})}{e^{9.76} + 271} \cdot \frac{1}{10 (8)}

$P = \frac{10 (9 e^{9.76})}{e^{9.76} + 271} \cdot \frac{1}{10 (8)}$

Step 2.3.2.3

Cancel the common factor.

P = \frac{10 (9 e^{9.76})}{e^{9.76} + 271} \cdot \frac{1}{10 \cdot 8}

$P = \frac{10 (9 e^{9.76})}{e^{9.76} + 271} \cdot \frac{1}{10 \cdot 8}$

Step 2.3.2.4

Rewrite the expression.

P = \frac{9 e^{9.76}}{e^{9.76} + 271} \cdot \frac{1}{8}

$P = \frac{9 e^{9.76}}{e^{9.76} + 271} \cdot \frac{1}{8}$

P = \frac{9 e^{9.76}}{e^{9.76} + 271} \cdot \frac{1}{8}

$P = \frac{9 e^{9.76}}{e^{9.76} + 271} \cdot \frac{1}{8}$

Step 2.3.3

Multiply

\frac{9 e^{9.76}}{e^{9.76} + 271}

$\frac{9 e^{9.76}}{e^{9.76} + 271}$ by

\frac{1}{8}

$\frac{1}{8}$ .

P = \frac{9 e^{9.76}}{(e^{9.76} + 271) \cdot 8}

$P = \frac{9 e^{9.76}}{(e^{9.76} + 271) \cdot 8}$

Step 2.3.4

Move

8

$8$ to the left of

e^{9.76} + 271

$e^{9.76} + 271$ .

P = \frac{9 e^{9.76}}{8 (e^{9.76} + 271)}

$P = \frac{9 e^{9.76}}{8 (e^{9.76} + 271)}$

P = \frac{9 e^{9.76}}{8 (e^{9.76} + 271)}

$P = \frac{9 e^{9.76}}{8 (e^{9.76} + 271)}$

P = \frac{9 e^{9.76}}{8 (e^{9.76} + 271)}

$P = \frac{9 e^{9.76}}{8 (e^{9.76} + 271)}$

Step 3

The result can be shown in multiple forms.

Exact Form:

P = \frac{9 e^{9.76}}{8 (e^{9.76} + 271)}

$P = \frac{9 e^{9.76}}{8 (e^{9.76} + 271)}$

Decimal Form:

P = 1.10767522 \dots

$P = 1.10767522 \dots$