Trigonometry Examples

$p (53) = \frac{90}{1 + 271 e^{- 0.122 \cdot 53}}$

Step 1

Simplify.

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Step 1.1

Multiply $- 0.122$ by $53$ .

$p (53) = \frac{90}{1 + 271 e^{- 6.466}}$

Step 1.2

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

$p (53) = \frac{90}{1 + 271 \frac{1}{e^{6.466}}}$

Step 1.3

Combine $271$ and $\frac{1}{e^{6.466}}$ .

$p (53) = \frac{90}{1 + \frac{271}{e^{6.466}}}$

Step 1.4

Simplify the denominator.

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Step 1.4.1

Write $1$ as a fraction with a common denominator.

$p (53) = \frac{90}{\frac{e^{6.466}}{e^{6.466}} + \frac{271}{e^{6.466}}}$

Step 1.4.2

Combine the numerators over the common denominator.

$p (53) = \frac{90}{\frac{e^{6.466} + 271}{e^{6.466}}}$

Step 1.5

Multiply the numerator by the reciprocal of the denominator.

$p (53) = 90 \frac{e^{6.466}}{e^{6.466} + 271}$

Step 1.6

Combine $90$ and $\frac{e^{6.466}}{e^{6.466} + 271}$ .

$p (53) = \frac{90 e^{6.466}}{e^{6.466} + 271}$

Step 2

Divide each term in $p (53) = \frac{90 e^{6.466}}{e^{6.466} + 271}$ by $53$ and simplify.

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Step 2.1

Divide each term in $p (53) = \frac{90 e^{6.466}}{e^{6.466} + 271}$ by $53$ .

$\frac{p (53)}{53} = \frac{\frac{90 e^{6.466}}{e^{6.466} + 271}}{53}$

Step 2.2

Simplify the left side.

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Step 2.2.1

Cancel the common factor of $53$ .

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Step 2.2.1.1

Cancel the common factor.

$\frac{p \cdot 53}{53} = \frac{\frac{90 e^{6.466}}{e^{6.466} + 271}}{53}$

Step 2.2.1.2

Divide $p$ by $1$ .

$p = \frac{\frac{90 e^{6.466}}{e^{6.466} + 271}}{53}$

Step 2.3

Simplify the right side.

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Step 2.3.1

Multiply the numerator by the reciprocal of the denominator.

$p = \frac{90 e^{6.466}}{e^{6.466} + 271} \cdot \frac{1}{53}$

Step 2.3.2

Multiply $\frac{90 e^{6.466}}{e^{6.466} + 271}$ by $\frac{1}{53}$ .

$p = \frac{90 e^{6.466}}{(e^{6.466} + 271) \cdot 53}$

Step 2.3.3

Move $53$ to the left of $e^{6.466} + 271$ .

$p = \frac{90 e^{6.466}}{53 (e^{6.466} + 271)}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$p = \frac{90 e^{6.466}}{53 (e^{6.466} + 271)}$

Decimal Form:

$p = 1.19457323 \dots$