Trigonometry Examples

$m (45) = 13 e^{- 0.015 \cdot 45}$

Step 1

Simplify.

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Step 1.1

Multiply $- 0.015$ by $45$ .

$m (45) = 13 e^{- 0.675}$

Step 1.2

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

$m (45) = 13 \frac{1}{e^{0.675}}$

Step 1.3

Combine $13$ and $\frac{1}{e^{0.675}}$ .

$m (45) = \frac{13}{e^{0.675}}$

Step 2

Divide each term in $m (45) = \frac{13}{e^{0.675}}$ by $45$ and simplify.

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Step 2.1

Divide each term in $m (45) = \frac{13}{e^{0.675}}$ by $45$ .

$\frac{m (45)}{45} = \frac{\frac{13}{e^{0.675}}}{45}$

Step 2.2

Simplify the left side.

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Step 2.2.1

Cancel the common factor of $45$ .

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Step 2.2.1.1

Cancel the common factor.

$\frac{m \cdot 45}{45} = \frac{\frac{13}{e^{0.675}}}{45}$

Step 2.2.1.2

Divide $m$ by $1$ .

$m = \frac{\frac{13}{e^{0.675}}}{45}$

Step 2.3

Simplify the right side.

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Step 2.3.1

Multiply the numerator by the reciprocal of the denominator.

$m = \frac{13}{e^{0.675}} \cdot \frac{1}{45}$

Step 2.3.2

Combine.

$m = \frac{13 \cdot 1}{e^{0.675} \cdot 45}$

Step 2.3.3

Simplify the expression.

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Step 2.3.3.1

Multiply $13$ by $1$ .

$m = \frac{13}{e^{0.675} \cdot 45}$

Step 2.3.3.2

Move $45$ to the left of $e^{0.675}$ .

$m = \frac{13}{45 e^{0.675}}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$m = \frac{13}{45 e^{0.675}}$

Decimal Form:

$m = 0.14708963 \dots$