Trigonometry Examples

$1800 = 600 {(1 + \frac{r}{1})}^{20}$

Step 1

Rewrite the equation as $600 {(1 + \frac{r}{1})}^{20} = 1800$ .

$600 {(1 + \frac{r}{1})}^{20} = 1800$

Step 2

Divide $r$ by $1$ .

$600 {(1 + r)}^{20} = 1800$

Step 3

Divide each term in $600 {(1 + r)}^{20} = 1800$ by $600$ and simplify.

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Step 3.1

Divide each term in $600 {(1 + r)}^{20} = 1800$ by $600$ .

$\frac{600 {(1 + r)}^{20}}{600} = \frac{1800}{600}$

Step 3.2

Simplify the left side.

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Step 3.2.1

Cancel the common factor of $600$ .

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Step 3.2.1.1

Cancel the common factor.

$\frac{600 {(1 + r)}^{20}}{600} = \frac{1800}{600}$

Step 3.2.1.2

Divide ${(1 + r)}^{20}$ by $1$ .

${(1 + r)}^{20} = \frac{1800}{600}$

Step 3.3

Simplify the right side.

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Step 3.3.1

Divide $1800$ by $600$ .

${(1 + r)}^{20} = 3$

Step 4

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

$1 + r = \pm \sqrt[20]{3}$

Step 5

The complete solution is the result of both the positive and negative portions of the solution.

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Step 5.1

First, use the positive value of the $\pm$ to find the first solution.

$1 + r = \sqrt[20]{3}$

Step 5.2

Subtract $1$ from both sides of the equation.

$r = \sqrt[20]{3} - 1$

Step 5.3

Next, use the negative value of the $\pm$ to find the second solution.

$1 + r = - \sqrt[20]{3}$

Step 5.4

Subtract $1$ from both sides of the equation.

$r = - \sqrt[20]{3} - 1$

Step 5.5

The complete solution is the result of both the positive and negative portions of the solution.

$r = \sqrt[20]{3} - 1, - \sqrt[20]{3} - 1$

Step 6

The result can be shown in multiple forms.

Exact Form:

$r = \sqrt[20]{3} - 1, - \sqrt[20]{3} - 1$

Decimal Form:

$r = 0.05646730 \dots, - 2.05646730 \dots$