Trigonometry Examples

$12 = \frac{1}{2} \cdot (r^{2} (0.9))$

Step 1

Rewrite the equation as $\frac{1}{2} r^{2} \cdot 0.9 = 12$ .

$\frac{1}{2} r^{2} \cdot 0.9 = 12$

Step 2

Simplify $\frac{1}{2} r^{2} \cdot 0.9$ .

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Step 2.1

Combine $\frac{1}{2}$ and $r^{2}$ .

$\frac{r^{2}}{2} \cdot 0.9 = 12$

Step 2.2

Combine $\frac{r^{2}}{2}$ and $0.9$ .

$\frac{r^{2} \cdot 0.9}{2} = 12$

Step 2.3

Move $0.9$ to the left of $r^{2}$ .

$\frac{0.9 \cdot r^{2}}{2} = 12$

Step 2.4

Factor $0.9$ out of $0.9 \cdot r^{2}$ .

$\frac{0.9 (r^{2})}{2} = 12$

Step 2.5

Factor $2$ out of $2$ .

$\frac{0.9 (r^{2})}{2 (1)} = 12$

Step 2.6

Separate fractions.

$\frac{0.9}{2} \cdot \frac{r^{2}}{1} = 12$

Step 2.7

Divide $0.9$ by $2$ .

$0.45 \frac{r^{2}}{1} = 12$

Step 2.8

Divide $r^{2}$ by $1$ .

$0.45 r^{2} = 12$

Step 3

Divide each term in $0.45 r^{2} = 12$ by $0.45$ and simplify.

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Step 3.1

Divide each term in $0.45 r^{2} = 12$ by $0.45$ .

$\frac{0.45 r^{2}}{0.45} = \frac{12}{0.45}$

Step 3.2

Simplify the left side.

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Step 3.2.1

Cancel the common factor of $0.45$ .

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Step 3.2.1.1

Cancel the common factor.

$\frac{0.45 r^{2}}{0.45} = \frac{12}{0.45}$

Step 3.2.1.2

Divide $r^{2}$ by $1$ .

$r^{2} = \frac{12}{0.45}$

Step 3.3

Simplify the right side.

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Step 3.3.1

Divide $12$ by $0.45$ .

$r^{2} = 26.\overline{6}$

Step 4

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

$r = \pm \sqrt{26.\overline{6}}$

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.

$r = \sqrt{26.\overline{6}}$

Step 5.2

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

$r = - \sqrt{26.\overline{6}}$

Step 5.3

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

$r = \sqrt{26.\overline{6}}, - \sqrt{26.\overline{6}}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$r = \sqrt{26.\overline{6}}, - \sqrt{26.\overline{6}}$

Decimal Form:

$r = 5.16397779 \dots, - 5.16397779 \dots$