Trigonometry Examples

$6 = 0.5 r^{2} (\frac{1}{4})$

Step 1

Rewrite the equation as $0.5 r^{2} (\frac{1}{4}) = 6$ .

$0.5 r^{2} (\frac{1}{4}) = 6$

Step 2

Simplify $0.5 r^{2} (\frac{1}{4})$ .

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Step 2.1

Cancel the common factor of $0.5$ .

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Step 2.1.1

Factor $0.5$ out of $0.5 r^{2}$ .

$0.5 (r^{2}) \frac{1}{4} = 6$

Step 2.1.2

Factor $0.5$ out of $4$ .

$0.5 (r^{2}) \frac{1}{0.5 (8)} = 6$

Step 2.1.3

Cancel the common factor.

$0.5 r^{2} \frac{1}{0.5 \cdot 8} = 6$

Step 2.1.4

Rewrite the expression.

$r^{2} \frac{1}{8} = 6$

Step 2.2

Combine $r^{2}$ and $\frac{1}{8}$ .

$\frac{r^{2}}{8} = 6$

Step 3

Multiply both sides of the equation by $8$ .

$8 \frac{r^{2}}{8} = 8 \cdot 6$

Step 4

Simplify both sides of the equation.

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Step 4.1

Simplify the left side.

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Step 4.1.1

Cancel the common factor of $8$ .

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Step 4.1.1.1

Cancel the common factor.

$8 \frac{r^{2}}{8} = 8 \cdot 6$

Step 4.1.1.2

Rewrite the expression.

$r^{2} = 8 \cdot 6$

Step 4.2

Simplify the right side.

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Step 4.2.1

Multiply $8$ by $6$ .

$r^{2} = 48$

Step 5

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

$r = \pm \sqrt{48}$

Step 6

Simplify $\pm \sqrt{48}$ .

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Step 6.1

Rewrite $48$ as $4^{2} \cdot 3$ .

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Step 6.1.1

Factor $16$ out of $48$ .

$r = \pm \sqrt{16 (3)}$

Step 6.1.2

Rewrite $16$ as $4^{2}$ .

$r = \pm \sqrt{4^{2} \cdot 3}$

Step 6.2

Pull terms out from under the radical.

$r = \pm 4 \sqrt{3}$

Step 7

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

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Step 7.1

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

$r = 4 \sqrt{3}$

Step 7.2

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

$r = - 4 \sqrt{3}$

Step 7.3

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

$r = 4 \sqrt{3}, - 4 \sqrt{3}$

Step 8

The result can be shown in multiple forms.

Exact Form:

$r = 4 \sqrt{3}, - 4 \sqrt{3}$

Decimal Form:

$r = 6.92820323 \dots, - 6.92820323 \dots$