Finite Math Examples

$m = 2 {(\frac{5.5 e r f^{- 1} (0.99)}{4.48})}^{2}$

Step 1

Rewrite the equation as $2 {(\frac{5.5 e r f^{- 1} \cdot 0.99}{4.48})}^{2} = m$ .

$2 {(\frac{5.5 e r f^{- 1} \cdot 0.99}{4.48})}^{2} = m$

Step 2

Simplify.

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Step 2.1

Multiply $5.5$ by $e$ .

$2 {(\frac{14.95055005 r f^{- 1} \cdot 0.99}{4.48})}^{2} = m$

Step 2.2

Multiply $0.99$ by $14.95055005$ .

$2 {(\frac{14.80104455 r f^{- 1}}{4.48})}^{2} = m$

Step 3

Divide each term in $2 {(\frac{14.80104455 r f^{- 1}}{4.48})}^{2} = m$ by $2$ and simplify.

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Step 3.1

Divide each term in $2 {(\frac{14.80104455 r f^{- 1}}{4.48})}^{2} = m$ by $2$ .

$\frac{2 {(\frac{14.80104455 r f^{- 1}}{4.48})}^{2}}{2} = \frac{m}{2}$

Step 3.2

Simplify the left side.

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Step 3.2.1

Cancel the common factor of $2$ .

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Step 3.2.1.1

Cancel the common factor.

$\frac{2 {(\frac{14.80104455 r f^{- 1}}{4.48})}^{2}}{2} = \frac{m}{2}$

Step 3.2.1.2

Divide ${(\frac{14.80104455 r f^{- 1}}{4.48})}^{2}$ by $1$ .

${(\frac{14.80104455 r f^{- 1}}{4.48})}^{2} = \frac{m}{2}$

Step 3.2.2

Move $f^{- 1}$ to the denominator using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

${(\frac{14.80104455 r}{4.48 f})}^{2} = \frac{m}{2}$

Step 3.2.3

Factor $14.80104455$ out of $14.80104455 r$ .

${(\frac{14.80104455 (r)}{4.48 f})}^{2} = \frac{m}{2}$

Step 3.2.4

Factor $4.48$ out of $4.48 f$ .

${(\frac{14.80104455 (r)}{4.48 (f)})}^{2} = \frac{m}{2}$

Step 3.2.5

Separate fractions.

${(\frac{14.80104455}{4.48} \cdot \frac{r}{f})}^{2} = \frac{m}{2}$

Step 3.2.6

Divide $14.80104455$ by $4.48$ .

${(3.30380458 \frac{r}{f})}^{2} = \frac{m}{2}$

Step 3.2.7

Combine $3.30380458$ and $\frac{r}{f}$ .

${(\frac{3.30380458 r}{f})}^{2} = \frac{m}{2}$

Step 3.2.8

Use the power rule ${(a b)}^{n} = a^{n} b^{n}$ to distribute the exponent.

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Step 3.2.8.1

Apply the product rule to $\frac{3.30380458 r}{f}$ .

$\frac{{(3.30380458 r)}^{2}}{f^{2}} = \frac{m}{2}$

Step 3.2.8.2

Apply the product rule to $3.30380458 r$ .

$\frac{{3.30380458}^{2} r^{2}}{f^{2}} = \frac{m}{2}$

Step 3.2.9

Raise $3.30380458$ to the power of $2$ .

$\frac{10.91512475 r^{2}}{f^{2}} = \frac{m}{2}$

Step 4

Multiply both sides by $f^{2}$ .

$\frac{10.91512475 r^{2}}{f^{2}} f^{2} = \frac{m}{2} f^{2}$

Step 5

Simplify.

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Step 5.1

Simplify the left side.

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Step 5.1.1

Cancel the common factor of $f^{2}$ .

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Step 5.1.1.1

Cancel the common factor.

$\frac{10.91512475 r^{2}}{f^{2}} f^{2} = \frac{m}{2} f^{2}$

Step 5.1.1.2

Rewrite the expression.

$10.91512475 r^{2} = \frac{m}{2} f^{2}$

Step 5.2

Simplify the right side.

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Step 5.2.1

Combine $\frac{m}{2}$ and $f^{2}$ .

$10.91512475 r^{2} = \frac{m f^{2}}{2}$

Step 6

Solve for $r$ .

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Step 6.1

Divide each term in $10.91512475 r^{2} = \frac{m f^{2}}{2}$ by $10.91512475$ and simplify.

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Step 6.1.1

Divide each term in $10.91512475 r^{2} = \frac{m f^{2}}{2}$ by $10.91512475$ .

$\frac{10.91512475 r^{2}}{10.91512475} = \frac{\frac{m f^{2}}{2}}{10.91512475}$

Step 6.1.2

Simplify the left side.

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Step 6.1.2.1

Cancel the common factor of $10.91512475$ .

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Step 6.1.2.1.1

Cancel the common factor.

$\frac{10.91512475 r^{2}}{10.91512475} = \frac{\frac{m f^{2}}{2}}{10.91512475}$

Step 6.1.2.1.2

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

$r^{2} = \frac{\frac{m f^{2}}{2}}{10.91512475}$

Step 6.1.3

Simplify the right side.

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Step 6.1.3.1

Multiply the numerator by the reciprocal of the denominator.

$r^{2} = \frac{m f^{2}}{2} \cdot \frac{1}{10.91512475}$

Step 6.1.3.2

Combine.

$r^{2} = \frac{m f^{2} \cdot 1}{2 \cdot 10.91512475}$

Step 6.1.3.3

Multiply.

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Step 6.1.3.3.1

Multiply $m$ by $1$ .

$r^{2} = \frac{f^{2} \cdot m}{2 \cdot 10.91512475}$

Step 6.1.3.3.2

Multiply $2$ by $10.91512475$ .

$r^{2} = \frac{f^{2} \cdot m}{21.83024951}$

Step 6.1.3.4

Factor $1$ out of $f^{2} \cdot m$ .

$r^{2} = \frac{1 (f^{2} \cdot m)}{21.83024951}$

Step 6.1.3.5

Factor $21.83024951$ out of $21.83024951$ .

$r^{2} = \frac{1 (f^{2} \cdot m)}{21.83024951 (1)}$

Step 6.1.3.6

Separate fractions.

$r^{2} = \frac{1}{21.83024951} \cdot \frac{f^{2} \cdot m}{1}$

Step 6.1.3.7

Divide $1$ by $21.83024951$ .

$r^{2} = 0.04580799 \frac{f^{2} \cdot m}{1}$

Step 6.1.3.8

Divide $f^{2} \cdot m$ by $1$ .

$r^{2} = 0.04580799 f^{2} m$

Step 6.2

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

$r = \pm \sqrt{0.04580799 f^{2} m}$

Step 6.3

Simplify $\pm \sqrt{0.04580799 f^{2} m}$ .

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Step 6.3.1

Rewrite $0.04580799 f^{2} m$ as ${(0.21402802 f)}^{2} m$ .

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Step 6.3.1.1

Rewrite $0.04580799$ as ${0.21402802}^{2}$ .

$r = \pm \sqrt{{0.21402802}^{2} f^{2} m}$

Step 6.3.1.2

Rewrite ${0.21402802}^{2} f^{2}$ as ${(0.21402802 f)}^{2}$ .

$r = \pm \sqrt{{(0.21402802 f)}^{2} m}$

Step 6.3.2

Pull terms out from under the radical.

$r = \pm 0.21402802 f \sqrt{m}$

Step 6.4

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

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Step 6.4.1

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

$r = 0.21402802 f \sqrt{m}$

Step 6.4.2

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

$r = - 0.21402802 f \sqrt{m}$

Step 6.4.3

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

$r = 0.21402802 f \sqrt{m}$

$r = - 0.21402802 f \sqrt{m}$

$r = 0.21402802 f \sqrt{m}$

$r = - 0.21402802 f \sqrt{m}$

$r = 0.21402802 f \sqrt{m}$

$r = - 0.21402802 f \sqrt{m}$