Finite Math Examples

$60 = \frac{980 {(t)}^{2}}{4 {(3.14)}^{2}}$

Step 1

Rewrite the equation as $\frac{980 t^{2}}{4 \cdot {3.14}^{2}} = 60$ .

$\frac{980 t^{2}}{4 \cdot {3.14}^{2}} = 60$

Step 2

Cancel the common factor of $980$ and $4$ .

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Step 2.1

Factor $4$ out of $980 t^{2}$ .

$\frac{4 (245 t^{2})}{4 \cdot {3.14}^{2}} = 60$

Step 2.2

Cancel the common factors.

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Step 2.2.1

Factor $4$ out of $4 \cdot {3.14}^{2}$ .

$\frac{4 (245 t^{2})}{4 ({3.14}^{2})} = 60$

Step 2.2.2

Cancel the common factor.

$\frac{4 (245 t^{2})}{4 \cdot {3.14}^{2}} = 60$

Step 2.2.3

Rewrite the expression.

$\frac{245 t^{2}}{{3.14}^{2}} = 60$

Step 3

Multiply both sides by ${3.14}^{2}$ .

$\frac{245 t^{2}}{{3.14}^{2}} \cdot {3.14}^{2} = 60 \cdot {3.14}^{2}$

Step 4

Simplify.

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Step 4.1

Simplify the left side.

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Step 4.1.1

Simplify $\frac{245 t^{2}}{{3.14}^{2}} \cdot {3.14}^{2}$ .

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Step 4.1.1.1

Raise $3.14$ to the power of $2$ .

$\frac{245 t^{2}}{9.8596} \cdot {3.14}^{2} = 60 \cdot {3.14}^{2}$

Step 4.1.1.2

Factor $245$ out of $245 t^{2}$ .

$\frac{245 (t^{2})}{9.8596} \cdot {3.14}^{2} = 60 \cdot {3.14}^{2}$

Step 4.1.1.3

Factor $9.8596$ out of $9.8596$ .

$\frac{245 (t^{2})}{9.8596 (1)} \cdot {3.14}^{2} = 60 \cdot {3.14}^{2}$

Step 4.1.1.4

Separate fractions.

$\frac{245}{9.8596} \cdot \frac{t^{2}}{1} \cdot {3.14}^{2} = 60 \cdot {3.14}^{2}$

Step 4.1.1.5

Divide $245$ by $9.8596$ .

$24.84887825 \frac{t^{2}}{1} \cdot {3.14}^{2} = 60 \cdot {3.14}^{2}$

Step 4.1.1.6

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

$24.84887825 t^{2} \cdot {3.14}^{2} = 60 \cdot {3.14}^{2}$

Step 4.1.1.7

Raise $3.14$ to the power of $2$ .

$24.84887825 t^{2} \cdot 9.8596 = 60 \cdot {3.14}^{2}$

Step 4.1.1.8

Multiply $9.8596$ by $24.84887825$ .

$245 t^{2} = 60 \cdot {3.14}^{2}$

Step 4.2

Simplify the right side.

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Step 4.2.1

Simplify $60 \cdot {3.14}^{2}$ .

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Step 4.2.1.1

Raise $3.14$ to the power of $2$ .

$245 t^{2} = 60 \cdot 9.8596$

Step 4.2.1.2

Multiply $60$ by $9.8596$ .

$245 t^{2} = 591.576$

Step 5

Solve for $t$ .

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Step 5.1

Divide each term in $245 t^{2} = 591.576$ by $245$ and simplify.

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Step 5.1.1

Divide each term in $245 t^{2} = 591.576$ by $245$ .

$\frac{245 t^{2}}{245} = \frac{591.576}{245}$

Step 5.1.2

Simplify the left side.

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Step 5.1.2.1

Cancel the common factor of $245$ .

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Step 5.1.2.1.1

Cancel the common factor.

$\frac{245 t^{2}}{245} = \frac{591.576}{245}$

Step 5.1.2.1.2

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

$t^{2} = \frac{591.576}{245}$

Step 5.1.3

Simplify the right side.

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Step 5.1.3.1

Divide $591.576$ by $245$ .

$t^{2} = 2.41459591$

Step 5.2

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

$t = \pm \sqrt{2.41459591}$

Step 5.3

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

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Step 5.3.1

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

$t = \sqrt{2.41459591}$

Step 5.3.2

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

$t = - \sqrt{2.41459591}$

Step 5.3.3

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

$t = \sqrt{2.41459591}, - \sqrt{2.41459591}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$t = \sqrt{2.41459591}, - \sqrt{2.41459591}$

Decimal Form:

$t = 1.55389701 \dots, - 1.55389701 \dots$