Evaluate Using the Given Value (1/2)*400t^2=20 , 0

$(\frac{1}{2}) \cdot 400 t^{2} = 20$ , $0$

Step 1

Multiply both sides of the equation by $\frac{1}{\frac{1}{2} \cdot 400}$ .

$\frac{1}{\frac{1}{2} \cdot 400} (\frac{1}{2} \cdot (400 t^{2})) = \frac{1}{\frac{1}{2} \cdot 400} \cdot 20$

Step 2

Simplify both sides of the equation.

Simplify the left side.

Simplify $\frac{1}{\frac{1}{2} \cdot 400} (\frac{1}{2} \cdot (400 t^{2}))$ .

Combine $\frac{1}{2}$ and $400$ .

$\frac{1}{\frac{400}{2}} (\frac{1}{2} \cdot (400 t^{2})) = \frac{1}{\frac{1}{2} \cdot 400} \cdot 20$

Divide $400$ by $2$ .

$\frac{1}{200} (\frac{1}{2} \cdot (400 t^{2})) = \frac{1}{\frac{1}{2} \cdot 400} \cdot 20$

Cancel the common factor of $200$ .

Factor $200$ out of $\frac{1}{2} \cdot (400 t^{2})$ .

$\frac{1}{200} (200 (\frac{1}{2} \cdot (2 t^{2}))) = \frac{1}{\frac{1}{2} \cdot 400} \cdot 20$

Cancel the common factor.

$\frac{1}{200} (200 (\frac{1}{2} \cdot (2 t^{2}))) = \frac{1}{\frac{1}{2} \cdot 400} \cdot 20$

Rewrite the expression.

$\frac{1}{2} \cdot (2 t^{2}) = \frac{1}{\frac{1}{2} \cdot 400} \cdot 20$

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

$\frac{2}{2} \cdot t^{2} = \frac{1}{\frac{1}{2} \cdot 400} \cdot 20$

Combine $\frac{2}{2}$ and $t^{2}$ .

$\frac{2 t^{2}}{2} = \frac{1}{\frac{1}{2} \cdot 400} \cdot 20$

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 t^{2}}{2} = \frac{1}{\frac{1}{2} \cdot 400} \cdot 20$

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

$t^{2} = \frac{1}{\frac{1}{2} \cdot 400} \cdot 20$

Simplify the right side.

Simplify $\frac{1}{\frac{1}{2} \cdot 400} \cdot 20$ .

Combine $\frac{1}{2}$ and $400$ .

$t^{2} = \frac{1}{\frac{400}{2}} \cdot 20$

Divide $400$ by $2$ .

$t^{2} = \frac{1}{200} \cdot 20$

Cancel the common factor of $20$ .

Factor $20$ out of $200$ .

$t^{2} = \frac{1}{20 (10)} \cdot 20$

Cancel the common factor.

$t^{2} = \frac{1}{20 \cdot 10} \cdot 20$

Rewrite the expression.

$t^{2} = \frac{1}{10}$

Step 3

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

$t = \pm \sqrt{\frac{1}{10}}$

Step 4

Simplify $\pm \sqrt{\frac{1}{10}}$ .

Rewrite $\sqrt{\frac{1}{10}}$ as $\frac{\sqrt{1}}{\sqrt{10}}$ .

$t = \pm \frac{\sqrt{1}}{\sqrt{10}}$

Any root of $1$ is $1$ .

$t = \pm \frac{1}{\sqrt{10}}$

Multiply $\frac{1}{\sqrt{10}}$ by $\frac{\sqrt{10}}{\sqrt{10}}$ .

$t = \pm \frac{1}{\sqrt{10}} \cdot \frac{\sqrt{10}}{\sqrt{10}}$

Combine and simplify the denominator.

Multiply $\frac{1}{\sqrt{10}}$ by $\frac{\sqrt{10}}{\sqrt{10}}$ .

$t = \pm \frac{\sqrt{10}}{\sqrt{10} \sqrt{10}}$

Raise $\sqrt{10}$ to the power of $1$ .

$t = \pm \frac{\sqrt{10}}{{\sqrt{10}}^{1} \sqrt{10}}$

Raise $\sqrt{10}$ to the power of $1$ .

$t = \pm \frac{\sqrt{10}}{{\sqrt{10}}^{1} {\sqrt{10}}^{1}}$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$t = \pm \frac{\sqrt{10}}{{\sqrt{10}}^{1 + 1}}$

Add $1$ and $1$ .

$t = \pm \frac{\sqrt{10}}{{\sqrt{10}}^{2}}$

Rewrite ${\sqrt{10}}^{2}$ as $10$ .

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{10}$ as $10^{\frac{1}{2}}$ .

$t = \pm \frac{\sqrt{10}}{{(10^{\frac{1}{2}})}^{2}}$

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$t = \pm \frac{\sqrt{10}}{10^{\frac{1}{2} \cdot 2}}$

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

$t = \pm \frac{\sqrt{10}}{10^{\frac{2}{2}}}$

Cancel the common factor of $2$ .

Cancel the common factor.

$t = \pm \frac{\sqrt{10}}{10^{\frac{2}{2}}}$

Rewrite the expression.

$t = \pm \frac{\sqrt{10}}{10^{1}}$

Evaluate the exponent.

$t = \pm \frac{\sqrt{10}}{10}$

Step 5

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

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

$t = \frac{\sqrt{10}}{10}$

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

$t = - \frac{\sqrt{10}}{10}$

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

$t = \frac{\sqrt{10}}{10}, - \frac{\sqrt{10}}{10}$

Step 6

Replace the variable $t$ with $\frac{\sqrt{10}}{10}$ in the expression.

$0$

Evaluate Using the Given Value (1/2)*400t^2=20 , 0

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