QuestionSolve for $t$ in the equation $s=\frac{1}{15} g t^{2}$ . Find $\mathrm{t}= \pm \square$ .

Studdy Solution

STEP 1

Assumptions1. The given equation is $s=\frac{1}{15} g t^{}$ . We are asked to solve for $t$ .
3. $s$ and $g$ are known constants.
4. $g$ is not equal to0.

STEP 2

First, we need to isolate $t^{2}$ on one side of the equation. We can do this by multiplying both sides of the equation by15 and dividing by $g$ .
$t^{2} = \frac{15s}{g}$

STEP 3

Now, we need to solve for $t$ . We can do this by taking the square root of both sides of the equation. Remember, when we take the square root of a number, we get two solutions one positive and one negative.
$t = \pm \sqrt{\frac{15s}{g}}$

STEP 4

We are asked to rationalize all denominators. To do this, we multiply the numerator and denominator of the fraction under the square root by $g$ .
$t = \pm \sqrt{\frac{15sg}{g^2}}$

STEP 5

implify the equation.
$t = \pm \frac{\sqrt{15sg}}{g}$ So, the solution for $t$ is $t = \pm \frac{\sqrt{15sg}}{g}$ .

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QuestionSolve for $t$ in the equation $s=\frac{1}{15} g t^{2}$ . Find $\mathrm{t}= \pm \square$ .

Studdy Solution

STEP 1

Assumptions1. The given equation is $s=\frac{1}{15} g t^{}$ . We are asked to solve for $t$ .
3. $s$ and $g$ are known constants.
4. $g$ is not equal to0.

STEP 2

First, we need to isolate $t^{2}$ on one side of the equation. We can do this by multiplying both sides of the equation by15 and dividing by $g$ .
$t^{2} = \frac{15s}{g}$

STEP 3

Now, we need to solve for $t$ . We can do this by taking the square root of both sides of the equation. Remember, when we take the square root of a number, we get two solutions one positive and one negative.
$t = \pm \sqrt{\frac{15s}{g}}$

STEP 4

We are asked to rationalize all denominators. To do this, we multiply the numerator and denominator of the fraction under the square root by $g$ .
$t = \pm \sqrt{\frac{15sg}{g^2}}$

STEP 5

implify the equation.
$t = \pm \frac{\sqrt{15sg}}{g}$ So, the solution for $t$ is $t = \pm \frac{\sqrt{15sg}}{g}$ .

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QuestionSolve for ttt in the equation s=115gt2s=\frac{1}{15} g t^{2}s=151​gt2. Find t=±□\mathrm{t}= \pm \squaret=±□.

Studdy Solution

STEP 1

Assumptions1. The given equation is s=115gts=\frac{1}{15} g t^{}s=151​gt . We are asked to solve for ttt.3. sss and ggg are known constants.4. ggg is not equal to0.

STEP 2

First, we need to isolate t2t^{2}t2 on one side of the equation. We can do this by multiplying both sides of the equation by15 and dividing by ggg.t2=15sgt^{2} = \frac{15s}{g}t2=g15s​

STEP 3

Now, we need to solve for ttt. We can do this by taking the square root of both sides of the equation. Remember, when we take the square root of a number, we get two solutions one positive and one negative.t=±15sgt = \pm \sqrt{\frac{15s}{g}}t=±g15s​​

STEP 4

We are asked to rationalize all denominators. To do this, we multiply the numerator and denominator of the fraction under the square root by ggg.t=±15sgg2t = \pm \sqrt{\frac{15sg}{g^2}}t=±g215sg​​

STEP 5

implify the equation.t=±15sggt = \pm \frac{\sqrt{15sg}}{g}t=±g15sg​​So, the solution for ttt is t=±15sggt = \pm \frac{\sqrt{15sg}}{g}t=±g15sg​​.

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QuestionSolve for $t$ in the equation $s=\frac{1}{15} g t^{2}$ . Find $\mathrm{t}= \pm \square$ .

Assumptions1. The given equation is $s=\frac{1}{15} g t^{}$ . We are asked to solve for $t$ .
3. $s$ and $g$ are known constants.
4. $g$ is not equal to0.

First, we need to isolate $t^{2}$ on one side of the equation. We can do this by multiplying both sides of the equation by15 and dividing by $g$ .
$t^{2} = \frac{15s}{g}$

Now, we need to solve for $t$ . We can do this by taking the square root of both sides of the equation. Remember, when we take the square root of a number, we get two solutions one positive and one negative.
$t = \pm \sqrt{\frac{15s}{g}}$

We are asked to rationalize all denominators. To do this, we multiply the numerator and denominator of the fraction under the square root by $g$ .
$t = \pm \sqrt{\frac{15sg}{g^2}}$

implify the equation.
$t = \pm \frac{\sqrt{15sg}}{g}$ So, the solution for $t$ is $t = \pm \frac{\sqrt{15sg}}{g}$ .