Solved on Sep 27, 2023

Find the value of $t$ when $v=100$ in the quadratic equation $v=0.1 t^{2}+60$ .

STEP 1

Assumptions1. The quadratic relation is given by $v=0.1 t^{}+60$ . . We need to find the value of $t$ when $v=100$ .

STEP 2

First, we need to set up the equation with the given value of $v$ .
$100 =0.1 t^{2} +60$

STEP 3

Next, we need to isolate the term with $t$ on one side of the equation. We can do this by subtracting60 from both sides of the equation.
$100 -60 =0.1 t^{2} +60 -60$

STEP 4

implify the equation.
$40 =0.1 t^{2}$

STEP 5

To further isolate $t$ , we need to divide both sides of the equation by0.1.
$\frac{40}{0.1} = \frac{0.1 t^{2}}{0.1}$

STEP 6

implify the equation.
$400 = t^{2}$

STEP 7

Finally, to solve for $t$ , we need to take the square root of both sides of the equation. Note that we only consider the positive root because time cannot be negative.
$t = \sqrt{400}$

STEP 8

Calculate the value of $t$ .
$t = \sqrt{400} =20$ So, when $v=100$ , the value of $t$ is20.

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Find the value of $t$ when $v=100$ in the quadratic equation $v=0.1 t^{2}+60$ .

STEP 1

Assumptions1. The quadratic relation is given by $v=0.1 t^{}+60$ . . We need to find the value of $t$ when $v=100$ .

STEP 2

First, we need to set up the equation with the given value of $v$ .
$100 =0.1 t^{2} +60$

STEP 3

Next, we need to isolate the term with $t$ on one side of the equation. We can do this by subtracting60 from both sides of the equation.
$100 -60 =0.1 t^{2} +60 -60$

STEP 4

implify the equation.
$40 =0.1 t^{2}$

STEP 5

To further isolate $t$ , we need to divide both sides of the equation by0.1.
$\frac{40}{0.1} = \frac{0.1 t^{2}}{0.1}$

STEP 6

implify the equation.
$400 = t^{2}$

STEP 7

Finally, to solve for $t$ , we need to take the square root of both sides of the equation. Note that we only consider the positive root because time cannot be negative.
$t = \sqrt{400}$

STEP 8

Calculate the value of $t$ .
$t = \sqrt{400} =20$ So, when $v=100$ , the value of $t$ is20.

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Find the value of ttt when v=100v=100v=100 in the quadratic equation v=0.1t2+60v=0.1 t^{2}+60v=0.1t2+60.

STEP 1

Assumptions1. The quadratic relation is given by v=0.1t+60v=0.1 t^{}+60v=0.1t+60. . We need to find the value of ttt when v=100v=100v=100.

STEP 2

First, we need to set up the equation with the given value of vvv.100=0.1t2+60100 =0.1 t^{2} +60100=0.1t2+60

STEP 3

Next, we need to isolate the term with ttt on one side of the equation. We can do this by subtracting60 from both sides of the equation.100−60=0.1t2+60−60100 -60 =0.1 t^{2} +60 -60100−60=0.1t2+60−60

STEP 4

implify the equation.40=0.1t240 =0.1 t^{2}40=0.1t2

STEP 5

To further isolate ttt, we need to divide both sides of the equation by0.1.400.1=0.1t20.1\frac{40}{0.1} = \frac{0.1 t^{2}}{0.1}0.140​=0.10.1t2​

STEP 6

implify the equation.400=t2400 = t^{2}400=t2

STEP 7

Finally, to solve for ttt, we need to take the square root of both sides of the equation. Note that we only consider the positive root because time cannot be negative.t=400t = \sqrt{400}t=400​

STEP 8

Calculate the value of ttt.t=400=20t = \sqrt{400} =20t=400​=20So, when v=100v=100v=100, the value of ttt is20.

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Find the value of $t$ when $v=100$ in the quadratic equation $v=0.1 t^{2}+60$ .

Assumptions1. The quadratic relation is given by $v=0.1 t^{}+60$ . . We need to find the value of $t$ when $v=100$ .

First, we need to set up the equation with the given value of $v$ .
$100 =0.1 t^{2} +60$

Next, we need to isolate the term with $t$ on one side of the equation. We can do this by subtracting60 from both sides of the equation.
$100 -60 =0.1 t^{2} +60 -60$

implify the equation.
$40 =0.1 t^{2}$

To further isolate $t$ , we need to divide both sides of the equation by0.1.
$\frac{40}{0.1} = \frac{0.1 t^{2}}{0.1}$

implify the equation.
$400 = t^{2}$

Finally, to solve for $t$ , we need to take the square root of both sides of the equation. Note that we only consider the positive root because time cannot be negative.
$t = \sqrt{400}$

Calculate the value of $t$ .
$t = \sqrt{400} =20$ So, when $v=100$ , the value of $t$ is20.