Question

BRAINLIEST GURANTEED

Answer 1

Given:

The function is

$h=3+25t-5t^2$

To find:

The values of t where h is 8 meters.

Solution:

We have,

$h=3+25t-5t^2$

Putting h=8, we get

$8=3+25t-5t^2$

$0=3+25t-5t^2-8$

$0=-5+25t-5t^2$

$0=-5(1-5t+t^2)$

Dividing both sides by -5 and interchanging the sides, we get

$1-5t+t^2=0$

$t^2-5t+1=0$

Here, $a=1,b=-5,c=1$.

Using quadratic formula, we get

$t=\dfrac{-b\pm \sqrt{b^2-4ac}}{2a}$

$t=\dfrac{-(-5)\pm \sqrt{(-5)^2-4(1)(1)}}{2(1)}$

$t=\dfrac{5\pm \sqrt{25-4}}{2}$

$t=\dfrac{5\pm \sqrt{21}}{2}$

It can be written as

$t=\dfrac{5-\sqrt{21}}{2}$ and $t=\dfrac{5+\sqrt{21}}{2}$

$t=0.20871215$ and $t=4.7912878$

$t\approx 0.21$ and $t\approx 4.79$

Therefore, the required values of t are 0.21 and 4.79.