Given:
The function is
[tex]h=3+25t-5t^2[/tex]
To find:
The values of t where h is 8 meters.
Solution:
We have,
[tex]h=3+25t-5t^2[/tex]
Putting h=8, we get
[tex]8=3+25t-5t^2[/tex]
[tex]0=3+25t-5t^2-8[/tex]
[tex]0=-5+25t-5t^2[/tex]
[tex]0=-5(1-5t+t^2)[/tex]
Dividing both sides by -5 and interchanging the sides, we get
[tex]1-5t+t^2=0[/tex]
[tex]t^2-5t+1=0[/tex]
Here, [tex]a=1,b=-5,c=1[/tex].
Using quadratic formula, we get
[tex]t=\dfrac{-b\pm \sqrt{b^2-4ac}}{2a}[/tex]
[tex]t=\dfrac{-(-5)\pm \sqrt{(-5)^2-4(1)(1)}}{2(1)}[/tex]
[tex]t=\dfrac{5\pm \sqrt{25-4}}{2}[/tex]
[tex]t=\dfrac{5\pm \sqrt{21}}{2}[/tex]
It can be written as
[tex]t=\dfrac{5-\sqrt{21}}{2}[/tex] and [tex]t=\dfrac{5+\sqrt{21}}{2}[/tex]
[tex]t=0.20871215[/tex] and [tex]t=4.7912878[/tex]
[tex]t\approx 0.21[/tex] and [tex]t\approx 4.79[/tex]
Therefore, the required values of t are 0.21 and 4.79.
