Respuesta :
Answer:
The time that the rocket will hit the ground is 12.87 seconds.
Step-by-step explanation:
Given : The rocket is launched from a tower [tex]y=-16x^2+199x+90[/tex]. The height of the rocket, y in feet, is related to the time after launch, x in seconds, by the given equation.
To find : The time that the rocket will hit the ground ?
Solution :
When the rocket hit the ground i.e. height became zero y=0,
Equation is [tex]y=-16x^2+199x+90[/tex]
Substitute y=0,
[tex]-16x^2+199x+90=0[/tex]
Using quadratic formula, [tex]x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]
[tex]x=\frac{-(199)\pm\sqrt{(199)^2-4(-16)(90)}}{2(-16)}[/tex]
[tex]x=\frac{-199\pm\sqrt{45361}}{-32}[/tex]
[tex]x=\frac{-199+\sqrt{45361}}{-32},\frac{-199-\sqrt{45361}}{-32}[/tex]
[tex]x=-0.43,12.87[/tex]
Reject negative value.
The time taken is 12.87 seconds.
