Answer:
t = 7 seconds
Step-by-step explanation:
The height of a rocket x seconds after it is launched from a hill that is 224 feet high is modeled by the function :
f (x) = -16x² + 80x + 224
We need to find how long does it take the rocket to hit the ground. At that point,
f(x) = 0
[tex]-16x^2 + 80x + 224=0\\\\\dfrac{-16x^2}{16}+\dfrac{80x}{16}+\dfrac{224}{16}=0\\\\-x^2+5x+14=0\\\\-x^2+(7-2)x+14=0\\\\-x^2+7x-2x+14=0\\\\x(-x+7)+2(-x+7)=0\\\\(x+2)(-x+7)=0\\\\x=-2\ \text{and}\ x=7[/tex]
Neglecting -2. Hence, the rocket will take 7 seconds to hit the ground.
