Question

CHECK ALL ANSWERS THAT APPLY*

Answer 1

Answer:

We get t= 7.22 and t=0.28

The correct options are Option A and Option G

Step-by-step explanation:

The height h of toy rocket at time t seconds after  launch is given by the equation $h(t) = -16t^2 + 120t + 8$

We need to find how many seconds  until the rocket is 40 feet?

We are given height of rocket h(t) = 40 feet

and we need to find time t

Using the equation $h(t) = -16t^2 + 120t + 8$ we can find time t

We have h(t)=40

$h(t) = -16t^2 + 120t + 8\\Put\:h(t)=40\\40= -16t^2 + 120t + 8\\16t^2-120t-8+40=0\\16t^2-120t+32=0$

Now, we will solve the quadratic equation using quadratic formula: $t=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$

We have a =16, b=-120 and c=32

Putting values and finding t

$t=\frac{-b\pm\sqrt{b^2-4ac}}{2a}\\t=\frac{-(-120)\pm\sqrt{(-120)^2-4(16)(32)}}{2(16)}\\t=\frac{120\pm\sqrt{14400-2048}}{32}\\t=\frac{120\pm\sqrt{12352}}{32}\\t=\frac{120\pm111.12}{32}\\t=\frac{120+111.12}{32}, t=\frac{120-111.12}{32}\\t=7.22\:,\:t=0.28$

So, we get t= 7.22 and t=0.28

The correct options are Option A and Option G