A rocket carrying fireworks is launched form a hill 80 above a lake. The rocket will fall into the lake after exploding at its maximum height. The rocket's height above the surface of the lake is given by: h left parenthesis t right parenthesis equals space minus 16 left parenthesis t minus 2 right parenthesis squared plus 144

After 5 s

Step-by-step explanation:

We are told the equation that models the height of the rocket is:

(1)

Where is the height and is the time.

This equation can be rewritten as follows:

(2)

(3)

So, we have to find the time at which the rocket hits the lake, this means when :

(4)

Dividing both sides of the equation by 16:

(5)

Multiplying both sides of the equation by -1:

(6)

This is a quadratic equation of the form , and we have to use the quadratic formula if we want to find  :  

(7)

Where , ,  

Substituting the known values and choosing the positive result of the equation:  

 (8)

Hence, the rocket hits the lake 5 seconds after its launch.

answer: the correct answer is -32

step-by-step explanation:

x-3y=4

step-by-step e