Question

Need help with math homework

Answer 1

Hello!

The answer for A is:

`X1=-1\\X2=5`

The answer for B is: The rocket will hit the lake surface in 5 seconds.

Why?

Defining the terms:

`a=-16\\b=64\\c=80\\`

So, replacing it in the quadratic equation (it's given to you in the exercise)\\

`x=\frac{-b+-\sqrt{b^(2)-4*a*c } }{2*a}`

`x=\frac{-64+-\sqrt{64^(2)-4*-16*80 } }{2*-16}`

`x=\frac{-64+-\sqrt{64^(2)+5120} }{-32}=(-64+-√(4096+5120) )/(-32)\\x=(-64+-√(9216) )/(-32)=(-64+-\ 96 )/(-32)\\x=(-64+-\ 96 )/(-32)\\x1=(-64+\ 96 )/(-32)=(32)/(-32) =-1\\\\x1=(-64-\ 96 )/(-32)=(-160)/(-32) =5\\`

We are working with a quadratic equation, so we will have two possible results,

`X1=-1\\X2=5\\`

Now, we are asked to find the time, time can not be a negative value, we have to discard X1 (-1) since it's a negative value, knowing that, the rocket will hit the lake after 5 seconds.

Have a nice day!