Question

Guys please help me solve this its so stressful

Answer 1

Given:-
`y=-5x^3+10x+20`

A parabola attain maximum height at the vertex: formula to find x-coordinate of vertex is,
`x=-(b)/(2a)`

plug in a=-5 and b=10

so,
`x=-(10)/(2(-5)) =-(10)/(-10) =1`

Now plug in x=1 to get maximum height,

`y=-5(-1)^2+10(1)+20`

`=-5+10+20`

`=+25`

so, maximum heigh reached by the rocket was 25 yards

Rocket will hit the ground when y=0

`0=-5x^2+10x+20`

`0=-5(x^2-2x-4)`

`(0)/(-5) =(-5)/(-5) (x^2-2x-4)`

So,
`x^2-2x-4=0`

quadratic formula is,

`x=(-b+-√(b^2-4ac) )/(2a)`

plug in a=1, b=-2,and c=-4

`x=-((-2)=-√((-2)^2-4(1)(-4)) )/(2(1))`

`=(2=-√(4+16) )/(2)`

`=(2+-√(20) )/(2)`

`=(2+-2√(5) )/(2)`

`=1+-√(5)`

`=1-√(5) ,1+√(5)`

`=1-5.236,1+2.236`

`=-1.236,3.236`

So, it takes 3.2 seconds to hit the ground.

OAmalOHopeO