bootiesniffer69
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PLEASE HELP!!!!
On top of a hill, a rocket is launched from a distance 80 feet above a lake. The rocket will fall into the lake after its engine burns out. The rocket's height, h, in feet above the surface of the lake, is given by the equation, h = -16t ∧2 + 64t + 80, where t is time in seconds. The maximum height of the rocket is ______ feet.

Respuesta :

Answer:

144

Step-by-step explanation:

[tex]h=-16t^2+64t+80[/tex]

So you have to figure out which number t results in the maximum h.

First find the range.

[tex]64t+80>16t^2[/tex]

[tex]4t+5>t^2[/tex]

[tex]t^2-4t-5<0[/tex]

[tex](t-5)(t+1)<0[/tex]

[tex]t<5, t>-1[/tex]

It looks like t has to be less than 5 and greater than -1 to be positive.

Now just try the numbers 0, 1, 2, 3, 4

0: 80

1: 128

2: 144

3: 128

4:  80

wegnerkolmp2741o

Answer:

144 ft

Step-by-step explanation:

h = -16t ^2 + 64t + 80,

We want to find the maximum height or the vertex

This occurs when at

t = -b/2a

t = -64/ (2(-16)

  = -64/-32 = 2

When t=2

h(2) = -16 (2)^2 +64(2) +80

     = -16*4+128 +80

     =-64 +128 +80

     =144

h(2) = 144

The maximum height is 144

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