While hovering near the top of Ribbon Falls in Yosemite National Park at 1600 feet, a helicopter pilot accidentally drops his sunglasses. The height h(t) of the sunglasses
after t seconds is given by the polynomial function.
h(t) = -16t^2 + 1600.
When will the sunglasses hit the ground?

a)The sunglasses hit the ground at t=0 seconds

b)The maximum height  h(t) = 1600feet

Step-by-step explanation:

Step(i):-

Given that the polynomial function

                     h(t) = -16 t² + 1600 ...(i)

Differentiating equation (i) with respective to 't' , we get

Equating zero

       ⇒ -32t =0

      ⇒   t =0

The sunglasses hit the ground at t=0 seconds

Step(ii):-

Again differentiating with respective to 't', we get

The maximum height at t=0

 h(t) = -16 t² + 1600

 h(t) = 1600feet

f(x) = - 2/3x + 5; f(5/2)

substitute 5/2 in for x:

f(5/2) = -2/3(5/2) + 5

simplify the right side:

f(5/2) = -5/3 + 5

f(5/2) = 10/3

answer:

f(5/2) = 10/3

i hope this you!