When a cannon balls fired the equation of his pathway can be modeled by h= -16t^2 + 128t
find the maximum height of the cannonball and find a time it will take for the cannonball to reach the ground

The maximum height of the cannonball  'h' = 256

The time will take for the cannonball to reach the ground 't' =4

Step-by-step explanation:

Explanation:-

The given equation  h(t) = -16 t² + 128 t   ...(i)

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

- 32 t = -128

    t = 4

Now

Again differentiating with respective to 'x'

The function is Maximum at  t = 4

The maximum value

h(t) =-16 t² + 128 t  

h(4) = - 16 (4)² + 128(4) = 256

Conclusion:-

The maximum height of the cannonball  'h' = 256

The time will take for the cannonball to reach the ground 't' =4

its 50 miles away from the starting point

let y equal to

the total fare and x is the mile of taxi ride. so the equation is

y = 0.55x + 1.75

since susie has

$10 to spend for a taxi cab, so he can have

10 = 0.55x +

1.75

x = 15 miles of

taxi ride

so the system of

inequality is

10 < 0.55x +

1.75

x > 2