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

true

step-by-step explanation:

x = ±sqrt(10)

step-by-step explanation:

5 - 2x² = -15

subtract 5 from each side

5-5 - 2x² = -15-5

-2x^2   = -20

divide by -2 on each side

-2x^2   /-2= -20/-2

x^2 =10

take the square root on each side

sqrt(x^2 )=±sqrt(10)

x = ±sqrt(10)

check:

5 - 2x² = -15

+sqrt(10)

5 - 2(sqrt(10))² = -15

5 -2(10) = -15

5 -20 = -15

-15 = -15

-sqrt(10)

5 - 2(-sqrt(10))² = -15

5 -2(10) = -15

5 -20 = -15

-15 = -15