For this case we have the following function:
[tex] h = -0.025d ^ 2 + d
[/tex]
To find the distance between the pillars, we must match the equation to zero:
[tex] -0.025d ^ 2 + d = 0
[/tex]
From here, we clear the value of d:
[tex] d (-0.025d + 1) = 0
[/tex]
The roots are:
Root 1:
[tex] d = 0
[/tex]
Root 2:
[tex] -0.025d + 1 = 0
0.025d = 1
d = 1 / 0.025
d = 40[/tex]
Thus, the pillars are 40 units away.
The maximum height, we obtain it by deriving:
[tex] h = -0.025d ^ 2 + d
h '= - 0.050d + 1[/tex]
We equal zero and clear d:
[tex] -0.050d + 1 = 0
0.050d = 1
d = 1 / 0.050
d = 20
[/tex]
Then, we substitute the value of d = 20 in the equation for the height:
[tex] h = -0.025 * (20) ^ 2 + (20)
h = 10[/tex]
The maximum height is 10 units of distance
