Question

Two pillars support the archway entrance of a castle. The archway can be modelled by the relation h=-0.025d^2 +d

Answer 1

For this case we have the following function:

`h = -0.025d ^ 2 + d`
To find the distance between the pillars, we must match the equation to zero:

`-0.025d ^ 2 + d = 0`
From here, we clear the value of d:

`d (-0.025d + 1) = 0`
The roots are:
Root 1:

`d = 0`
Root 2:

`-0.025d + 1 = 0 0.025d = 1 d = 1 / 0.025 d = 40`
Thus, the pillars are 40 units away.

The maximum height, we obtain it by deriving:

`h = -0.025d ^ 2 + d h '= - 0.050d + 1`
We equal zero and clear d:

`-0.050d + 1 = 0 0.050d = 1 d = 1 / 0.050 d = 20`
Then, we substitute the value of d = 20 in the equation for the height:

`h = -0.025 * (20) ^ 2 + (20) h = 10`
The maximum height is 10 units of distance