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