M (d) = -0.123x^2+148.83x-21.07

When will it reach maximum height of 45000 feet

Answer: time to reach maximum height = 605

Step-by-step explanation:

The expression that relates height with time is

M (d) = -0.123x^2+148.83x-21.07

Where time = x

d = height

The expression is a quadratic equation. If height of the object is plotted against time, the resulting graph is a parabola whose vertex is equal to the maximum height attained by the object. The time, x corresponding to the vertex is the time for it to reach maximum height.

To find x,

x = - b/2a

Where a = 0.123

b = 148.83

x = - 148.83 / - 2 * - 0.123

x = - 148.83 / - 0.246

= 605

Substituting x = 605 in the equation,

M (d) = -0.123x^2+148.83x-21.07

d = - 0.123 * 605^2 + 148.83*605

= - 45021.075 + 90042.15

= 45020.4

Approximately 45000 feet