Question

An arch has the shape of the parabola y = 36 − x2. A rectangle is fit under the arch by selecting a point (x, y) on the parabola.

(a) Express the area A of the rectangle in terms of x.
(b) If x = 1, the rectangle has base 2 and height 35. Find the base of a second rectangle that has the same area.

Answer 1

a)

2x* (33-x^2) = 64
x*(33-x^2) = 32

we get

x^3 - 33x + 32=0

this is the area of triangle in term of x