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

thats fairly easy too

Answer 2

not the best picture , but good enough

Answer 3

assuming its symmetric about y axis , which it most likely is

the area is (2x) y , ie base times height

Answer 4

A=2xy

but y= 36-x^2

so A=2x ( 36-x^2)

Answer 5

so base is 2x

and all theyare asking for second part is to solve A= 70

Answer 6

72x -2x^3 =70

Answer 7

this is a cubic, requires polynomial division etc like all the others you have been doing

Answer 8

Okay got it! You're amazing!