Parabolic arch An arch has the shape of the parabola y = 4 −x2. A rectangle is fit under t...

Parabolic arch An arch has the shape of the parabola y = 4 −x2. A rectangle is fit under the arch by selecting a point (x, y) on the parabola (see the figure).

(a) Express the area A of the rectangle in terms of x.

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(b) If x = 1, the rectangle has base 2 and height 3. Find the base of a second rectangle that has the same area.

EXERCISE