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## Homework Statement

In the picture above, line y = c intersects with parabola y = 6x-x^2 in the first quadrant.

If the gray area below line y = c and the gray area above line y=c are equal, then value of c is ...

A. 19/4

B.21/4

C.23/4

D.25/4

E. 27/4

## Homework Equations

Area under parabola = 2/3* base * height

Area above parabola = 1/3 * base* height

Area = definite integral

## The Attempt at a Solution

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Parabola y=6x-x^2 has peak point (3,9)

Suppose a is the x-intercept of the line and parabola.

At x = a, c equals 6a-a^2

So, the gray area below the line is 1/3 * a * (6a-a^2)

The base for the upper gray parabola area is 2(3) - 2a = 6-2a

So, the gray area above the line is 2/3 * (6-2a) * (9-(6a-a^2))

I get a = 1.592

and c = 6a-a^2 = 7.017

However, I'm sure the correct answer is 27/4 (I've tested it using integral method)

Please help...