There is a line through the origin that divides the region bounded by the parabola y=6x−2x^2 and the x-axis into two regions with equal area. What is the slope of that line? Hint: Draw a picture, write the area between the parabola and the line in terms of the slope of the line, and solve for the slope.

Algebra: Structure And Method, Book 1
(REV)00th Edition
ISBN:9780395977224
Author:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Publisher:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Chapter9: Systems Of Linear Equations
Section9.1: The Graphing Method
Problem 24WE
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There is a line through the origin that divides the region bounded by the parabola y=6x−2x^2 and the x-axis into two regions with equal area. What is the slope of that line?

Hint: Draw a picture, write the area between the parabola and the line in terms of the slope of the line, and solve for the slope.

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