# P.o.t.W. #5

■ GDC is allowed ■A slice of bread is modelled by a two-dimensional shape consisting of a rectangle with the graph of $$y = 1 - {x^2},\; - 1 \le x \le 1$$ on top of the rectangle, as shown in the figure. The line segment AC (dashed) has endpoints $${\rm{A}}\left( { - 1,\; - 1} \right)$$ and $${\rm{C}}\left( {c,\;1 - {c^2}} \right)$$. Show that if AC divides the shape into two regions of equal area then the value of c is the one real number solution to the cubic equation $${c^3} + 3{c^2} + 6c - 6 = 0$$.downloadable file: P.o.t.W....

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