A sector of a circle of radius r cm has an angle radians, where <

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A sector of a circle of radius r cm has an angle θ radians, where θ < π. The perimeter of the sector is 30 cm.

a. Show that the area, A cm2, of the sector is given by A = 15r – r2.

b. Given that r can vary, find the maximum area of the sector.

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