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Consider the following sequence of problems related to grazing goats tied to a rope. A circular corral

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Consider the following sequence of problems related to grazing goats tied to a rope.

A circular corral of unit radius is enclosed by a fence. A goat inside the corral is tied to the fence with a rope of length 0 ≤ a ≤ 2 (see figure). What is the area of the region (inside the corral) that the goat can graze? Check your answer with the special cases a = 0 and a = 2.

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Suppose that the goat is tethered at the origin and that the ...View the full answer


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