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Question: a thin metal sheet has the shape of the cardioid...

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A thin metal sheet has the shape of the cardioid so that when it is properly aligned with the origin its edge is traced out by r-a (1 + cos θ). If the density of the properly aligned sheet at any point is proportional to the distance between that point and the origin, then what is the total mass of the sheet? What is its average density?

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