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Find the Center of Mass of a Lamina in the Shape

Question 155

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Find the center of mass of a lamina in the shape of an isosceles right triangle with equal sides of length a=15a = 15 if the density at any point is proportional to the square of the distance from the vertex opposite the hypotenuse. Assume the vertex opposite the hypotenuse is located at (0,0)( 0,0 ) , and that the sides are along the positive axes.

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