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Litcyb
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Homework Statement
Find the center of mass of a lamina in the shape of an isosceles right triangle with equal sides of length a if the density at any point is proportional to the square of the distance from the vertex opposite the hypotenuse.
Homework Equations
∫∫ (f(x,y) dA
mx= 1/m(∫∫ x(fx,y) dA
my= 1/m(∫∫ y(f(x,y) dA
The Attempt at a Solution
how do you calculate the bounds?
I know its the distance from the 90° angle to the the hypotenuse, but how to calculate that length? According to the book that length is √(x^2+y^2) why? Please, Help me how to visualize this problem.
I know how to calculate the density and centers of mass, I am just struggling in visualizing the problem and coming with an equation to integrate. Thank you. Ps- Happy Thanksgiving to those who celebrate it.
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