Mathematics, 16.04.2020 19:24, thornlilly17

1. [12pts] Let LaTeX: \mathcal TT be the triangular region in the LaTeX: xyx y-plane with vertices LaTeX: (0,0), (m,0), (m, n) ,( 0 , 0 ) , ( m , 0 ) , ( m , n ) , where LaTeX: m, nm , n are positive constants. Use a double integral in polar coordinates to calculate the average value of the LaTeX: xx-coordinate, taken over all points in LaTeX: \mathcal T T. You may assume the formula for the area of the triangle.

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1. [12pts] Let LaTeX: \mathcal TT be the triangular region in the LaTeX: xyx y-plane with vertices L...