1. Calculate the mass of the D heterogeneous plate, given the limited lines, if the areal density at each point μ = μ (x, y)
1.19. D: y = 0, y = 2x, x + y = 6, μ = x2
2. Calculate the static moment of a homogeneous plate the D, limited data lines, with respect to said axis, using polar coordinates.
2.19. D: x2 + y2 - 2ax = 0, x2 + y2 - ax = 0, y ≤ 0, Ox
3. Calculate the coordinates of the center of mass of a homogeneous body, occupying the area of the V, bounded by said surfaces.
3.19. V: x2 + z2 = 4y, y = 9
4. Calculate the moment of inertia with respect to said homogeneous body axes, occupying the area of the V, the limited data surfaces. body density δ taken equal to 1.
4.19. V: x2 = y2 + z2, y2 + z2 = 4, x = 0, Ox
Detailed solution. Decorated in Microsoft Word 2003 (Quest decided to use the formula editor)
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