1. Calculate the mass of the D heterogeneous plate, given the limited lines, if the areal density at each point μ = μ (x, y)
1.6. D: x2 + y2 = 1, μ = 2 - x - y
2. Calculate the static moment of a homogeneous plate the D, limited data lines, with respect to said axis, using polar coordinates.
2.6. D: x2 + y2 - 2ay ≥ 0, x2 + y2 + 2ax ≤ 0, y ≥ 0, Oy
3. Calculate the coordinates of the center of mass of a homogeneous body, occupying the area of the V, bounded by said surfaces.
3.6. V: x = 6√y2 + z2, y2 + z2 = 9, x = 0
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.
4.6. V: y = x2 + z2, y = 2, Oy
Detailed solution. Decorated in Microsoft Word 2003 (Quest decided to use the formula editor)
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