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- For the sphers x-12+y+22+z-42=36 and x2+y2+z2=64, find the ratio of their a surface areas. b volumes.Suppose that a thin metal plate of area A and constant density doccupies a region R in the xy-plane, and let My be the plate’s momentabout the y-axis. Show that the plate’s moment about the linex = b is My - bδA if the plate lies to the right of the line, andFind the volume of the wedge cut from the first octant by the cylinder z = 12 - 3y2 and the plane x + y = 2
- find the center of mass of a thin triangular plate bounded by y-axis and the line y = x and y = 2-x if δ (x,y)=6x+3y+3Find the moment of inertia of the region between the parabola y=4-x^2 and the line y=1-2x from x=0 to x=2 with respect to y axisFind the moment of inertia of the region between the parabola y = 6 − x2 and the line y = 1 – 2x from x=0 to x=2 with respect to y-axis.
- Find the center of mass of a thin plate of variable density d(x) = 4x2 coveringthe region bounded above by parabola x2 = 4y and below the line y =1.Find the area of the “triangular” region in the xy-plane that is bounded on the right by the parabola y = x2, on the left by the line x + y = 2, and above by the line y = 4.(a) Express the mass M of a thin wire in 3-space as a line integral. (b) Express the length of a curve as a line integral
- Find the area bounded by the curve y = 4x over the square root of (1 - 2x) and lines y = 0, x = -4 and x = 0.Determine the ordinate of the centroid of the area bounded by the curve x^2 =8y and the line 2x-y=0What is the solid formed when the area bounded by the line 2x+y=2 and rhe coordinate axis is revolved about the y axis.