B. Compute the shared mass between the polar curves (r = 1+ cose) and (r = 1- cose), usę density equal to (6).
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- Which lines or line segments or rays must be drawn or constructed in a triangle to locate its a orthocenter? b centroid?B. Compute the shared mass between the polar curves (r = 2a cose) and (r = 2a sin@). use density equal to (6).7) Find the area of the surface when y = Vx, from (4, 2) to (9, 3) is rotated about the x-axis. %3D
- A hole is drilled through the center of a sphere x² + y² + z² = R,², leaving a ring-shape solid. If the drill used is cylindrical in shape with radius Rd, use polar coordinates to formulate the volume V of the remaining solid. %3D(b) A hole is drilled through the center of a sphere x² + y² + z² = R,², leaving a ring-shape solid. If the drill used is cylindrical in shape with radius R4, use polar coordinates to formulate the volume V of the remaining solid.Find the area of the region inside the r=1+ cos Outside r= cost Curve the and polar region: above the
- Suppose the solid W in the figure is the spherical half-shell consisting of the points above the xy-plane that are between concentric spheres centered at the origin of radii 4 cm and 10 cm. Suppose the density 8 of the material increases linearly with the distance from the origin, and that at the inner surface the density is 8 g/cm³ while at the outer surface it is 10 g/cm. (a) Using spherical coordinates, write d as a function of p. Enter p as rho. 8(e) = 25/9(rho-4) (5.0 (b) Set up the integral to calculate the mass of the shell in the form below. If necessary, enter o as phi, and 0 as theta. B D CLI 25/9(rho-4)rho^2sinphi "OP Ópdp A = 0 B = 2pi C = 0 D= pi/2 (Drag to rotate) E- 4 F= 10 (c) Find the mass of the shell. 4536piFind the length of the polar spiral r = 0² from 0 < 0 < v5.Determine the distance to the centroid of the beam's cross-sectional area; then determine the moment of inertia about the x' axis.
- Find the area enclosed by one loop of this polar curve: r=3sqrt(cos2theta) from 0 to 2pi using the formula A=1/2 integral from 0 to 2pi (r)^2 for parametric curve.The boundary of a lamina consists of the semicircles y = V1 - x2 and y = 9 - x2 together with the portions of the x-axis that join them. Find the center of mass of the lamina if the density at any point is inversely proportional to its distance from the origin. Hint: use polar coordinates 60 (x, V) = ( 0,- 13nFind the center of mass, the moment of inertia about the coordinate axes, and the polar moment of inertia of a thin triangular plate bounded by the lines y = x, y = -x, and y = 1 if d(x, y) = y + 1 kg/m.