3. Find the volume of the solid in the first octant that lies above the cone...
3. Find the volume of the solid in the first octant that lies above the cone z = 13(x+ + y) and inside the sphere x2 + y2 + y2 = 42. Use spherical coordinates. 4. Determine if the vectorfield F(x, y) - (x + y)i + (2xy + y) is conservative If it is, find a potential function
Use spherical coordinates: 36) Find the volume of the solid outside the cone z2 = x2 + y2 and inside the sphere x2 + y2 + z2 1. Sketch the drawing of the graph. Use spherical coordinates: 36) Find the volume of the solid outside the cone z2 = x2 + y2 and inside the sphere x2 + y2 + z2 1. Sketch the drawing of the graph.
Use spherical coordinates. Find the volume of the solid that lies within the sphere x2 + y2 + z2 = 4, above the xy-plane, and below the cone z =√( x2 + y2)
Use spherical coordinates to find the volume of the solid that lies above the cone z = 3x2 + 3y2 and below the sphere x2 + y2 + z? first octant. Write = 1 in the v=L"!" " * sinħapapao 1. 0 2. 1 d = 3. À b = 4. 7T 2 f= 5. 6 a = < 6. Í C = 7. 21 ve Ja Ja Ja p sin qapaqau 1. 0 2. 1 d = 3. b=...
(a) Let R be the solid in the first octant which is bounded above by the sphere 22 + y2+2 2 and bounded below by the cone z- r2+ y2. Sketch a diagram of intersection of the solid with the rz plane (that is, the plane y 0). / 10. (b) Set up three triple integrals for the volume of the solid in part (a): one each using rectangular, cylindrical and spherical coordinates. (c) Use one of the three integrals...
1. (13 pts.) Use spherical coordinates to set up the triple integral for the solid that is constructed from a portion of a sphere, x2 +y2 +Z2-1 that lies above the cone φ = π/4 . Do NOT evaluate. 1. (13 pts.) Use spherical coordinates to set up the triple integral for the solid that is constructed from a portion of a sphere, x2 +y2 +Z2-1 that lies above the cone φ = π/4 . Do NOT evaluate.
(1 point Find the volume of the solid that lies within the sphere x2 + 2 + z-64 above the xy plane, and outside the cone z 8V x2 y2 (1 point Find the volume of the solid that lies within the sphere x2 + 2 + z-64 above the xy plane, and outside the cone z 8V x2 y2
Question 9 8 pts (8) Let S be the solid in the first octant that lies inside the sphere p = 2 and underneath the cone == 33° + 3y". Set up a triple integral in spherical coordinates that represents the volume of S.
plane, and outside the cone z-5V x2 (1 point Find the volume of the solid that lies within the sphere x2 ,2 + z2-25, above the x (1 point) Find the mass of the triangular region with vertices (0,0), (1, 0), and (0, 5), with density function ρ (x,y) = x2 +y. plane, and outside the cone z-5V x2 (1 point Find the volume of the solid that lies within the sphere x2 ,2 + z2-25, above the x (1...
1 point) Find the surface area of the part of the sphere x2 + y2 + z2-1 that lies above the cone z = x2+y2 Surface Area (1 point) Find the surface area of the part of the plane 2a 4y+z 1 that lies inside the cylinder 2y21. Surface Area2pi 1 point) Find the surface area of the part of the sphere x2 + y2 + z2-1 that lies above the cone z = x2+y2 Surface Area (1 point) Find...