The region is a right circular cone, 2 = Var? + y2 with height 29. Find...
The region is a cone, z == ? + ytopped by a sphere of radius 4. Find the limits of integration on the triple integral for the volume of the snowcone using Cartesian, cylindrical, and spherical coordinates and the function to be integrated. For your answers 0 = theta, o =phi, and p = rho. Cartesian V= "SC"}, "plz,y,z2) dz dydz where A B = .D= and p(x, y, z) = E= F= Cylindrical v=L" S "*P10,0,2)dz dr do where...
The region is a right circular cylinder of radius 2, with the bottom at -5 and top at 5. Find the limits of integration on the triple integral for the volume of the cylinder using Cartesian, cylindrical, and spherical coordinates and the function to be integrated. For your answers 8 theta, o =phi, and prho. Cartesian v=1" / ")*P(2,9,2) dyde de where A= -2 B= 2 E = -5 -sqrt(4-x^2) D= sqrt(4-x^2) and p(x, y, z) = F = 5...
(1 point) The region W is the cone shown below. C The angle at the vertex is /2, and the top is flat and at a height of 5 Write the limits of integration for f dV in the following coordinates (do not reduce the domain of integration by taking advantage of symmetry) (a) Cartesian: With a b d and f eb d Volume (b) Cylindrical: With a= b d and f eb ed f d Volume = (c) Spherical:...
(1 point) Consider a right circular solid cone S standing on its tip at the origin. The height of the cone is 3 and the radius of the top is 8. Find the centroid of the cone by following the steps below. Assume the density of the cone is constant 1. a. The mass of the cone is m Jls 1 d(x, y, 2) b. Let Q(2) be the disk that is the intersection of the cone with the horizontal...
(9 points) Suppose f(x, y, z) = - and D is the domain inside the sphere x2 + y2 + z2 x2 + y2 + z2 = 1 and outside the cone za Enter p as rho, as phi, and as theta. As an iterated integral, BRD (F sav = SITE dp do do JA JC JE with limits of integration
(1 point) The region W is the cone shown below. The angle at the vertex is #/3, and the top is flat and at a height of 3v3. Write the limits of integration for wdV in the following coordinates (do not reduce the domain of integration by taking advantage of symmetry): (a) Cartesian: With a = .b = .d = and f = e = Volume = / ddd (b) Cylindrical: With a = CE and f = ddd e...
Suppose you have to use spherical coordinates to evaluate the triple integral III z av where D is the solid region that lies inside the cone z = /22 + y2 and inside the sphere 22 + y2 + 2 = 121 D Then the triple ingral in terms of spherical coordinates is given by Select all that apply pcos o dp do de z dV = cos sin o dp do de D z DV = D pocos o...
2) (27 points) Let D be the region bounded from below by the plane : 0, from above by the plane z-2J3 and laterally by the hyperboloid of one sheet x2 + y2-1-24. a) (3 points) Draw the region D. b) (12 points) Set up triple integrals representing the volume of D in spherical coordinates according to the order of integration dp do de c) (12 points) Set up triple integrals representing the volume of D in cylindrical coordinates according...
(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...
23. Parametrize the surface of the region D bounded by the cone x2 + y2 = (2-1) and the plane z = 0. **+-12-17 24. Find the flux of P = (zº, y + 1) over the curve C defined by the portion of the parabola y = x2 from (0,0) to (2,4).