2. Find the area of the part of the surface of the sphere x2 + y2 + Z2-42 that lies within the paraboloid z-x2 + y2. Hints: * Complete the square for ×2 + y2 + Z2-42+ (it is a sphere with center (0, 0,) Find the intersection to determine the region of integration 2. Find the area of the part of the surface of the sphere x2 + y2 + Z2-42 that lies within the paraboloid z-x2 + y2....
) Find the center and radius of the circle with equation x2 + 6x + y2 - 4y = 12. a) o center is (-3, 2) and radius is 5 b) o center is (3, -2) and radius is 5 c) center is (3, -2) and radius is 2/3 center is (-3, 2) and radius is 2/3 4) The equation of the parabola with focus (-3, 2) and vertex at (-3, 0) is (x +3) = - 8(y 2) a)...
orientation. Find the volume of the piece of the sphere x2 + y2 + z2-1 which lies both inside the cylinder x2 + y2-1/2 and inside the first coordinate octant (that is, x,y,z 2 0). 4. 5. For the vector field F (2x(y +2)-y2-Z2), what is the surface integral of this field over the unit-radius
Find the area of the surface. The portion of the sphere x2 + y2 + z2 = 625 inside the cylinder x2 + y2 = 400 d Help? Read It Talk! Talk to a Tutor Tutor
2. (20 pts) Find the surface area of that part of the sphere x2 + y2 + z2-4 that lies inside the paraboloid z x2 + y2. 2. (20 pts) Find the surface area of that part of the sphere x2 + y2 + z2-4 that lies inside the paraboloid z x2 + y2.
5. Let S be the sphere of radius one x2 + y2 + z2 1. Consider the following local chart for S: ο(φ, θ)-(cos@) sin(d), sin(0) sin(d), cos(d)), 0 < φ < π, Ο < θ < 2T. (a) (10 points) Find all Christoffel symbols of the sphere in the local chart σ.
Find the volume of the solid bounded on top by sphere x2+y2+z2= 9 , on the bottom by the plane z = 0, around the side by the cylinder x2+y2= 4.
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)
You have been asked to find the points on the sphere x2 + y2 + z2 = 36 that are closest to and farthest from the point (1, 2, 2). Then which of the following is incorrect from the following: Select one: A. The point on the sphere farthest to the point (1,2,2) is (-2,-4,-4) B. The point on the sphere closest to the point (1,2,2) is (2, 4,4) C. The solutions to the question can be found by solving...
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...