The part of the sphere x² + y² + z² = 1 inside the upper part of the cone x² + y? = z².

Q: Consider the unit sphere x² + y² + z² = 1. Find the average distance from its north pole to a point…

A: Given: x2+y2+z2=1 It is equation of sphere of radius r=1 unit. We have to find the average distance…

Q: find a parametrization of the surface. The cap cut from the sphere x2 + y2 + z2 = 9 by the cone z =…

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Q: Find the surface area of the part of the spherex +y² +z = 16 that lies above the plane z = 2.

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Q: Find the extreme values of ƒ(x, y, z) = x - y + z on the unit sphere x2 + y2 + z2 = 1.

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Q: parametrizes the portion of the sphere x² + y² + z² = 9 that is above the xy-plane and below the…

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Q: Find the area of the surface. The part of the sphere x2 + y2 + z² = 4z that lies inside the…

A: Given sphere is x2+y2+z2=4z that lies inside the paraboloid  z=x2+y2. We have to find the area f the…

Q: Find the surface area of the part of the sphere x2+y2+z2=49 that lies above the cone z=(x2+y2)1/2

A: Consider the provided question,

Q: Find the points on the cone z2 = x² + y² that are closest to the point (1,-1,0) %3D

A: Given that, z2=x2+y2 and the point is (1, -1,0). Form the equation of distance as follows.…

Q: Find the area of the part of the sphere x2 + y2 + z2 = 4z that lies inside the paraboloid z = x2 +…

A: Given, x2+y2+z2=4z  and  z=x2+y2 Equation of the sphere and paraboloid in cylindrical coordinates is…

Q: Find the area of the surface. The part of the paraboloid z = 1 − x2 − y2 that lies above the plane…

A: Given that the part of the parabola z=1-x2 -y2 that lies above the plane z= -6 . Here we have to…

Q: Find the area of the surface. The part of the hyperbolic paraboloid  z = y2 − x2  that lies between…

A: In the question we have to find the value of area enclosed by the function of given figures.

Q: Find the area of the surface. The surface cut from the bottom of the paraboloid z = x2 + y2 by the…

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Q: Find the area of the surface. The part of the sphere x2 + y2 + z2 = 16 that lies above the plane z =…

A: The objective is to find the area of the surface of the part of the sphere x2+y2+z2=16 that lies…

Q: A solid lies above the cone z = V x² + y2 and below the sphere x2 + y2 + z2 = z. Write a description…

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Q: Find the area of the surface. The part of the sphere x2 + y2 + z2 = 16 that lies above the plane z =…

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Q: Find the surface area of the portion of the sphere x2 + y2 + z2 = 25 inside the cylinder x2 + y2 =…

A: Recall:  The formula of surface area is S=∫∫S1+∂z∂x2+∂z∂y2 dA

Q: Find the points on the sphere x +y +z = 154 where f(x,y,z) = 3x + 8y + 9z has its maximum and…

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Q: Find the area of the surface for the portion of the sphere x+y +z = 225 inside the cylinder x-+y-=…

A: Given that  Sphere x^2+y^2+z^2=225  Cylinder x^2+y^2=144 To find the area of the surface

Q: Find the area of the surface. The part of the sphere x2 + y2 + z² = 81 that lies above the plane z =…

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Q: Verify Stoke's for F = (2x – y)i – yz²j – y²zk where S is the upper half of the sphere x? + y? +z² =…

A: Solution is given below

Q: Find the area of the surface. The part of the paraboloid z = x² + y2 that lies inside the cylinder…

A: Area of the surface f(x ,y) above a region R of the xy-plane is given by…

Q: 2. The portion of a cylinder of radius 3 centered along the y-axis that lies between the planes y =…

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Q: The sphere x² + y² +z² = 100 has the center (0,0,0) and a radius of length 50. Select one: True…

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Q: Find the area of the cap cut from the sphere x2 + y2 + z2 = 2 by the cone z = √(x2 + y2).

A: to find the area

Q: a) Evaluate x²z dS where o is part of a sphere x² +y² + z² = 8 above %3D the plane 2.

A: Given that, ∬sx2zds And, x2+y2+z2=s⇒z2=s-x2-y2 Take the derivative,…

Q: Find all points on the isometric dot plane, Ax,1 yl, with x and y integers, that are ex- actly V133…

A: a)The distance from origin to point x,y is 133. b)The distance from origin to point x,y is 217.

Q: Verify Stoke's theorem for A=(2x-y)i-yz²j-y*zk where S is the upper half 5A. surface of the sphere *…

A: Consider the given vector and sphere equation. A→=2x−yi−yz2j−y2zk and x2+y2+z2=1 Since S is the…

Q: Find the point lying on the intersection of the plane x + y + 4 z = 0 and the sphere x2 + y2 + z2 =…

A: Determine z from the equation of plane.

Q: Find the extreme values of ƒ(x, y, z) = x2yz + 1 on the intersection of the plane z = 1 with the…

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Q: he cone z^2= x^2+ y^2, for z ≥0, cuts the sphere x^2+ y^2+ z^2= 16 along a curve C. That is, C is…

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Q: 4. Find the area of portion of the sphere x²+y²+z = 9 between the planes z = 1 and 2 = 0. Draw the…

A: Surface area of a surface z=f(x,y)  A=∫∫D1+fx2+fy2dA Here D is a point on xy plane

Q: Find a parametrization for the portion of the sphere x2 +y2 + z2 - 16 between the planes z =- 2/2…

A: we have been given a sphere x2+y2+z2=16 between the planes z=-22 and z=2

Q: Find the surface area of the part of the sphere x^2+y^2+z^2=49 that lies above the cone…

A: Given:

Q: Find the surface area of the portion of the cone x² + y² = z² above the region inside the…

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Q: Find the points on the cone z = x° + y° that are closest to the point (1,-1,0) %3D +1

A: Given,

Q: )الكــره the Sphere OThe Portion of planes z=l x +y+Z² = \6 between the %3D and z=2.

A: Volume of the sphere x2+y2+z2=16 or x2+y2=16-z2 is: V=∫z=12∬x2+y2≤16-z2dxdydz   =∫z=12π16-z2dz…

Q: Find the surface area of the part of the sphere x2+y2+z2=9 that lies above the cone z=√x2+y2

A: answer is below

Q: Find the flux of F = z²k upward through the part of the sphere x² + y² + z² = a² in the first octant…

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Q: Sketch the curve of intersection of the surfaces. The paraboloids z = x² + y° and z = 25 – x² – y² .

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Q: Find the area of the surface. The part of the sphere x2 + y2 + z2 = 4z that lies inside the…

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Q: The part of the sphere x^2+y^2+z^2=4z that lies inside the paraboloid z=x^2+y^2

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Q: Find the area of the surface. 12. The part of the sphere x2 + y2 + z2 = 4z that lies inside the…

A: Solution:GivenSphere:   x2+y2+z2=4zParaboloid: z=x2+y2To find the area of the…

Q: Find the extreme values of ƒ(x, y, z) = x2yz + 1 on the intersection of the plane z = 1 with the…

A: consider the following equations  f(x,y,z)=x2yz+1                                  (1)h(x,y,z)=z-1…

Q: Find the area of the surface. The part of the plane z = 7+ 2x + 3y that lies above the rectangle [0,…

A: We have to find the area of the surface of the given problem.

Q: Find the area of the part of the sphere x2 + y2 + z2 = a2 that lies inside the cylinder x2 + y2 =…

A: answer is A = a2(π -2) detailed solution with explanation is given below

Q: (A) Find the surface area of the portion of the half ball with radius a which cuts off by the…

A: Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: Find the area of the surface. The part of the paraboloid z = 1 - x² – y2 that lies above the plane z…

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Q: Find the surface area of the portion of the cone z = x2 + y2 in between the planes z = 3 and z = 4.

A: The area of the surface z=fx,y above a region R of the xy-plane is given as follows.…

Q: Find the area of the surface. The part of the sphere x2 + y2 + z² = 36 that lies above the plane z =…

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