Find the area of the surface. The part of the plane z = 7 + 5x + 2y that lies above the rectangle [0, 5] × [1, 6]

Q: Evaluate x² zdS, where S is the part of the plane z = 3 + 4x + y above the rectangle [0, 4] × [0,…

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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 area of the surface. The part of the plane  z = 3 + 2x + 5y  that lies above the rectangle…

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Q: Find the area of the portion of the plane 2x + 3y + 4z = 28 lyingabove the rectangle 1 ≤ x ≤ 3, 2 ≤…

A: GIVEN  2x + 3y + 4z = 28  We need to find the area of the plane  lyingabove the rectangle 1 ≤ x ≤ 3,…

Q: Find the surface area of the portion of the bowl z = 8+x² + y that lies below the plane z = 14.

A: Given, z=8+x2+y2 ,z=14 Now substitute z=14 into the given surface for finding the intersection of…

Q: Find the area of the cap cut from the paraboloid y + z? = 3x by the plane x = 1.

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Q: Find the area of the portion of the paraboloid z=x^2+y^2 that lies inside the cylinder x^2+y^2=4.

A: Given that ,  paraboloid   z=x2+y2 cylinder        x2+y2=4

Q: Find the points on the surface represented by x2 + y? + z2 - 4x – 6y + 2z = -10 which are closest to…

A: To find - Find the points on the surface represented by x2 + y2 + z2 - 4x - 6y + 2z = -10 which are…

Q: • Find the area of the portion of the Sphere x² + y² + 2²² = 9 between the planes Z=1 and 2 = 0.…

A: The given equation of  plane is x2+y2+z2=9. The polar coordinates are x=rcosθ & y=rsinθ. The…

Q: Find the area of the surface.The part of the surface 2y + 4z − x2 = 5 that lies above the triangle…

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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 surfaces The surface cut from the bottom of the paraboloid z = x2 + y2 bythe…

A: The formula for the surfaces area of the paraboloid above the region R is: A=∬Rzx2+zy2+1dxdy Where,…

Q: Enclosed by the paraboloid z = x² + 3y? and the planes x = 0, y = 1, y = x, z = 0

A: We know that, volume under surface z=fx,y and above the region D in xy-plane is given as…

Q: Let W be the region that is cut out from r² + y² < 4 by the paraboloid z = r² + y² and the plane z =…

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Q: Find the area of the surface. The part of the surface 2y + 4z - x2 = 5 that lies above the triangle…

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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: 10. Find the area of the portion of the sphere x2 + y² + z² = 16 between the planes %3D z=1, z=2.

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Q: The solid enclosed by the sphere x² +y² +z? = 4a* and the planes z = O and z = a.

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Q: The portion of the sphere x² + y² + z² = 25 inside the cylinder x2 + y² = 9

A: Given: The portion of the sphere x2+y2+z2=25inside the cylinder x2+y2=9 To find the area of the…

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

A: Givenz=1-x2-y2z=-2Suppose the surface is defined byz=f(x,y) for x∈R, then the area of the surface is…

Q: Evaluate x* zdS, where S is the part of the plane z = 1+4x + 3y above the rectangle [0, 3] x [0, 5]

A: Please see the below picture for detailed solution.

Q: Find the area of the part of the paraboloid z=x² + y² that lies under the plane z=9.

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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: Find the area of the surface of the part of the plane 3x + 2y + z = 6 that lies in the first octant.

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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: Find the area of the part of the plane 3x + 3y + z = 9 that lies inside the cylinder x2 + y2 = 25.

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Q: Find the point lying on the intersection of the plane x + y +z = 0 and the sphere x2 + y? + z? = 25…

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Q: Find the area of the surface. The part of the surface  2y + 4z − x2 = 5  that lies above the…

A: According to the given information, it is required to find the area of the surface.

Q: Find the surface area of the part of the plane 3x + 2y + 4z = 24 that lies in the first octant…

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Q: Q4(a) Find the surface area of the part of the paraboloid z=10-x -y' that lies above the plane :=1.

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Q: Find the area of the surface. The part of the paraboloid x = y² + z² that lies inside the cylinder…

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Q: 3) Find the surface area of the portion of the paraboloid z = x2 + y2 below the plane z = 1. %3D

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Q: Find the area of the surface. The part of the plane  z = 4 + 3x + 2y  that lies above the rectangle…

A: Consider the part of the plane that lies above the rectangle .

Q: + + Find the area of the portion of Sphere x² + y² + 2 = 9 betw= the planes Z=1 and 2 = 0. Draw

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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 area of the surface. The part of the plane 3x + 2y + z = 6 that lies inside the cylinder…

A: Find the area of the surface. The part of the plane 3x + 2y + z = 6 that lies inside the cylinder…

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 area of the part of the plane x + 4, y + z = 4 that lies in the first octant. 1. A = 12 2.…

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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 surface. The part of the plane z = 8 + 5x + 2y that lies above the rectangle…

A: Area of the surface z=f(x,y) A(s)=∬1+fx2+fy2f(x,y)=8+5x+2yfx=5fy=2

Q: Find the surface area of the part of the plane z = 4 + 6x + 2y that lies above the rectangle [1, 4]…

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Q: Find the area of the surface. The part of the surface  2y + 4z − x2 = 5  that lies above the…

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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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Q: Find the area of the surface. The part of the plane 2x + 4y + z = 8  that lies inside the cylinder…

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Q: Find the area of the surface of the part of the plane 3x + 2y + 4z = 2 that lies inside the cylinder…

A: Here, surface S has an equation of the form z=f(x,y), where (x,y)  D and f has continuous partial…

Q: (a) Find the surface area of the plane 3x +2y + z = 6 that lies in the first octant.

A: If z=fx, y then surface area is, AS=∫∫D1+zx2+zy2dA