The solid in the first octant bounded by the cone z = 1- Vr? + y² and the plane x + y + z = 1

Q: Evaluate the surface integral LL 6xzdS where S is the part of the plane 2x + 2y + z = 4 that lies in…

A: Thanks for the question :)And your upvote will be really appreciable ;)

Q: Find the area and centroid bounded by the curve 5y? = 16x and the curve y2 = 8x – 24.

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

Q: The region in the first octant bounded by the coordinate planes, the plane y + z = 2, and the…

A: 25.   Given that:   The plane y+z=2 and the cylinder x=4-y^2. The region in the first octant bounded…

Q: Q3// A surface S is defined by 2x2 + z = 1 and the bounded by the planes y = 0,y 2, x 0,z = 0 in the…

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Q: Let S be the solid bounded by the planes z = o and y + z = 3, and the cylinder x2+y2 =2y-

A: answer is in next step

Q: The area of the plane z = 2x + 1 above the disk of radius 1 centered at the origin is (а) 4л. (b)…

A: As we know, z=fx,y defines a surface in xyz-space.  Formula for the surface area of the surface…

Q: (a) Integrate g(x,y,z) = Inx+y over the surface of the region cut from the plane 4x+3y+2z=1 by the…

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Q: 2. Calculate the centroid of the thin plate R which bounded by a = 1, y = 0 and, x² + y² = 4.

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Q: The solid region bounded on the sides by the paraboloid z = 4-x-y, above by the plane z= 3, and…

A: The Equation of paraboloid: z = 4-x2-y2The equation of upper plane: z = 3The equation of lower…

Q: The solid in the first octant bounded by the coordinate planes and the plane z = 8 – x – y dz dy dx

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Q: Find the surface area of that portion of the surface z = V4 -x that lies above the rectangle R in…

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Q: Consider the solid that is bounded above by x² + y? + z? = 169 and below by z=5. %3D

A: In this question, we have to write the triple integral to find the volume of the solid bounded by…

Q: 4. Find the volume V of the solid S that is bounded by the elliptic paraboloid defined by 2x2 + y2…

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Q: Give a parametrization, including the appropriate u- and v-bounds, for the portion a cylinder of…

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Q: Let R denote the solid in the first octant bounded by the planes 2x + 6y + 3z = 6, x = 0, y = 0, z =…

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Q: Evaluate the surface integral xyzdS where S is the part of the plane z = 1 + 2x + 3y that lies above…

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Q: Use Stokes' Theorem to caleulate ſ. F - dř, where F = zyi+3=3+5zk, and C is the closed path around a…

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Q: A solid G is bounded by the paraboloid z = 4 - x? – y?, the cylinder x² + y? = 4 and the plane z =…

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Q: 2. Use a parametrization to express the area of the given surface as a double integral and then…

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Q: The solid bounded by x = y? – 1, z = 1 – y², z = 4 – x, and z = 0.

A: Given that,

Q: Integrate F(x, y, z) = z - x, over the cone z = sqrt(x2 + y2), 0<= z <=1

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Q: Evaluate where G is the solid in the first octant bounded by paraboloid : = + y, the cylinder r+ y 9…

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Q: 4. Find each volume. (a) A solid is being bounded by paraboloids z = 2x² + y? and z = 27 – x² – 2y?.…

A: We have to find the volume  from the given condition

Q: 2. Fnd the area of the sur face in the first octant cut from the cone z2 = x2 y2 by the plane x +y =…

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Q: Q3// A surface S is defined by 2x2 + z 1 and the bounded by the planes y = 0,y 2, x = 0,z = 0 in the…

A: A surface S is defined by 2x2+z=1 which is bounded by the planes y=0, y=2, x=0, z=0 in the first…

Q: Evaluate. where G is a solid that lies in the first octant bounded by x^2 + y^2 = 3z and z = 3.

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Q: Integrate G(x, y, z) = x - y - z over the portion of the plane x + y = 1 in the first octant between…

A: Given G(x,y,z)=x-y-z

Q: Integrate g(x, y, z) = x + y + z over the portion of the plan 2x + 2y + z = 2 that lies in the first…

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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: 1. Find the surface area of the cone z = Jx2 + y2 that lies between the plane y = x and the cylinder…

A: Surface area in xy-plane

Q: Consider the plane region bounded by the graphs of y = k, y = 0, x = 0, and x = b, where k > 0…

A: Given: The plane region is bounded by the graphs given as follows, The plane is drawn for the given…

Q: E is the solid in R3 bounded by the cone surface z = square root (x2+ y2 ) and the plane z = 3, and…

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Q: Find the area of the part of the plane 4x + 3y + z = 12 that lies in the first octant.

A: to find:- surface area, A.

Q: 2. Use a parametrization to express the area of the given surface as a double integral and then…

A: Given ,x2+y2+z2 = 22       _________(I)and z = x2+y2     __________(II)Putting the value of z from…

Q: Let D be the solid region bounded above by z = -5x² +y? and below by z =-5. Then the projection of D…

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Q: a) Evaluate ||| x²yz dV, where G is solid in the first octant that is bounded by parabolic cylinder…

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Q: The solid in the first octant bounded by the coordinate planes and the plane z = 3 – x –y dz dy dx

A: Answer is:∫03∫03-x∫03-x-ydzdydx Proof is attached below.

Q: Find the centroid of the polyhedron with four triangular faces in the first octant that is bounded…

A: The region is bounded by the three coordinate planes and the plane x+y+z=1. Thus, the region can be…

Q: 2. Calculate the centroid of the thin plate R which bounded by r = 1, y = 0 and, 2² + y² = 4.

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Q: Integrate g(x,y,z) = x + 5y + z over the portion of the plane 4x + 8y + z = 8 that lies in the first…

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Q: Find the centroid of the solid bounded by the parabolic cylinder 1- y? and the three planes given…

A: To find the centroid of the solid bounded by the parabolic cylinder: The region is defined as…

Q: Evaluate the surface integral. JI (12 + y2 + 2) ds S is the part of the cylinder x2 + y2 = 9 that…

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Q: The region cut from the solid elliptical cylinder x2 + 4y2≤ 4 by the xy-plane and the plane z = x +…

A: Given that, z=x+2 , x2+y2≤4

Q: A solid G is bounded by the paraboloid z = 4 – r - y², the cylinder 2+ y = 4 and the plane z = 5.…

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Q: E) Sketch the solid bounded by the cylinder ** +y = 4 and the planes y+z = 4 and z = 0

A: Here, we need to sketch the solid bounded by the cylinder x2+y2=4 and the planes y+z=4 and z=0.

Q: Compute ,F · dS for F = (xy, 5y,0), S being the cone z² = x + y²,x² + y? 0, with the normal %3D…

A: The vector field is F=⟨xy, 5y, 0⟩ and the parametric equation of the cone is  Rr, θ=rcosθ, rsinθ, r…

Q: Find the area of the part of the plane z=3x+5 y+3 that lies above the region R=(x,y) 2≤x≤3; 1sys5.

A: The given plane is z=3x+5y+3. Differentiate partially with respect to x, y respectively to obtain…

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: Cvaluate AP G is a solid in the first octant bounded by the plane y+ z = 2 and the urface y = 1 -…

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Q: 2. The solid in the first octant bounded by the planes x = 0, y = 0, z = 1, z = 2 – y, and the…

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