a) Let G be the wedge in the first octant that is cut from the cylindrical solid y² + z² ≤ 4 by the planes y = 2x and x = 0. Evaluate SS S xyz dV.

Q: Calculate :/ F. ds, where F (x, y, z) = (-6x³ + 2yz)i + (-6y³ + sin¯¹ (3xz)) j+ (2z+cos (3x²y²)) k…

A: Given F(x,y,z)=-6x3+2yzi^+-6y3+sin-13xzj^+2z+cos3x2y2k^ and S is the outward-oriented surface of the…

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

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Q: Find the volume of the solid that lies under the plane 4x + 6y − 2z + 15 = 0 and above the rectangle…

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Q: Find the surface area of the portion of the part of the paraboloid z = 7 - 2x² – 2y² that lies above…

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Q: Let S be the solid tetrahedron bounded by the four planes a = 0, y = , z = 30, and z = 4x + y. !!…

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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: A fluid has density 900 kg/m³ and flows with velocity v = zi+yj + zk, where x, y, and z are measured…

A: Given: Density ρx,y,z=900 kg/m3  , v→=xi^+yj^+zk^. To find: The rate of flow outward through the…

Q: 2. A solid is in the first octant lies inside the hemisphere z = 4 - x² - y², outside the cone z =…

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Q: A fluid has density 600 kg/m³ and flows with velocity xi+yj + zk, where x, y, and z are measured in…

A: From the given information we get:

Q: Graph the solid that lies between the surface z= 2xy/( x2 + 1) and the plane z =x + 2y and is…

A: Given surfaces are z=2xyx2+1, z=x+2y  and are bounded by planes x=0 , x=2 , x=-1 , y=0 , y=4. To…

Q: Find the volume of the solid bounded by the ellipic paraboloid z = 3 + 4x2 + 2y², the planes x = 2…

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Q: What is the surface area of a hyperbolic paraboloid described by parametric eqn: z = xy, where x,…

A: The surface area of a hyperbolic paraboloid described by the parametric equation z = xy, where x = u…

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: A region R consists of a square bounded by the lines x = -5, x = 5, y = 0, and y = -10 and a half…

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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