x2 + y? that lies below the plane z = 4 (see diagram above), Let F = zkand let S be the portion of the paraboloid z = oriented upward. Find C. F. dÃ. Please give your answer as a decimal rounded to the nearest 0.001.

Q: he curve C is the intersection of the plane z + y = 2 and the cylinder x? + y? = 1. Assume a…

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Q: b) M. dv, where G is the solid region that lies between the sphere x? + y? + r+y?+z? z2 = 36 and the…

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Q: Find the surface area of the paraboloid z= 1 - (x2 + y?) that lies between the sphere x? + y? + z² =…

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Q: The plane y=2 intersects the elliptic paraboloid ē =4x ty parabobo. Fied the slope ot the fangenh to…

A: Given :     y = 2      z = 4x2 + y2

Q: Evaluate [[ (x + y? +=?)2 dV, where 2 is the solid hemisphere (half of the sphere) enclosed by x +…

A: Change the given system to a spherical coordinate system and solve it.

Q: 9. S is the part of the cone surface z = oriented upward (no top). Vx2 + y? that lies under the…

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Q: Find the surface area of the portion of the paraboloid z = 9- r - y? between the cylinders r?+ y? =…

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

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Q: Find the surface area of the part of the plane z = 5 + 7x + 2y that lies inside the cylinder x² + y?…

A: Part of the plane is z = 5 + 7x + 2y, so this is given in terms of f(x,y). If part of the plane is…

Q: Evaluate: I| (x2 + y?) ds over the surface S of the sphere x2 + y? + z? = 5. Use Formula (5.22a)…

A: The solution is given below:

Q: Consider the ellipsoid 4x? + y?+ 222 = 25. Find all the points where the tangent plane to this…

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Q: Evaluate fff 1- x2 - y2-z2 dx dy dz where V is the volume of the sphere x? + y? + z2 = a? by…

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Q: A cube with a cylinder cut from its center is cut along the plane shown. Which of the following is…

A: In this figure cube is just coated outside the cylinder

Q: Find the surface area of the part of the plane z = 5 + 4x + 3y that lies inside the cylinder a² + y?…

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Q: Find the surface area of the part of the plane z = 5 + 7x + 2y that lies inside the cylinder a2 + y?…

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Q: e |/| e² dV where E is enclosed by the paraboloid z = 4 + a?² + y², the cylinder Evaluate 2² + y² =…

A: Here we have to evaluate ∫∫∫Eez dV  where E is enclosed by the paraboloid z=4+x2+y2, the cylinder…

Q: Evaluate [[[(x2 + y² +z?)2 dV, where 2 is the solid hemisphere (half of the sphere) enclosed by x +…

A: Apply the spherical coordinate to find the volume integral, x=ρsinφcosθ ; y=ρsinφsinθ ; z=ρcosφ And,…

Q: Türkçe: z = 16 - x? – y? paraboloidi, x? + y? = 8 silindiri ve xy-düzlemi ile sınırlandırılmış katı…

A: Given, z=16-x2-y2 paraboloidx2+y2=8 circle To find: Volume of solid

Q: Evaluate .(x+y² +=?) dS, where S is the portion of the paraboloid x=5+y² + z? contained within the…

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Q: 1. Find the area of the portion of the plane Зх — Зу + 2 — 12 that lies inside the cylinder y? + 22…

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Q: Evaluate fff(r +y²+y dV, "AP where 2 is the solid hemisphere (half of the sphere) enclosed by x +y…

A: Converting into spherical  coordinates

Q: re 2" dr + (x* + 2a²y?)dy where C is the boundary of the region between the circles a² + y? = 1 and…

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Q: Find the area of the part of the sphere x2+y2+z23D 9z that lies inside the paraboloid z =r+y?. a.…

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Q: Compute the surface area of the portion of the sphere with center the origin and radius 4 that lies…

A: We have to compute the surface area of the portion of the sphere with center the origin and radius 4…

Q: Use cylindrical or spherical coordinates, whichever seems more appropriate, to evaluate lies above…

A: Solution: ∬∫E z dV z = x2 +y2  ,     z =4

Q: Find the area of the surface . The part of the paraboloid x = y? + z? that lies inside the cylinder…

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Q: 1. Consider the surface which is the part of the sphere r? + y? + 2? = 4 that lies above the cone z…

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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: In isosceles trapezoid WXYZ with bases ZY and WX, ZY = 4, YX = 10, and WX = 20. Y. D. Find height h…

A: Consider the given figure, First find value of EX. Lets assume EX=x As it is isosceles trapezoid, so…

Q: Evaluate [[(x +y +=')² dV, where Q is the solid hemisphere (E sphere) enclosed by x +y² +z² =1 and…

A: ∫∫Ω∫x2+y2+z232 dv,   f:x2+y2+z2=1 use spherical conditions x=ρ sinϕ cosθ, y=ρ sinϕ sinθ, z=ρ cosϕ…

Q: Find the surface area S of the paraboloid z = x + y' below the plane z = 1, using the figure at…

A: According to our guideline we can only answer first question and rest can be reposted.

Q: Evaluate e dV where E is enclosed by the paraboloid z = 6 + x² + y°, the cylinder 2? + y? = 5, and…

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Q: Evaluate ff, (x²z + y?z)dS where S is the part of the plane z = 4 +x+ y with positive orientation…

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Q: Find a parametrization, using cos(t) and sin(t), of the following curve: The intersection of the…

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Q: Find a parametrization, using cos (t) and sin(t), of the following curve: The intersection of the…

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Q: Find the area of the surface . The part of the paraboloid x = y? + z? that lies inside the cylinder…

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Q: Find the surface area of the part of the plane z = 2 + 6x + 3y that lies inside the cylinder a? + y?…

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Q: Which cylindrical surface below is perpendicular to the yz-plane? O x^2 + y^2 - z^2 = 1 O x = y^2 +…

A: If a cylinder is perpendicular to any plane then it will represent  a circle at a point parallel to…

Q: The surface area of the cap cut from the paraboloid y + z? = 3x by the plane x = 2 is Select one or…

A: Given the paraboloid  y2+z2=3x  we have to find the surface area of the cap cut from the paraboloid…

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: Evaluate [[[(x + y² +=?)? dV, where 2 is the solid hemisphere (half of the sphere) enclosed by x? +…

A: Solved below...

Q: a) Find and sketch the curve of intersection between the paraboloids z = a? + y, = 8 – a² – žy². b)…

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Q: A tangent plane to the ellipsoid x². y? a b2 meets the axes in A, B, C. Show that the envelope of…

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Q: Find the surface area of a) The part of the plane 3x + 2y +z = 6 that lies in the first octant b)…

A: You have asked multiple unrelated questions in the same post. I have addressed the first one. Please…

Q: The distance from a point S(xo, Yo, Zo) to a plane M: ax + by + cz + d = 0 is given by In PS| d :…

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Q: Let C be the curve of intersection of the cylinder x2+y? = 2 and the hyperbolic paraboloid x? – y? +…

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Q: /| a² + y? – z dS where S is the part of the cone z² x2 + y? that lies between the planes Evaluate z…

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Q: yz ds where o is the part of the plane x + y+ z = 1 that lies in the first octant.

A: Given The given integral ∫∫σyzds over the region x+y+z=1 that lies in the first octant can evaluated…