Express the volume of the solid lying inside the sphere r2 + y? + 22 8 and outside the cylinder ? + y? = 2 with triple integral in cartesian coordinates, cylindrical coordinates and spherical coordinates respectively.

Q: Describe the surfaces r = R in cylindrical coordinates and ρ = R in spherical coordinates.

A: Given cylindrical and spherical coordinates.

Q: Convert the point (ρ , θ , φ) =(3, π/6 , π/3)from spherical to cylindrical coordinates

A: Spherical to cylindrical conversion (r,θ,ϕ)->(ρ,θ,z)ρ=r sinϕθ=θz=r cosϕ

Q: . Find the distance between (5, 3?/2 , 0) and (5, ?/2 , 10)in cylindrica

A: Let the given two points are converted into cartesian system and then and find out the distance

Q: (3, 7 ) Convert the spherical point (p, 0, $) to Cartesian coordinates.

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Q: Conver 4z = r2cosθ + r4sin2θ in cylindrical coordinates to cartesian coordinates. Thank you for the…

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Q: 2. Convert the point (V6, , v2 ) from cylindrical to spherical coordinates. (12등, ) (b) (vZ;. )…

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Q: Determine the coordinates of the centroid of the shaded area. y 20 60 188 20 40 50 Answers: 50 40.…

A: Break the given shaded area into the five different areas as shown below:

Q: 27 Convert the poínt (58,I,s) from cylincdirical to Spherical Coordinats.

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Q: find The volume of Ihe solid generated by revolving each vegion enclosed by he triangle wilh…

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Q: Use cylindrical coordinates. Find the volume of the solid that is enclosed by the cone z = Vx² + y2…

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Q: Exercise 9.6. Find the average distance of the space between a sphere of radius 2 and a sphere of…

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Q: Verify in cylindrical coordinates that V-(ïv)=(V -ū5+ū -Vỹ

A: Given: ∇.u→v→=∇.u→v→+u→.∇v→

Q: Change from rectangular to cylindrical coordinates. (a) (0, -4, 5) (r, 0, z) = (b) (-7,7/3, 3) (r,…

A: The relation between the Rectangular coordinates x, y, z and Cylindrical coordinates r, θ, z is…

Q: express the point (x,y,z) = (0,1,0) in spherical coordinates. Show full and complete procedure

A: To express the point (x,y,z)=(0,1,0) in spherical coordinates,Using spherical coordinates…

Q: 2. Convert the point (V6, , V2 ) from cylindrical to spherical coordinates. (a) (V2,플, ) (b) (vz. )…

A: Option C is correct answer.

Q: 2. By changing to cylindrical coordinate, evaluate r1 (V1-x2 c16 L 2+y2x² dzdydx

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Q: Use spherical coordinates to evaluate 1-²1-x²-x² 2-y2 (x² + y² + z²)² dz dy dx

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Q: choose The correct ansuer when transforming The triple integral 3. メーム 9-xーy 9-x2 to spherical…

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Q: Use spherical coordinates to find the volume of a solid that lies above the xy- plane, outside the…

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Q: Evaluate by changing to spherical coordinates: /2–x²-y² xydzdydx x²+y2

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Q: Change from rectangular to cylindrical coordinates. (a) (0, -8, 6) (r, 0, z) = (b) (-8, 8√3, 7) (r,…

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