Express the volume of the solid lying inside the sphere z + y? + z? = 20 and outside the cylinder z + y² = 5 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 an equation of the line passing through the point (−1, 6) and parallel to the line joining the…

A: To Find an equation of the line passing through the point (−1, 6) and parallel to the line joining…

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

A:

Q: B) Show that V=367 is the volume of a sphere of radius 3 by using spherical coordinates.

A:

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

A:

Q: Use spherical coordinates to find the volumes of the two solids obtained when the hemisphere z =…

A: Let  x=rsinθcosφy=rsinθsinφz=rcosθJ=∂x,y,z∂r,θ,ϕ=r2sinθdrdθdϕ The plane x=3 divide the hemisphere…

Q: Find the volume of the solid region which lies inside the sphere x2 + y² + z² = 4z and outside of…

A: This question is about application of integration

Q: The following questions refer to a coordinate graph with the variable X on the horizontal axis and…

A: If (x1,y1) and (x2,y2) be two points on a line , then the slope of that line is =y2-y1x2-x1.

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

A:

Q: Evaluate ∫W z dV, where W is the first-octant portion of the solid sphere of radius 2 centered at…

A:

Q: Solve for the y-component (in cm

A: Given, a=103.4cm, b=133.7  and   r=74.3cm

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

A: Given: ∇.u→v→=∇.u→v→+u→.∇v→

Q: Use spherical coordinates to find the volume of the top half of the sphere x? + y? + z? = 4 that…

A: Given that a sphere x2+y2+z2=4 and a cone is z2=x2+y2 We have to find the volume of the top of the…

Q: Find the volume of the solid region which lies inside the sphere x² + y? + z² = 4z and outside of…

A:

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: Find the volume of the solid that lies within both the cylinder x² + y² = 4 and the sphere x² + y² +…

A:

Q: Express the volume of the solid lying inside the sphere r2 + y? + 22 8 and outside the cylinder ? +…

A: Given:  Solid lying in a sphere x2+y2+z2=16 and outside the cylinder  x2+y2=2

Q: 2. Find the volume inside the sphere x² + y² + z² = 10², by using spherical coordinates.

A: equation of sphere

Q: Express the point (x, y, z) = (-2, 2, 2/2) in spherical coordinates.

A:

Q: 2. Convert the point (V6, , v2) from cylindrical to spherical coordinates. (e) (2VZ,품, 끌) (d) (vZ )…

A: The solution is given as

Q: _(2²² + y² + z²)³/²dzdydx 1-z²-yª

A: Given ∫-11∫01-x2∫1-x2-y20(x2+y2+z2)32dzdydx Given instruction: To solve this integral convert…

Q: find the spherical coordinate of that point has rectangular coordinates RADIA RAQIA UNIVERSITY (x,…

A: Given point in rectangular coordinates, (x, y, z)=(2, -2, 2)

Q: Please review the screenshot and provide a solution. Please make sure that the solution is formatted…

A: