Let B = xa,. Express B in %3D (a) cylindrical coordinates, (b) spherical coordinates.

Q: Find an equation for the paraboloid z = 3 – (x² + y) in cylindrical coordinates. (Type theta for 0…

A: The given equation of the paraboloid is: z=3-x2+y2 To find the equation of the paraboloid in…

Q: A hole is drilled through the center of a sphere x²+y² +z? = R,², leaving a ring-shape solid. If the…

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Q: Describe how the surface with spherical equation p²(1 + A cos² ¢) = 1 depends on the constant A.

A: Given : ρ2(1+Acos2ϕ)=1To describe: How the surface with spherical equation  ρ2(1+Acos2ϕ)=1depends on…

Q: What are the cylindrical coordinates of the point whose rectangular coordinates are (x = 4, y = 5, z…

A: A rectangular coordinate or cartesian coordinate system is a system that specifies the position of a…

Q: 2² dz dx dy By converting to spherical coordinates, evaluate

A: Given:  ∫02∫04-y2∫x2+y28-x2-y2z2dzdxdy we need to find following integeral by using spherical…

Q: Use spherical coordinates. Evaluate ∭z dV, where E is between the spheres x ^ 2 + y ^ 2 + z ^ 2 = 16…

A: Triple integral is used to integrate function of three variable in three dimensional region.

Q: Find the radius of curvature at 0 = t of the parametric equations x = 3(0 + cos 0), y = 3(1 – cos…

A: To find the radius of curvature, first find out dxdθ and d2xdθ2. x=3θ+cos θdxdθ=31-sin θd2xdθ2=-3cos…

Q: ) Find an equation for the plane y = 2 in cylindrical coordinates. (Type theta for 0 in your…

A: Given the equation in recatngualr co-ordinatesy=2

Q: Show that the cylindrical equationr 2(1 − 2 sin2 θ ) + z 2= 1is a hyperboloid of one sheet.

A: The cylindrical co-ordinates is converted into rectangular co-ordinate as x=rcosθ         ⋯⋯1y=rsinθ…

Q: Find and equatin for the parabolid z = x^2+y^2 in spherical coordinates

A: Given query is to find equation of paraboloid in spheo coordinates.

Q: Express x2y2+ z2 = 2z in cylindrical and spherical coordinates.

A: Given,

Q: Identify the surface whose equation in spherical coordinates is given by p= 2 cos o

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Q: Use spherical coordinates to find [[[, z2 dV.

A: In this question, we find the triple integral by using spherical coordinate with a sketch of solids

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

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Q: Use spherical coordinates to find phi. Z=3sqrt(x^+y^2)

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Q: Use spherical polar coordinates to evaluate LLEN V4-x2 x² + y2 + z² dz dy dx. -V4-x2

A: Solution is given below:

Q: (c) Evaluate zdz dy dr using spherical coordinates.

A: Triple integral is used to integrate the function of three variable over the three-dimensional…

Q: Find an equation in rectangular coordinates for the surface represented by the cylindrical equation…

A: Cylindrical co-ordinates of the point P are (r,θ,z) rectangular co-ordinates of the point P are…

Q: Verify that dV = p sin o dp de dy when using spherical coordinates. %3D

A: We have to represent a differential element.

Q: A hole is drilled through the center of a sphere x +y +z? = R,', leaving a ring-shape solid. If the…

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Q: Find an equation for the paraboloid z = 5 – (x2 + y2) in cylindrical coordinates. (Type theta for 0…

A: We have to find an equation for the paraboloid z=5-x2+y2 in cylindrical 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: Convert (r, θ , z) =(3, π/6 , 4)from cylindrical to spherical coordinates.

A: Given coordinate (r, θ , z) =(3, π/6 , 4)

Q: Exercise 2 Use spherical coordinates to evaluate [[[(9-x - y³) dV , where E is the solid hemisphere…

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Q: Find an equation in rectangular coordinates for the surface represented by the cylindrical equation…

A: To find an equation in rectangular coordinates for the surface represented by the cylindrical…

Q: Let N be the lower hemisphere of the sphere of radius 5 and let H • Construct dS for 2. Try using…

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Q: A hole is drilled through the center of a sphere x?+y² + z² = R,?, leaving a ring-shape solid. If…

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Q: Convert the point (x, y, z) = (4, 4, 3) to cylindrical coordinates. Give answers either as…

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Q: 5. Use spherical coordinates to evaluate r2+ y2 +22 dz dy dr. 16-

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Q: 2. By changing to cylindrical coordinate, evaluate So 1-x²1542x² dzdydx

A: Introduction: Sometimes, a triple integral given in the rectangular coordinate system is very…

Q: Verify that dV = p² sin y dp de dp when using spherical coordinates. %3D

A: You have posted multiple questions. As per the instruction, we will be answering only the first…

Q: c. Based on the orientation of your rectangle would we integrate with respect to x or y? С.

A: Follow the procedure given below.

Q: Translate the spherical equation below into a cylindrical equation! tan2(Φ) = 1

A: We have to find the transformation

Q: x2-y는 군.Give the spherical coordingtes.

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Q: 48. Use spherical coordinates to evaluate y'Vx +y +z dz dx dy

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Q: 它们也称 Use spherical coordinate to evaluate Vr² + y² + z² dz dy dx. 0,

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Q: Convert the point (x, y, z) = ( – 1, – 4, 3) to cylindrical coordinates. Give answers either as…

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Q: Use Spherical coordinates to evaluate Cx*+ ya+22)² dV where Bis the B. ball with anter at the ongin…

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Q: The r in cylindrical coordinates must be positive or zero. O True O False

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Q: 5. Convert the integral 9-x2 9-x²-y² Vx? + y? + z² dzdydx to spherical coordinates then evaluate.

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Q: (b) Use spherical coordinates to evaluate l y²dV_where E is the solid hemisphere a? +y² + z² 0. E

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Q: Find the area of the surface obtained by rotating the curve of parametric equations T = 2 cos 0, y =…

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Q: Evaluate | xz dz dy dx by changing to spherical coordinates.

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Q: F in circular cylindrical coordinates.

A: Hello. Since your question has multiple parts, we will solve first question for you. If you want…

Q: 5. Use spherical coordinates to evaluate LIVE √√= ²+ y² + 2² dz dy dr.

A: Given ∫-44∫-16-x216-x2∫x2+y24x2+y2+z2 dzdydx

Q: Describe the given set of rectangular coordinates in cylindrical coordinat x2 + y? y

A: Concept:

Q: Convert from rectangular to cylindrical coordinates. (v3, 3, 3) (r, 0, z) = ( ||

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Q: ) Evaluate x²dzdydx by switching to cylindrical coordinates.

A: To solve this problem we use her Cylindrical Coordinate .  x=r cos(theta)  y= r sin(theta) z=z