Problem 20 For the volume of a hemisphere defined by verify the divergence theorem for the vector in spherical coordinates. x² + y² +2³ ≤ 9, Ē (x, y, z)= y + xy + (2x - 1)2,

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: 1) Use spherical coordinates to evaluate 4-x² -y² 4-x2-y2 4-y² LaSNa- y²/x² + y² + z² dzdxdy

A: The given problem is to evaluate the given triple integral using spherical coordinates, We have to…

Q: Find a parametrization and the equation associated with the cylindrical surface whose directrix and…

A: Use the director vector and then substitute y=0 to find the value of x and z . Then substitute the…

Q: (x, y, :) (p, 0, ) p² sin(o [Practice] Demonstrate the fact that the Jacobian when we convert from…

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Q: Consider the point whose Cartesian coordinates are (-1, –1,1) What are its cylindrical coordinates?…

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Q: Consider the point whose Cartesian coordinates are (-1, —1, 1). What are its cylindrical…

A: The objective of this question is to convert the given Cartesian coordinates into cylindrical…

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: Suppose that a point P has, respectively, spherical coordinates, rectangular coordinates, and…

A: The coordinates of point P is given as , Rectangular coordinates = x,y,z Spherical coordinates =…

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

A: Given: ∇.u→v→=∇.u→v→+u→.∇v→

Q: 6) Use Stokes' Theorem and Theorem 10 in section 16.7 to find § F · dř. F(x, y, z) = (2y, xz, x + y…

A: .C is oriented counterclockwise, and it is the intersection of the plane  and the cylinder .To Find:…

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: Convert the point (x, y, z) = (2,2v3, 4) to spherical %3D coordinates (p, 0, 4).

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Q: Find a parametrization and the equation associated with the cylindrical surface whose directrix and…

A: answer is in step 2

Q: The point (x, y, z) = (-1, –1, –1) under rectangular coordinates in R³ can be described through…

A: Let's find.

Q: #5. Find the rectangular coordinates of the point (3,57/4, 7/6) given in spherical coordi- nates.

A: We have given a spherical coordinates:…

Q: cimals to at least one decimal place,

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Q: V = M2x2 (R) let M = { A€ V A = A²} N = { A = V A = -A ² } Subset of the vector space V V = MON…

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Q: Convert the point (x, y, z) = (5, -1, 5) to cylindrical coordinates. Give answers either as…

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Q: Valero's 5k Fun Run was held yesterday in the downtown district. The top runner 4 runners (one of…

A: Given 1. Ralph finished 1 minute after the competitor in the white shirt. 2. The competitor in the…

Q: ff curl(x²yi - rzk). n do over the closed surface of the ellipsoid 4 16 Warning: Stokes' theorem…

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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)