Question

Change from rectangular to spherical coordinates. (Let ρ ≥ 0, 0 ≤ θ ≤ 2π, and 0 ≤ ϕ ≤ π.)

(a) (0, −3, 0):

(ρ, θ, ϕ) = (3, −π 2 , π 2) <---- (WRONG!!!!)

(b) (−1, 1, − 2 ):

(ρ, θ, ϕ) = (2, − π 4 , π 4) <------ (WRONG!!!!)

Answer #1

Change from rectangular to spherical coordinates. (Let ρ ≥ 0, 0
≤ θ ≤ 2π, and 0 ≤ ϕ ≤ π.) (a) (0, −3, 0) (b) (−1, 1, − sqrt 2 )

Evaluate, in spherical coordinates, the triple integral of
f(ρ,θ,ϕ)=cosϕ, over the region 0≤θ≤2π, π/6≤ϕ≤π/2, 3≤ρ≤8.
integral =

Change from rectangular to cylindrical coordinates. (Let
r ≥ 0 and 0 ≤ θ ≤ 2π.)
(a) (3, −3, 5)
b) (-3,-3sqrt3,2)

Change from rectangular to cylindrical coordinates. (Let
r ≥ 0 and 0 ≤ θ ≤ 2π.)
(a) (-3,3,3)
(b) (-5,5sqrt(3),5)

Change from rectangular to cylindrical coordinates. (Let
r ≥ 0 and 0 ≤ θ ≤ 2π.)
(a) (-3,3,3)
(b) (-5,5sqrt(3),5)

Change from rectangular to cylindrical coordinates. (Let
r ≥ 0 and 0 ≤ θ ≤ 2π.)
(a)
(−8, 8, 8)
3
(b) (−3, 3, 5)

Change from rectangular to cylindrical coordinates. (Let
r ≥ 0 and 0 ≤ θ ≤ 2π.)
(a).
(−9, 9, 9)
(b).
(-5,5sqrt(3), 9)

Find the rectangular coordinates of the point whose spherical
coordinates are given. (a) (1, 0, 0) (x, y, z) = (b) (14, π/3, π/4)
(x, y, z) =

Use spherical coordinates.
Evaluate
xyz
dV
E
,
where E lies between the spheres ρ = 2 and
ρ = 5 and above the cone ϕ = π/3.

Plot the point whose spherical coordinates are given. Then find
the rectangular coordinates of the point.
(a)
(3, π/3, π/6)
(b)
(6, π/2, 3π/4)

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