Describe the regions whose equations in cylindrical or spherical coordinates are given below—either in words, or by drawing a picture, as you prefer.(a) The region satisfying the cylindrical conditions r + z ≤ 1 and z ≥ 0.(b) The region satisfying the spherical conditions 0 ≤ ρ ≤ 1, 0 ≤ θ ≤ π, and 0 ≤ ϕ ≤ π.(c) The region satisfying the cylindrical conditions r ≤ 1 and π/4 ≤ θ ≤ 3π/4(d) The region satisfying the spherical conditions ρ = 1/cos ϕ and 0 ≤ ϕ < π/2 Describe the regions whose equations in cylindrical or spherical coordinates are given below-either in words, or by drawing a picture, as you prefer.(a) The region satisfying the cylindrical conditions r+z≤1 and z > 0.(b) The region satisfying the spherical conditions 0 ≤ p ≤ 1, 0 ≤ 0 ≤ π, and 0 ≤ ≤π.(c) The region satisfying the cylindrical conditions r ≤ 1 and ¼ ≤ 0 ≤ ³.(d) The region satisfying the spherical conditions p = and 0<<.cos

In the cylindrical coordinate system, we use three coordinates (r, θ, z) where r is the radial…

Answered: Describe the regions whose equations in…

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter11: Topics From Analytic Geometry

Section11.3: Hyperbolas

Problem 24E

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Question

Describe the regions whose equations in cylindrical or spherical coordinates are given below—
either in words, or by drawing a picture, as you prefer.
(a) The region satisfying the cylindrical conditions r + z ≤ 1 and z ≥ 0.
(b) The region satisfying the spherical conditions 0 ≤ ρ ≤ 1, 0 ≤ θ ≤ π, and 0 ≤ ϕ ≤ π.
(c) The region satisfying the cylindrical conditions r ≤ 1 and π/4 ≤ θ ≤ 3π/4

(d) The region satisfying the spherical conditions ρ = 1/cos ϕ and 0 ≤ ϕ < π/2