Explanation Given: The quadric surface consisting the two cones ϕ = π 4 and ϕ = 3 π 4 Key concepts applied: In a spherical coordinate system , a point P in space is represented by an ordered triple ( ρ , θ , ϕ ) . ρ is the distance between P and the origin, ρ ≥ 0 . θ is the same angle used in cylindrical coordinates for r ≥ 0 . ϕ is the angle between the positive z − axis and the line segment O P → , 0 ≤ ϕ ≤ π . Note that the first and the third coordinates ρ and ϕ are non-negative. To convert from rectangular to spherical coordinates (or vice versa), use the conversion guidelines as shown below, To convert a point, Spherical to rectangular x = ρ sin ϕ cos θ y = ρ sin ϕ sin θ z = ρ cos ϕ Rectangular to spherical ρ 2 = x 2 + y 2 + z 2 tan θ = y x ϕ = arccos ( z x 2 + y 2 + z 2 ) To convert a set, use any of the above-mentioned equations as necessary. Calculation: Description ϕ = π 4 and ϕ = 3 π 4 Step 1...

4th Edition

ISBN: 9781319279813

Author: Rogawski

Publisher: MAC HIGHER

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Question

System that uses coordinates to uniquely determine the position of points. The most common coordinate system is the Cartesian system, where points are given by distance along a horizontal x-axis and vertical y-axis from the origin. A polar coordinate system locates a point by its direction relative to a reference direction and its distance from a given point. In three dimensions, it leads to cylindrical and spherical coordinates.

Chapter 12.7, Problem 78E

To determine

The equation of the quadric surface consisting the given two cones in rectangular coordinates

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Chapter 12.7, Problem 77E

Chapter 12.7, Problem 79E

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Chapter 12 Solutions

CALCULUS:EARLY TRANS.-SAPLINGPLUS

Ch. 12.1 - Prob. 1PQ Ch. 12.1 - Prob. 2PQ Ch. 12.1 - Prob. 3PQ Ch. 12.1 - Prob. 4PQ Ch. 12.1 - Prob. 5PQ Ch. 12.1 - Prob. 6PQ Ch. 12.1 - Prob. 1E Ch. 12.1 - Prob. 2E Ch. 12.1 - Prob. 3E Ch. 12.1 - Prob. 4E

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