Let a and c be fixed positive numbers. Consider the two surfaces z = c2 — (-2)² (x² + y²) and : S₂ z = x² + y² ~ in R³. Let V be the solid body bounded by the two surfaces, i.e., the finite region above S2 and below S₁ in R³. The boundary surface S of V is the union of S₁ S₂ = S₂ns (where S₁ns is the part of S belonging to S₁ for i = 1,2). S2 1. Calculate the volume of V. 2. Calculate the outward pointing unit normal vectors for S₁ and for S2. 3. Calculate the outward flux cross S of the vector field F = = S: Ո S and У X -i + −j + a a 22 22 k. ☑

Let a and c be fixed positive numbers. Consider the two surfaces z = c2 — (-2)² (x² + y²) and : S₂ z = x² + y² ~ in R³. Let V be the solid body bounded by the two surfaces, i.e., the finite region above S2 and below S₁ in R³. The boundary surface S of V is the union of S₁ S₂ = S₂ns (where S₁ns is the part of S belonging to S₁ for i = 1,2). S2 1. Calculate the volume of V. 2. Calculate the outward pointing unit normal vectors for S₁ and for S2. 3. Calculate the outward flux cross S of the vector field F = = S: Ո S and У X -i + −j + a a 22 22 k. ☑

Elementary Geometry For College Students, 7e

7th Edition

ISBN:9781337614085

Author:Alexander, Daniel C.; Koeberlein, Geralyn M.

Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.

Chapter10: Analytic Geometry

Section10.6: The Three-dimensional Coordinate System

Problem 41E: Does the sphere x2+y2+z2=100 have symmetry with respect to the a x-axis? b xy-plane?

See similar textbooks