To find the average value of a function f(x, y, z) on a solid region E, we have the formula 1 avg(f) /// f(x, y, z) dV volume(E) E (a) Find a function f(x, y, z) which gives the distance from a point (x, y, z) to the origin (0,0,0). (b) Suppose E is a solid ball of radius 2 centered at the origin. Use the formula above to find the average value of f (from part (a)) on the E. Hint: the volume of a sphere of radius r is V = (c) Is the average distance from a point in E to the origin more or less than half the radius of E?

To find the average value of a function f(x, y, z) on a solid region E, we have the formula 1 avg(f) /// f(x, y, z) dV volume(E) E (a) Find a function f(x, y, z) which gives the distance from a point (x, y, z) to the origin (0,0,0). (b) Suppose E is a solid ball of radius 2 centered at the origin. Use the formula above to find the average value of f (from part (a)) on the E. Hint: the volume of a sphere of radius r is V = (c) Is the average distance from a point in E to the origin more or less than half the radius of E?

Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)

6th Edition

ISBN:9781337111348

Author:Bruce Crauder, Benny Evans, Alan Noell

Publisher:Bruce Crauder, Benny Evans, Alan Noell

ChapterA: Appendix

SectionA.2: Geometric Constructions

Problem 10P: A soda can has a volume of 25 cubic inches. Let x denote its radius and h its height, both in...

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