Calculus
7th Edition
ISBN: 9781524916817
Author: SMITH KARL J, STRAUSS MONTY J, TODA MAGDALENA DANIELE
Publisher: Kendall Hunt Publishing
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Question
Chapter 3.7, Problem 60PS
(a)
To determine
To find:The angle
(b)
To determine
To find:The value of
(c)
To determine
To find:The rate of change in the angle.
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Chapter 3 Solutions
Calculus
Ch. 3.1 - Prob. 1PSCh. 3.1 - Prob. 2PSCh. 3.1 - Prob. 3PSCh. 3.1 - Prob. 4PSCh. 3.1 - Prob. 5PSCh. 3.1 - Prob. 6PSCh. 3.1 - Prob. 7PSCh. 3.1 - Prob. 8PSCh. 3.1 - Prob. 9PSCh. 3.1 - Prob. 10PS
Ch. 3.1 - Prob. 11PSCh. 3.1 - Prob. 12PSCh. 3.1 - Prob. 13PSCh. 3.1 - Prob. 14PSCh. 3.1 - Prob. 15PSCh. 3.1 - Prob. 16PSCh. 3.1 - Prob. 17PSCh. 3.1 - Prob. 18PSCh. 3.1 - Prob. 19PSCh. 3.1 - Prob. 20PSCh. 3.1 - Prob. 21PSCh. 3.1 - Prob. 22PSCh. 3.1 - Prob. 23PSCh. 3.1 - Prob. 24PSCh. 3.1 - Prob. 25PSCh. 3.1 - Prob. 26PSCh. 3.1 - Prob. 27PSCh. 3.1 - Prob. 28PSCh. 3.1 - Prob. 29PSCh. 3.1 - Prob. 30PSCh. 3.1 - Prob. 31PSCh. 3.1 - Prob. 32PSCh. 3.1 - Prob. 33PSCh. 3.1 - Prob. 34PSCh. 3.1 - Prob. 35PSCh. 3.1 - Prob. 36PSCh. 3.1 - Prob. 37PSCh. 3.1 - Prob. 38PSCh. 3.1 - Prob. 39PSCh. 3.1 - Prob. 40PSCh. 3.1 - Prob. 41PSCh. 3.1 - Prob. 42PSCh. 3.1 - Prob. 43PSCh. 3.1 - Prob. 44PSCh. 3.1 - Prob. 45PSCh. 3.1 - Prob. 46PSCh. 3.1 - Prob. 47PSCh. 3.1 - Prob. 48PSCh. 3.1 - Prob. 49PSCh. 3.1 - Prob. 50PSCh. 3.1 - Prob. 51PSCh. 3.1 - Prob. 52PSCh. 3.1 - Prob. 53PSCh. 3.1 - Prob. 54PSCh. 3.1 - Prob. 55PSCh. 3.1 - Prob. 56PSCh. 3.1 - Prob. 57PSCh. 3.1 - Prob. 58PSCh. 3.1 - Prob. 59PSCh. 3.1 - Prob. 60PSCh. 3.2 - Prob. 1PSCh. 3.2 - Prob. 2PSCh. 3.2 - Prob. 3PSCh. 3.2 - Prob. 4PSCh. 3.2 - Prob. 5PSCh. 3.2 - Prob. 6PSCh. 3.2 - Prob. 7PSCh. 3.2 - Prob. 8PSCh. 3.2 - Prob. 9PSCh. 3.2 - Prob. 10PSCh. 3.2 - Prob. 11PSCh. 3.2 - Prob. 12PSCh. 3.2 - Prob. 13PSCh. 3.2 - Prob. 14PSCh. 3.2 - Prob. 15PSCh. 3.2 - Prob. 16PSCh. 3.2 - Prob. 17PSCh. 3.2 - Prob. 18PSCh. 3.2 - Prob. 19PSCh. 3.2 - Prob. 20PSCh. 3.2 - Prob. 21PSCh. 3.2 - Prob. 22PSCh. 3.2 - Prob. 23PSCh. 3.2 - Prob. 24PSCh. 3.2 - Prob. 25PSCh. 3.2 - Prob. 26PSCh. 3.2 - Prob. 27PSCh. 3.2 - Prob. 28PSCh. 3.2 - Prob. 29PSCh. 3.2 - Prob. 30PSCh. 3.2 - Prob. 31PSCh. 3.2 - Prob. 32PSCh. 3.2 - Prob. 33PSCh. 3.2 - Prob. 34PSCh. 3.2 - Prob. 35PSCh. 3.2 - Prob. 36PSCh. 3.2 - Prob. 37PSCh. 3.2 - Prob. 38PSCh. 3.2 - Prob. 39PSCh. 3.2 - Prob. 40PSCh. 3.2 - Prob. 41PSCh. 3.2 - Prob. 42PSCh. 3.2 - Prob. 43PSCh. 3.2 - Prob. 44PSCh. 3.2 - Prob. 45PSCh. 3.2 - Prob. 46PSCh. 3.2 - Prob. 47PSCh. 3.2 - Prob. 48PSCh. 3.2 - Prob. 49PSCh. 3.2 - Prob. 50PSCh. 3.2 - Prob. 51PSCh. 3.2 - Prob. 52PSCh. 3.2 - Prob. 53PSCh. 3.2 - Prob. 54PSCh. 3.2 - Prob. 55PSCh. 3.2 - Prob. 56PSCh. 3.2 - Prob. 57PSCh. 3.2 - Prob. 58PSCh. 3.2 - Prob. 59PSCh. 3.2 - Prob. 60PSCh. 3.3 - Prob. 1PSCh. 3.3 - Prob. 2PSCh. 3.3 - Prob. 3PSCh. 3.3 - Prob. 4PSCh. 3.3 - Prob. 5PSCh. 3.3 - Prob. 6PSCh. 3.3 - Prob. 7PSCh. 3.3 - Prob. 8PSCh. 3.3 - Prob. 9PSCh. 3.3 - Prob. 10PSCh. 3.3 - Prob. 11PSCh. 3.3 - Prob. 12PSCh. 3.3 - Prob. 13PSCh. 3.3 - Prob. 14PSCh. 3.3 - Prob. 15PSCh. 3.3 - Prob. 16PSCh. 3.3 - Prob. 17PSCh. 3.3 - Prob. 18PSCh. 3.3 - Prob. 19PSCh. 3.3 - Prob. 20PSCh. 3.3 - Prob. 21PSCh. 3.3 - Prob. 22PSCh. 3.3 - Prob. 23PSCh. 3.3 - Prob. 24PSCh. 3.3 - Prob. 25PSCh. 3.3 - Prob. 26PSCh. 3.3 - Prob. 27PSCh. 3.3 - Prob. 28PSCh. 3.3 - Prob. 29PSCh. 3.3 - Prob. 30PSCh. 3.3 - Prob. 31PSCh. 3.3 - Prob. 32PSCh. 3.3 - Prob. 33PSCh. 3.3 - Prob. 34PSCh. 3.3 - Prob. 35PSCh. 3.3 - Prob. 36PSCh. 3.3 - Prob. 37PSCh. 3.3 - Prob. 38PSCh. 3.3 - Prob. 39PSCh. 3.3 - Prob. 40PSCh. 3.3 - Prob. 41PSCh. 3.3 - Prob. 42PSCh. 3.3 - Prob. 43PSCh. 3.3 - Prob. 44PSCh. 3.3 - Prob. 45PSCh. 3.3 - Prob. 46PSCh. 3.3 - Prob. 47PSCh. 3.3 - Prob. 48PSCh. 3.3 - Prob. 49PSCh. 3.3 - Prob. 50PSCh. 3.3 - Prob. 51PSCh. 3.3 - Prob. 52PSCh. 3.3 - Prob. 53PSCh. 3.3 - Prob. 54PSCh. 3.3 - Prob. 55PSCh. 3.3 - Prob. 56PSCh. 3.3 - Prob. 57PSCh. 3.3 - Prob. 58PSCh. 3.3 - Prob. 59PSCh. 3.3 - Prob. 60PSCh. 3.4 - Prob. 1PSCh. 3.4 - Prob. 2PSCh. 3.4 - Prob. 3PSCh. 3.4 - Prob. 4PSCh. 3.4 - Prob. 5PSCh. 3.4 - Prob. 6PSCh. 3.4 - Prob. 7PSCh. 3.4 - Prob. 8PSCh. 3.4 - Prob. 9PSCh. 3.4 - Prob. 10PSCh. 3.4 - Prob. 11PSCh. 3.4 - Prob. 12PSCh. 3.4 - Prob. 13PSCh. 3.4 - Prob. 14PSCh. 3.4 - Prob. 15PSCh. 3.4 - Prob. 16PSCh. 3.4 - Prob. 17PSCh. 3.4 - Prob. 18PSCh. 3.4 - Prob. 19PSCh. 3.4 - Prob. 20PSCh. 3.4 - Prob. 21PSCh. 3.4 - Prob. 22PSCh. 3.4 - Prob. 23PSCh. 3.4 - Prob. 24PSCh. 3.4 - Prob. 25PSCh. 3.4 - Prob. 26PSCh. 3.4 - Prob. 27PSCh. 3.4 - Prob. 28PSCh. 3.4 - Prob. 29PSCh. 3.4 - Prob. 30PSCh. 3.4 - Prob. 31PSCh. 3.4 - Prob. 32PSCh. 3.4 - Prob. 33PSCh. 3.4 - Prob. 34PSCh. 3.4 - Prob. 35PSCh. 3.4 - Prob. 36PSCh. 3.4 - Prob. 37PSCh. 3.4 - Prob. 38PSCh. 3.4 - Prob. 39PSCh. 3.4 - Prob. 40PSCh. 3.4 - Prob. 41PSCh. 3.4 - Prob. 42PSCh. 3.4 - Prob. 43PSCh. 3.4 - Prob. 44PSCh. 3.4 - Prob. 45PSCh. 3.4 - Prob. 46PSCh. 3.4 - Prob. 47PSCh. 3.4 - Prob. 48PSCh. 3.4 - Prob. 49PSCh. 3.4 - Prob. 50PSCh. 3.4 - Prob. 51PSCh. 3.4 - Prob. 52PSCh. 3.4 - Prob. 53PSCh. 3.4 - Prob. 54PSCh. 3.4 - Prob. 55PSCh. 3.4 - Prob. 56PSCh. 3.4 - Prob. 57PSCh. 3.4 - Prob. 58PSCh. 3.4 - Prob. 59PSCh. 3.4 - Prob. 60PSCh. 3.5 - Prob. 1PSCh. 3.5 - Prob. 2PSCh. 3.5 - Prob. 3PSCh. 3.5 - Prob. 4PSCh. 3.5 - Prob. 5PSCh. 3.5 - Prob. 6PSCh. 3.5 - Prob. 7PSCh. 3.5 - Prob. 8PSCh. 3.5 - Prob. 9PSCh. 3.5 - Prob. 10PSCh. 3.5 - Prob. 11PSCh. 3.5 - Prob. 12PSCh. 3.5 - Prob. 13PSCh. 3.5 - Prob. 14PSCh. 3.5 - Prob. 15PSCh. 3.5 - Prob. 16PSCh. 3.5 - Prob. 17PSCh. 3.5 - Prob. 18PSCh. 3.5 - Prob. 19PSCh. 3.5 - Prob. 20PSCh. 3.5 - Prob. 21PSCh. 3.5 - Prob. 22PSCh. 3.5 - Prob. 23PSCh. 3.5 - Prob. 24PSCh. 3.5 - Prob. 25PSCh. 3.5 - Prob. 26PSCh. 3.5 - Prob. 27PSCh. 3.5 - Prob. 28PSCh. 3.5 - Prob. 29PSCh. 3.5 - Prob. 30PSCh. 3.5 - Prob. 31PSCh. 3.5 - Prob. 32PSCh. 3.5 - Prob. 33PSCh. 3.5 - Prob. 34PSCh. 3.5 - Prob. 35PSCh. 3.5 - Prob. 36PSCh. 3.5 - Prob. 37PSCh. 3.5 - Prob. 38PSCh. 3.5 - Prob. 39PSCh. 3.5 - Prob. 40PSCh. 3.5 - Prob. 41PSCh. 3.5 - Prob. 42PSCh. 3.5 - Prob. 43PSCh. 3.5 - Prob. 44PSCh. 3.5 - Prob. 45PSCh. 3.5 - Prob. 46PSCh. 3.5 - Prob. 47PSCh. 3.5 - Prob. 48PSCh. 3.5 - Prob. 49PSCh. 3.5 - Prob. 50PSCh. 3.5 - Prob. 51PSCh. 3.5 - Prob. 52PSCh. 3.5 - Prob. 53PSCh. 3.5 - Prob. 54PSCh. 3.5 - Prob. 55PSCh. 3.5 - Prob. 56PSCh. 3.5 - Prob. 57PSCh. 3.5 - Prob. 58PSCh. 3.5 - Prob. 59PSCh. 3.5 - Prob. 60PSCh. 3.6 - Prob. 1PSCh. 3.6 - Prob. 2PSCh. 3.6 - Prob. 3PSCh. 3.6 - Prob. 4PSCh. 3.6 - Prob. 5PSCh. 3.6 - Prob. 6PSCh. 3.6 - Prob. 7PSCh. 3.6 - Prob. 8PSCh. 3.6 - Prob. 9PSCh. 3.6 - Prob. 10PSCh. 3.6 - Prob. 11PSCh. 3.6 - Prob. 12PSCh. 3.6 - Prob. 13PSCh. 3.6 - Prob. 14PSCh. 3.6 - Prob. 15PSCh. 3.6 - Prob. 16PSCh. 3.6 - Prob. 17PSCh. 3.6 - Prob. 18PSCh. 3.6 - Prob. 19PSCh. 3.6 - Prob. 20PSCh. 3.6 - Prob. 21PSCh. 3.6 - Prob. 22PSCh. 3.6 - Prob. 23PSCh. 3.6 - Prob. 24PSCh. 3.6 - Prob. 25PSCh. 3.6 - Prob. 26PSCh. 3.6 - Prob. 27PSCh. 3.6 - Prob. 28PSCh. 3.6 - Prob. 29PSCh. 3.6 - Prob. 30PSCh. 3.6 - Prob. 31PSCh. 3.6 - Prob. 32PSCh. 3.6 - Prob. 33PSCh. 3.6 - Prob. 34PSCh. 3.6 - Prob. 35PSCh. 3.6 - Prob. 36PSCh. 3.6 - Prob. 37PSCh. 3.6 - Prob. 38PSCh. 3.6 - Prob. 39PSCh. 3.6 - Prob. 40PSCh. 3.6 - Prob. 41PSCh. 3.6 - Prob. 42PSCh. 3.6 - Prob. 43PSCh. 3.6 - Prob. 44PSCh. 3.6 - Prob. 45PSCh. 3.6 - Prob. 46PSCh. 3.6 - Prob. 47PSCh. 3.6 - Prob. 48PSCh. 3.6 - Prob. 49PSCh. 3.6 - Prob. 50PSCh. 3.6 - Prob. 51PSCh. 3.6 - Prob. 52PSCh. 3.6 - Prob. 53PSCh. 3.6 - Prob. 54PSCh. 3.6 - Prob. 55PSCh. 3.6 - Prob. 56PSCh. 3.6 - Prob. 57PSCh. 3.6 - Prob. 58PSCh. 3.6 - Prob. 59PSCh. 3.6 - Prob. 60PSCh. 3.7 - Prob. 1PSCh. 3.7 - Prob. 2PSCh. 3.7 - Prob. 3PSCh. 3.7 - Prob. 4PSCh. 3.7 - Prob. 5PSCh. 3.7 - Prob. 6PSCh. 3.7 - Prob. 7PSCh. 3.7 - Prob. 8PSCh. 3.7 - Prob. 9PSCh. 3.7 - Prob. 10PSCh. 3.7 - Prob. 11PSCh. 3.7 - Prob. 12PSCh. 3.7 - Prob. 13PSCh. 3.7 - Prob. 14PSCh. 3.7 - Prob. 15PSCh. 3.7 - Prob. 16PSCh. 3.7 - Prob. 17PSCh. 3.7 - Prob. 18PSCh. 3.7 - Prob. 19PSCh. 3.7 - Prob. 20PSCh. 3.7 - Prob. 21PSCh. 3.7 - Prob. 22PSCh. 3.7 - Prob. 23PSCh. 3.7 - Prob. 24PSCh. 3.7 - Prob. 25PSCh. 3.7 - Prob. 26PSCh. 3.7 - Prob. 27PSCh. 3.7 - Prob. 28PSCh. 3.7 - Prob. 29PSCh. 3.7 - Prob. 30PSCh. 3.7 - Prob. 31PSCh. 3.7 - Prob. 32PSCh. 3.7 - Prob. 33PSCh. 3.7 - Prob. 34PSCh. 3.7 - Prob. 35PSCh. 3.7 - Prob. 36PSCh. 3.7 - Prob. 37PSCh. 3.7 - Prob. 38PSCh. 3.7 - Prob. 39PSCh. 3.7 - Prob. 40PSCh. 3.7 - Prob. 41PSCh. 3.7 - Prob. 42PSCh. 3.7 - Prob. 43PSCh. 3.7 - Prob. 44PSCh. 3.7 - Prob. 45PSCh. 3.7 - Prob. 46PSCh. 3.7 - Prob. 47PSCh. 3.7 - Prob. 48PSCh. 3.7 - Prob. 49PSCh. 3.7 - Prob. 50PSCh. 3.7 - Prob. 51PSCh. 3.7 - Prob. 52PSCh. 3.7 - Prob. 53PSCh. 3.7 - Prob. 54PSCh. 3.7 - Prob. 55PSCh. 3.7 - Prob. 56PSCh. 3.7 - Prob. 57PSCh. 3.7 - Prob. 58PSCh. 3.7 - Prob. 59PSCh. 3.7 - Prob. 60PSCh. 3.8 - Prob. 1PSCh. 3.8 - Prob. 2PSCh. 3.8 - Prob. 3PSCh. 3.8 - Prob. 4PSCh. 3.8 - Prob. 5PSCh. 3.8 - Prob. 6PSCh. 3.8 - Prob. 7PSCh. 3.8 - Prob. 8PSCh. 3.8 - Prob. 9PSCh. 3.8 - Prob. 10PSCh. 3.8 - Prob. 11PSCh. 3.8 - Prob. 12PSCh. 3.8 - Prob. 13PSCh. 3.8 - Prob. 14PSCh. 3.8 - Prob. 15PSCh. 3.8 - Prob. 16PSCh. 3.8 - Prob. 17PSCh. 3.8 - Prob. 18PSCh. 3.8 - Prob. 19PSCh. 3.8 - Prob. 20PSCh. 3.8 - Prob. 21PSCh. 3.8 - Prob. 22PSCh. 3.8 - Prob. 23PSCh. 3.8 - Prob. 24PSCh. 3.8 - Prob. 25PSCh. 3.8 - Prob. 26PSCh. 3.8 - Prob. 27PSCh. 3.8 - Prob. 28PSCh. 3.8 - Prob. 29PSCh. 3.8 - Prob. 30PSCh. 3.8 - Prob. 31PSCh. 3.8 - Prob. 32PSCh. 3.8 - Prob. 33PSCh. 3.8 - Prob. 34PSCh. 3.8 - Prob. 35PSCh. 3.8 - Prob. 36PSCh. 3.8 - Prob. 37PSCh. 3.8 - Prob. 38PSCh. 3.8 - Prob. 39PSCh. 3.8 - Prob. 40PSCh. 3.8 - Prob. 41PSCh. 3.8 - Prob. 42PSCh. 3.8 - Prob. 43PSCh. 3.8 - Prob. 44PSCh. 3.8 - Prob. 45PSCh. 3.8 - Prob. 46PSCh. 3.8 - Prob. 47PSCh. 3.8 - Prob. 48PSCh. 3.8 - Prob. 49PSCh. 3.8 - Prob. 50PSCh. 3.8 - Prob. 51PSCh. 3.8 - Prob. 52PSCh. 3.8 - Prob. 53PSCh. 3.8 - Prob. 55PSCh. 3.8 - Prob. 56PSCh. 3.8 - Prob. 57PSCh. 3.8 - Prob. 58PSCh. 3.8 - Prob. 59PSCh. 3.8 - Prob. 60PSCh. 3 - Prob. 1PECh. 3 - Prob. 2PECh. 3 - Prob. 3PECh. 3 - Prob. 4PECh. 3 - Prob. 5PECh. 3 - Prob. 6PECh. 3 - Prob. 7PECh. 3 - Prob. 8PECh. 3 - Prob. 9PECh. 3 - Prob. 10PECh. 3 - Prob. 11PECh. 3 - Prob. 12PECh. 3 - Prob. 13PECh. 3 - Prob. 14PECh. 3 - Prob. 15PECh. 3 - Prob. 16PECh. 3 - Prob. 17PECh. 3 - Prob. 18PECh. 3 - Prob. 19PECh. 3 - Prob. 20PECh. 3 - Prob. 21PECh. 3 - Prob. 22PECh. 3 - Prob. 23PECh. 3 - Prob. 24PECh. 3 - Prob. 25PECh. 3 - Prob. 26PECh. 3 - Prob. 27PECh. 3 - Prob. 28PECh. 3 - Prob. 29PECh. 3 - Prob. 30PECh. 3 - Prob. 1SPCh. 3 - Prob. 2SPCh. 3 - Prob. 3SPCh. 3 - Prob. 4SPCh. 3 - Prob. 5SPCh. 3 - Prob. 6SPCh. 3 - Prob. 7SPCh. 3 - Prob. 8SPCh. 3 - Prob. 9SPCh. 3 - Prob. 10SPCh. 3 - Prob. 11SPCh. 3 - Prob. 12SPCh. 3 - Prob. 13SPCh. 3 - Prob. 14SPCh. 3 - Prob. 15SPCh. 3 - Prob. 16SPCh. 3 - Prob. 17SPCh. 3 - Prob. 18SPCh. 3 - Prob. 19SPCh. 3 - Prob. 20SPCh. 3 - Prob. 21SPCh. 3 - Prob. 22SPCh. 3 - Prob. 23SPCh. 3 - Prob. 24SPCh. 3 - Prob. 25SPCh. 3 - Prob. 26SPCh. 3 - Prob. 27SPCh. 3 - Prob. 28SPCh. 3 - Prob. 29SPCh. 3 - Prob. 30SPCh. 3 - Prob. 31SPCh. 3 - Prob. 32SPCh. 3 - Prob. 33SPCh. 3 - Prob. 34SPCh. 3 - Prob. 35SPCh. 3 - Prob. 36SPCh. 3 - Prob. 37SPCh. 3 - Prob. 38SPCh. 3 - Prob. 39SPCh. 3 - Prob. 40SPCh. 3 - Prob. 41SPCh. 3 - Prob. 42SPCh. 3 - Prob. 43SPCh. 3 - Prob. 44SPCh. 3 - Prob. 45SPCh. 3 - Prob. 46SPCh. 3 - Prob. 47SPCh. 3 - Prob. 48SPCh. 3 - Prob. 49SPCh. 3 - Prob. 50SPCh. 3 - Prob. 51SPCh. 3 - Prob. 52SPCh. 3 - Prob. 53SPCh. 3 - Prob. 54SPCh. 3 - Prob. 55SPCh. 3 - Prob. 56SPCh. 3 - Prob. 57SPCh. 3 - Prob. 58SPCh. 3 - Prob. 59SPCh. 3 - Prob. 60SPCh. 3 - Prob. 61SPCh. 3 - Prob. 62SPCh. 3 - Prob. 63SPCh. 3 - Prob. 64SPCh. 3 - Prob. 65SPCh. 3 - Prob. 66SPCh. 3 - Prob. 67SPCh. 3 - Prob. 68SPCh. 3 - Prob. 69SPCh. 3 - Prob. 70SPCh. 3 - Prob. 71SPCh. 3 - Prob. 72SPCh. 3 - Prob. 73SPCh. 3 - Prob. 74SPCh. 3 - Prob. 75SPCh. 3 - Prob. 76SPCh. 3 - Prob. 77SPCh. 3 - Prob. 78SPCh. 3 - Prob. 79SPCh. 3 - Prob. 80SPCh. 3 - Prob. 81SPCh. 3 - Prob. 82SPCh. 3 - Prob. 83SPCh. 3 - Prob. 84SPCh. 3 - Prob. 85SPCh. 3 - Prob. 86SPCh. 3 - Prob. 87SPCh. 3 - Prob. 88SPCh. 3 - Prob. 89SPCh. 3 - Prob. 90SPCh. 3 - Prob. 91SPCh. 3 - Prob. 92SPCh. 3 - Prob. 93SPCh. 3 - Prob. 94SPCh. 3 - Prob. 95SPCh. 3 - Prob. 96SPCh. 3 - Prob. 97SPCh. 3 - Prob. 98SPCh. 3 - Prob. 99SP
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- 2. Suppose that U(x, y, z) = x² + y²+ z² represents the temperature of a 3-dimensional solid object at any point (x, y, z). Then F(x, y, z) = -KVU (x, y, z) represents the heat flow at (x, y, z) where K > 0 is called the conductivity constant and the negative sign indicates that the heat moves from higher temperature region into lower temperature region. Answer the following questions. (A) [90%] Compute the inward heat flux (i.e., the inward flux of F) across the surface z = 1 - x² - y². (B) [10%] Use the differential operator(s) to determine if the heat flow is rotational or irrotational.arrow_forwardCould you show why the answer is B Using polar coordinates and the area formulaarrow_forward1. The parametric equations x = u, y = u cos v, z = usin v, with Ou≤ 2, 0 ≤ v ≤ 2π represent the cone that is obtained by revolving (about x-axis) the line y = x (for 0 ≤ x ≤2) in the xy-plane. Answer the following questions. (A) [50%] Sketch the cone and compute its surface area, which is given by dS = [ | Ər Or ди მა × du dv with S being the cone surface and D being the projection of S on the uv-plane. (B) [50%] Suppose that the density of the thin cone is σ(x, y, z) = 0.25x gr/cm². Compute the total mass of the cone.arrow_forward
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