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Given that the pressure of air at any point (x, y, z) is P(r, y, z) = e2y (x + 22) – 4rz?. At point (-1,0, –1), find the rate of change of the pressure P(x, y, z) in the direction of i+2j-k. Hence, determine the lowest rate of change in pressure P(x, y, z) and its direction in unit vector.

Given that the pressure of air at any point (x, y, z) is P(r, y, z) = e2y (x + 22) – 4rz?. At point (-1,0, –1), find the rate of change of the pressure P(x, y, z) in the direction of i+2j-k. Hence, determine the lowest rate of change in pressure P(x, y, z) and its direction in unit vector.

College Algebra (MindTap Course List)
College Algebra (MindTap Course List)
12th Edition
ISBN:9781305652231
Author:R. David Gustafson, Jeff Hughes
Publisher:R. David Gustafson, Jeff Hughes
Chapter2: Functions And Graphs
Section2.6: Proportion And Variation
Problem 17E: Find the constant of proportionality. y is directly proportional to x. If x=30, then y=15.
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c) Given that the pressure of air at any point (x, y, z) is P(x, y, z) = e2" (x + 22) – 4x22. At point (-1,0, –1), find the rate of change of the pressure P(x, y, z) in the direction of i+2j-k. Hence, determine the lowest rate of change in pressure P(x, y, z) and its direction in unit vector.
Transcribed Image Text:c) Given that the pressure of air at any point (x, y, z) is P(x, y, z) = e2" (x + 22) – 4x22. At point (-1,0, –1), find the rate of change of the pressure P(x, y, z) in the direction of i+2j-k. Hence, determine the lowest rate of change in pressure P(x, y, z) and its direction in unit vector.
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