b) (b) Verify that the following function is harmonicu(x, y) = -ey sin x - 2e-siny.Find a harmonic conjugate v of u, namely a function v such that the functionu(x, y) + iv(x, y) is an analytic function, such that v(0, 0) = 4. Justify all of your steps.

Here we have to verify that the function is harmonic and then find the harmonic conjugate.

Answered: (b) Verify that the following function…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Allergic reactions to poison ivy can be miserable. Plant oils cause the reaction. Researchers at Allergy Institute did a study to determine the effects of washing the oil off within 5 minutes of exposure. A random sample of 1000 people with known allergies to poison ivy participated in the study. Oil from the poison ivy plant was rubbed on a patch of skin. For 500 of the subjects, it was washed off within 5 minutes. For the other 500 subjects, the oil was washed off after 5 minutes. The results are summarized in the following table. Reaction None Mild Strong Column Total Within 5 Minutes After 5 Minutes 391 65 44 500 66 341 93 500 Row Total 457 406 137 1000 Let's use the following notation for the various events: W= washing oil off within 5 minutes, A = washing oil off after 5 minutes, N = no reaction, M = mild reaction, S = strong reaction. Find the following probabilities for a person selected at random from this sample of 1000 subjects. (Use 3 decimal places.)
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9 (b,c). The following data was collected from 1 bag of Hershey Kisses®. Each Kiss® was weighed in grams with the wrapper and recorded in the table below. Hershey claims that there are 368 grams of chocolate in one bag. The following data was collected from 1 bag of Hershey Kisses®. Each Kiss® was weighed in grams with the wrapper and recorded in the table below. Hershey claims that there are 368 grams of chocolate in one bag. Hershey Kiss Weights in Grams 4.76 4.72 4.74 4.55 4.91 4.74 4.78 4.71 4.80 4.78 4.78 4.75 4.79 4.82 4.91 4.83 4.68 4.74 4.70 4.80 4.70 4.76 4.70 4.83 4.93 4.74 4.84 4.82 4.76 4.77 4.72 4.78 4.83 4.75 4.74 4.68 4.84 4.71 4.71 4.76 4.66 4.78 4.73 4.74 4.92 4.77 4.80 4.79 4.86 4.64 4.78 4.70 4.75 4.78 4.76 4.83 4.66 4.77 4.83 4.78 4.69 4.81 4.68 4.78 4.88 4.72 4.85 4.85 4.81 4.74 4.80 4.82 4.84 4.70 4.85 4.70 4.81 4.72 4.79 4.73 4.61 Standard Deviation & the Empirical Rule: Variation is a big factor in the analysis of most any…
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A recent survey of college freshman asked if they had been to a movie or eaten at a restaurant during the past week. 816 responded. The following information was obtained: 266 had been to a movie, 337 had been to a restaurant and 387 had not been to a movie nor gone to a restaurant. How many of the college freshman that responded went to a movie or ate at a restaurant in the past week? Ⓒ 429 816 213 387

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(b) Verify that the following function is harmonic u(x, y) = −e sin x - 2e-siny. Find a harmonic conjugate v of u, namely a function v such that the function u(x, y) + iv(x, y) is an analytic function, such that v(0,0) = 4. Justify all of your steps.