Question 4 In a concert hall, the ceiling can be described by the plane x + y+ z = 30. An audio engineer is trying to fix a speaker on the ceiling. Assuming that the audience will be seated at the origin (0,0,0), he wants to find the position on the ceiling such that the intensity of the sound is strongest at the position of the audience. Given that the intensity of sound is inversely proportional to the squared of the distance away from the sound source, by finding the formula of the sound intensity the audience at (0,0, 0) will experience given that the speaker must be fixed on the ceiling x + y + z = 30, find the optimum position to fix the speaker so that the audience will experience maximum sound intensity. (a) (b) Apply Lagrange Multipliers now to solve this problem.
Question 4 In a concert hall, the ceiling can be described by the plane x + y+ z = 30. An audio engineer is trying to fix a speaker on the ceiling. Assuming that the audience will be seated at the origin (0,0,0), he wants to find the position on the ceiling such that the intensity of the sound is strongest at the position of the audience. Given that the intensity of sound is inversely proportional to the squared of the distance away from the sound source, by finding the formula of the sound intensity the audience at (0,0, 0) will experience given that the speaker must be fixed on the ceiling x + y + z = 30, find the optimum position to fix the speaker so that the audience will experience maximum sound intensity. (a) (b) Apply Lagrange Multipliers now to solve this problem.
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Transcribed Image Text:Question 4
In a concert hall, the ceiling can be described by the plane
x + y + z = 30.
An audio engineer is trying to fix a speaker on the ceiling. Assuming that the audience will be
seated at the origin (0,0,0), he wants to find the position on the ceiling such that the intensity
of
the
sound
is
strongest
at
the
position
of
the
audience.
Given that the intensity of sound is inversely proportional to the squared of the distance away
from the sound source,
(a)
by finding the formula of the sound intensity the audience at (0,0, 0) will experience
given that the speaker must be fixed on the ceiling x + y + z = 30, find the optimum
position to fix the speaker so that the audience will experience maximum sound
intensity.
(b)
Apply Lagrange Multipliers now to solve this problem.
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