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so basically what you're trying to find is the mean distances of the points within a disc that is bound by r = 1 and r = 3 to the center. so imagine one closed circle within the disc and we call it S. The circumference of this loop is ds = 2r, which is proportionate to the number of people within this loop, since we assume they are uniformely distributed. Hence rds corresponds to the cummulative distance of all the people within this loop and we want to sum up all these loops hence Total Distance from the center = integrate (from 1 to 3) r ds = 2pir^2 = (2/3)pi (26) Total number of people = integrate (from 1 to 3) ds = pir = 8 pi average distance from city central = Total dist/ Total poeple = ((2/3)*pi* (26))/(8*pi) = 2.16

so basically what you're trying to find is the mean distances of the points within a disc that is bound by r = 1 and r = 3 to the center. so imagine one closed circle within the disc and we call it S. The circumference of this loop is ds = 2r, which is proportionate to the number of people within this loop, since we assume they are uniformely distributed. Hence rds corresponds to the cummulative distance of all the people within this loop and we want to sum up all these loops hence Total Distance from the center = integrate (from 1 to 3) r ds = 2pir^2 = (2/3)pi (26) Total number of people = integrate (from 1 to 3) ds = pir = 8 pi average distance from city central = Total dist/ Total poeple = ((2/3)*pi* (26))/(8*pi) = 2.16

Advanced Engineering Mathematics
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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so basically what you're trying to find is the mean distances of the points within a disc that is bound by r = 1 and r = 3 to the center. so imagine one closed circle within the disc and we call it S. The circumference of this loop is ds = 2r, which is proportionate to the number of people within this loop, since we assume they are uniformely distributed. Hence rds corresponds to the cummulative distance of all the people within this loop and we want to sum up all these loops hence Total Distance from the center = integrate (from 1 to 3) r ds = 2pir^2 = (2/3)pi (26) Total number of people = integrate (from 1 to 3) ds = pir = 8 pi average distance from city central = Total dist/ Total poeple = ((2/3)*pi* (26))/(8*pi) = 2.16
Transcribed Image Text:so basically what you're trying to find is the mean distances of the points within a disc that is bound by r = 1 and r = 3 to the center. so imagine one closed circle within the disc and we call it S. The circumference of this loop is ds = 2r, which is proportionate to the number of people within this loop, since we assume they are uniformely distributed. Hence rds corresponds to the cummulative distance of all the people within this loop and we want to sum up all these loops hence Total Distance from the center = integrate (from 1 to 3) r ds = 2pir^2 = (2/3)pi (26) Total number of people = integrate (from 1 to 3) ds = pir = 8 pi average distance from city central = Total dist/ Total poeple = ((2/3)*pi* (26))/(8*pi) = 2.16
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