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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

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter7: Analytic Trigonometry
Section7.6: The Inverse Trigonometric Functions
Problem 93E
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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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