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The city of Mathville has a population density which depends solely on the radial distance to the centre of the city, which is marked with a statue of Euclid. Such radial density is given by p(r) = 7000e-0.03,² where r is the radius from Euclid's statute. (a) Historically, Downtown Mathville is the circular region centred at Euclid's statue with radius 5km. What is the population of Downtown Mathville? (b) For the purpose of understanding the Mathville suburbs, city officials want to understand how many people live in the annulus of width 1km immediately outside of Mathville Downtown. This is the outer ring immediately after Mathville Downtown going as far as 1km away on any direction. Compute the population on this region. (c) Scienceland, the country where Mathville is, wants to reshape the electoral ridings before next year elections. They want the Mathville riding be circular, be centred at Euclid's statue, and to include 700,000 people. What must be the radius of the new riding?

The city of Mathville has a population density which depends solely on the radial distance to the centre of the city, which is marked with a statue of Euclid. Such radial density is given by p(r) = 7000e-0.03,² where r is the radius from Euclid's statute. (a) Historically, Downtown Mathville is the circular region centred at Euclid's statue with radius 5km. What is the population of Downtown Mathville? (b) For the purpose of understanding the Mathville suburbs, city officials want to understand how many people live in the annulus of width 1km immediately outside of Mathville Downtown. This is the outer ring immediately after Mathville Downtown going as far as 1km away on any direction. Compute the population on this region. (c) Scienceland, the country where Mathville is, wants to reshape the electoral ridings before next year elections. They want the Mathville riding be circular, be centred at Euclid's statue, and to include 700,000 people. What must be the radius of the new riding?

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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The city of Mathville has a population density which depends solely on the radial distance to the centre of the city, which is marked with a statue of Euclid. Such radial density is given by p(r) = 7000€¯ -0.03r-² where r is the radius from Euclid's statute. (a) Historically, Downtown Mathville is the circular region centred at Euclid's statue with radius 5km. What is the population of Downtown Mathville? (b) For the purpose of understanding the Mathville suburbs, city officials want to understand how many people live in the annulus of width 1km immediately outside of Mathville Downtown. This is the outer ring immediately after Mathville Downtown going as far as 1km away on any direction. Compute the population on this region. (c) Scienceland, the country where Mathville is, wants to reshape the electoral ridings before next year elections. They want the Mathville riding be circular, be centred at Euclid's statue, and to include 700,000 people. What must be the radius of the new riding?
Transcribed Image Text:The city of Mathville has a population density which depends solely on the radial distance to the centre of the city, which is marked with a statue of Euclid. Such radial density is given by p(r) = 7000€¯ -0.03r-² where r is the radius from Euclid's statute. (a) Historically, Downtown Mathville is the circular region centred at Euclid's statue with radius 5km. What is the population of Downtown Mathville? (b) For the purpose of understanding the Mathville suburbs, city officials want to understand how many people live in the annulus of width 1km immediately outside of Mathville Downtown. This is the outer ring immediately after Mathville Downtown going as far as 1km away on any direction. Compute the population on this region. (c) Scienceland, the country where Mathville is, wants to reshape the electoral ridings before next year elections. They want the Mathville riding be circular, be centred at Euclid's statue, and to include 700,000 people. What must be the radius of the new riding?
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