Explanation Given: The region is a 4-km radius city centre (located at the origin) and the population density is δ ( x , y ) = 2000 ( x 2 + y 2 ) − 0.2 Formula used: The total population of a region D with a given population density δ ( x , y ) is the solution of the integration ∬ D δ ( x , y ) d A (in 2-dimention) where d A is an elementary area of the region D . Calculation: Here, ∬ D δ ( x , y ) d A = ∬ D 2000 ( x 2 + y 2 ) − 0.2 d x d y Now the region is a circular region, so, axes will divide it in 4 equal parts in each quadrant. So, we will calculate in population in the 1 st quadrant only and then will multiply it by 4 to get the total population in the circular area. Now by changing it to polar co-ordinates we have x = r cos θ , y = r sin θ and d x d y = r d r d θ . So, the integration in the 1 st quadrant will be [As the radius is 4-km] ∫ 0 2 π ∫ 0 4 2000 ( r 2 cos 2 θ + r 2 sin 2 θ ) − 0...

3rd Edition

ISBN: 9781464125263

Author: Jon Rogawski, Colin Adams

Publisher: W.H. Freeman & Co

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Chapter 16.5, Problem 4E

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The total population of a region assuming a population density $δ (x, y)$ .

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Chapter 16.5, Problem 3E

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The total population of a region assuming a population density δ ( x , y ) .

Solution Summary: The author explains how to determine the total population of a region assuming the population density (x, y) = 2000.

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The total population of a region assuming a population density $δ (x, y)$ .

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Chapter 16 Solutions

The total population of a region assuming a population density δ ( x , y ) .

Solution Summary: The author explains how to determine the total population of a region assuming the population density (x, y) = 2000.

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The total population of a region assuming a population density δ(x,y).

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The total population of a region assuming a population density $δ (x, y)$ .