A city surrounds a bay as shown in Figure 16.36. Thepopulation density of the city (in
Chapter 16, Problem 30(choose chapter or problem)
A city surrounds a bay as shown in Figure 16.36. Thepopulation density of the city (in thousands of people persquare km) is (r, ), where r and are polar coordinatesand distances are in km.(a) Set up an iterated integral in polar coordinates givingthe total population of the city(b) The population density decreases the farther you livefrom the shoreline of the bay; it also decreases thefarther you live from the ocean. Which of the followingfunctions best describes this situation?(i) (r, ) = (4 r)(2 + cos )(ii) (r, ) = (4 r)(2 + sin )(iii) (r, )=(r + 4)(2 + cos )(c) Estimate the population using your answers toparts (a) and (b).
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