Difference between revisions of "009B Sample Final 2, Problem 4"

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(Created page with "<span class="exam">Consider the region bounded by the following two functions: ::::::::<span class="exam"> <math style="vertical-align: -5px">y=2(-x^2+9)</math> and <math styl...")
 
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<span class="exam">Consider the region bounded by the following two functions:
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<span class="exam"> A city bordered on one side by a lake can be approximated by a semicircle of radius 7 miles, whose city center is on the shoreline. As we move away from the center along a radius the population density of the city can be approximated by:
::::::::<span class="exam"> <math style="vertical-align: -5px">y=2(-x^2+9)</math> and <math style="vertical-align: -4px">y=0</math>.
 
  
<span class="exam">a) Using the lower sum with three rectangles having equal width, approximate the area.
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::::<math>\rho(x)=25000e^{-0.15x}</math>
  
<span class="exam">b) Using the upper sum with three rectangles having equal width, approximate the area.  
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<span class="exam">people per square mile. What is the population of the city?
 
 
<span class="exam">c) Find the actual area of the region.
 
  
 
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Revision as of 20:14, 17 February 2017

A city bordered on one side by a lake can be approximated by a semicircle of radius 7 miles, whose city center is on the shoreline. As we move away from the center along a radius the population density of the city can be approximated by:

people per square mile. What is the population of the city?

Foundations:  

Solution:

(a)

Step 1:  
Step 2:  

(b)

Step 1:  
Step 2:  

(c)

Step 1:  
Step 2:  
Final Answer:  
(a)
(b)
(c)

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