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Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919

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Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919
Textbook Problem
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Population Density The population density (in people per square mile) for a coastal town can be modeled by

f ( x , y ) = 120 , 000 ( 2 + x + y ) 3 where x and y are measured in miles. What is the population inside the rectangular area defined by the vertices (0, 0), (2, 0), (0, 2), and (2, 2)? Is the average population density of the town more than 2000 people?

To determine

To calculate: The pollution inside the rectangular area defined by the vertices (0,0),(2,0),(0,2),(2,2) for given the population density (in people per square mile) for a coastal town can be modeled by f(x,y)=120,000(2+x+y)3.

Explanation

Given information:

The population density (in people per square mile) for a coastal town can be modeled by

f(x,y)=120,000(2+x+y)3.

Where x and y are measure in miles.

Formula used:

The average value of integral function z=f(x,y) over the region R with area A is

Average value=1ARf(x,y)dxdy

Calculation:

The population density function;

f(x,y)=120,000(2+x+y)3

Now the integrate the population for limits 0x2 and 0y2,

Pollution=0202120000(2+x+y)3dydx=02[60000(2+x+y)2]02dx=6000002[1(4+x)21(2+x)

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