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CalculusCalculus: An Applied Approach (MindTap Course List)10th Edition

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Chapter 7.9, Problem 26E
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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 on an island can be modeled by

f ( x , y ) = 5000 x e y 1 + 2 x 2 where x and y are measured in miles. What is the population inside the rectangular area defined by the vertices (0, 0), (4, 0), (0, −2), and (4, −2)? Is the average population density of the town more than 500 people?

To determine

To calculate: The pollution inside the rectangular area defined by the vertices (0,0),(4,0),(0,−2),(4,−2) for given the population density (in people per square mile) for a coastal town can be modeled by f(x,y)=5000xey1+2x2.

Explanation

Given information:

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

f(x,y)=5000xey1+2x2.

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=1A∬Rf(x,y)dxdy

Calculation:

The population density function;

f(x,y)=5000xey1+2x2

Now the integrate the population for limits 0≤x≤4 and −2≤y≤0,

Pollution=∫−20∫045000xey1+2x2dxdy=∫−20[5000ey(4x)1+2x2]04dy=1250∫−20ey[ln|1+2<

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Sect-7.1 P-1CPSect-7.1 P-2CPSect-7.1 P-3CPSect-7.1 P-4CPSect-7.1 P-5CPSect-7.1 P-6CPSect-7.1 P-7CPSect-7.1 P-1SWUSect-7.1 P-2SWUSect-7.1 P-3SWU
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Trigonometry (MindTap Course List)

For Exercises 1 and 2, consider a group of regular polygons. As the number of sides of a regular polygon increa...

Elementary Geometry For College Students, 7e

17. Use mathematical induction to prove that the stated property of the sigma notation is true for all positive...

Elements Of Modern Algebra

The refrigerant line from the outside condensing unit to the air handler must be bent in the shop and taken to ...

Elementary Technical Mathematics

Answer the following questions based on the Leisure Time Industries invoice on the following page. Who is the v...

Contemporary Mathematics for Business & Consumers

Using Properties of Limits In Exercises 58. find the indicated limit by using the limits lim(x,y)(a,b)f(x,y)=4a...

Calculus: Early Transcendental Functions (MindTap Course List)

Finding the Center of a Power Series In Exercises 5-8, state where the power series is centered. n=0(1)n(x)2n(2...

Calculus of a Single Variable

In Exercises 51-54, determine whether the statement is true or false. If it is true, explain why it is true. If...

Finite Mathematics for the Managerial, Life, and Social Sciences

Given the tangents with mRT=146, find : a mRST_ b m3_

Elementary Geometry for College Students

Sound Intensity The relationship between the number of decibels and the intensity of a sound I in watts per ce...

Calculus

Comparing VectorsIn Exercises 2126, determine whether u and v are orthogonal, parallel, or neither. u=2,3,1v=1,...

Calculus (MindTap Course List)

CONCEPT CHECK Linear Approximation What is meant by a linear approximation of z=f(x,y) at the point P(x0,y0)?

Multivariable Calculus

True or false:

Study Guide for Stewart's Multivariable Calculus, 8th

If A1 and A2 are the areas at the right then abf(x)dx= a) A1 A2 b) A1 + A2 c) A1 + A2 d) A1A2

Study Guide for Stewart's Single Variable Calculus: Early Transcendentals, 8th

Define applied research and basic research and identify examples of each.

Research Methods for the Behavioral Sciences (MindTap Course List)

Bar stock is being cut on a lathe. The tool feeds (advances) 364 inch each time the stock turns once (1 revolut...

Mathematics For Machine Technology

The admissions officer for Clearwater College developed the following estimated regression equation relating th...

STATISTICS F/BUSINESS+ECONOMICS-TEXT

Show that the multiplication of two complex numbers is commutative by multiplying the complex numbers a+bi and ...

College Algebra (MindTap Course List)

Corporate triple-A bond interest rates for 12 consecutive months follow. 9.59.39.49.69.89.79.810.59.99.79.69.6 ...

Statistics for Business & Economics, Revised (MindTap Course List)

Major League Baseball (MLB) includes two groups of teams, in leagues. There are 15 teams in each of the America...

Introduction To Statistics And Data Analysis

The following data show the pattern of results that was obtained in a study by Liguori and Robinson (2001) exam...

Research Methods for the Behavioral Sciences (MindTap Course List)

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