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Mathematical Applications for the Management, Life, and Social Sciences11th Edition

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Chapter 13.8, Problem 34E
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Mathematical Applications for the ...

11th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781305108042

Solutions

Chapter
Section
Problem 1CP
Problem 2CP
Problem 3CP
Problem 1E
Problem 2E
Problem 3E
Problem 4E
Problem 5E
Problem 6E
Problem 7E
Problem 8E
Problem 9E
Problem 10E
Problem 11E
Problem 12E
Problem 13E
Problem 14E
Problem 15E
Problem 16E
Problem 17E
Problem 18E
Problem 19E
Problem 20E
Problem 21E
Problem 22E
Problem 23E
Problem 24E
Problem 25E
Problem 26E
Problem 27E
Problem 28E
Problem 29E
Problem 30E
Problem 31E
Problem 32E
Problem 33E
Problem 34E
BuyFindarrow_forward

Mathematical Applications for the ...

11th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781305108042
Textbook Problem

Development costs A land developer is planning to dig a small lake and build a group of homes around it. To estimate the cost of the project, the area of the lake must be calculated from the proposed measurements (in feet) given in Figure 13.35 and in the data in the table. Use Simpson's Rule to approximate the area of the lake.

x Width w(x)
0 0
100 300
200 200
300 400
400 0

Chapter 13.8, Problem 34E, Development costs A land developer is planning to dig a small lake and build a group of homes around

To determine

To calculate: The area of the lake by the Trapezoidal Rule if the area of the lake is as per the given table and the diagram:

x Width w(x)
0 0
100 300
200 200
300 400
400 0

The provided graph is shown below:

Mathematical Applications for the Management, Life, and Social Sciences, Chapter 13.8, Problem 34E

Explanation

Given Information:

The area of the lake is as per the given table and the diagram:

x Width w(x)
0 0
100 300
200 200
300 400
400 0

The provided graph is shown below:

Formula Used:

As per the Trapezoidal Rule:

If f is continuous on [a,b], then,

∫abf(x)dx≈h2[f(x0)+2f(x1)+2f(x2)+2f(x3)+…+2f(xn−2)+2f(xn−1)+f(xn)]

Where h=b−an and n is the number of equal subdivisions of [a,b].

Calculation:

The area of the lake is as per the given table and the diagram:

x Width w(x)
0 0
100 300
200 200
300 400
400 0

The provided graph is shown below:

In order to apply the rule, the value of h is as follows:

h=100

So, the interval [0,400] is divided into 4 subintervals as follows,

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