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Mathematical Applications for the ...

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

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BuyFindarrow_forward

Mathematical Applications for the ...

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

In Problems 23-30, round all calculations to 2 decimal places.

Demand Suppose that the demand tor q units of a certain product at $p per unit is given by

p = 850 + 100 q 2 + 1

Use Simpsons Rule with n = 6 to approximate the average price as demand ranges from 3 to 9 items.

To determine

To calculate: The average price as demand ranges from 3 to 9 items using Simpson’s Rule with n=6 if the demand for q units of a certain product at $p is given as p=850+100q2+1.

Explanation

Given Information:

The demand for q units of a certain product at $p is given as p=850+100q2+1.

Formula Used:

As per the Simpson’s Rule:

If f(x) is continuous on [a,b] and [a,b] is divided into an even number n of equal subdivisions, then,

abf(x)dxh3[f(x0)+4f(x1)+2f(x2)+4f(x3)...+2f(xn2)+4f(xn1)+f(xn)]

Where h=ban.

Calculation:

The provided expression is p=850+100q2+1.

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

h=936=66=1

Hence, the value of h is 1.

So, the interval [3,9] is divided into 6 subintervals as follows,

Put the values of the xi's in the equation

abf(x)dxh2[f(x0)+2f(x1)+2f(x2)+2f(x3)++2f(xn2)+2f(xn1)+f(xn)]

Then,

39(850

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Chapter 13 Solutions

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