Explanation Definition used: The average value of the function over the rectangle with a ≤ x ≤ b and c ≤ y ≤ d is 1 ( b − a ) ( d − c ) ∬ f ( x , y ) d A . Given: The total amount of spending generated by the tax rebate is S ( x , y ) = y 1 − x , where 5 ≤ y ≤ 7 and 0.6 ≤ x ≤ 0.8 . Calculation: From definition, the values are a = 0.6 , b = 0.8 , c = 5 and d = 7 . The average value of S ( x , y ) over the rectangle with 5 ≤ y ≤ 7 and 0.6 ≤ x ≤ 0.8 is computed below. 1 ( b − a ) ( d − c ) ∬ R S ( x , y ) d A = 1 ( 0.8 − 0.6 ) ( 7 − 5 ) ∬ R y 1 − x d A = 1 ( 0.2 ) ( 2 ) ∬ R y 1 − x d A = 1 0.4 ∬ R y 1 − x d A Compute the integral with respect to y . 1 0.4 ∫ 0.6 0.8 ∫ 5 7 y 1 − x d y d x = 1 0.4 ∫ 0.6 0.8 1 1 − x [ ∫ 5 7 y d y ] d x = 1 0.4 ∫ 0.6 0.8 1 1 − x [ y 2 2 ] 5 7 d x Apply the limit value for y

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14th Edition

ISBN: 9780137553341

Author: Raymond Barnett, Michael Ziegler

Publisher: PEARSON+

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Chapter 14.6, Problem 47E

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To find: The average total amount of spending for the indicated ranges of the values of x and y.

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Chapter 14.6, Problem 46E

Chapter 14.6, Problem 48E

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Chapter 14 Solutions

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Ch. 14.1 - Matched Problem 1 Find C(20, 10) for the cost...Ch. 14.1 - Prob. 2MP Ch. 14.1 - Prob. 3MP Ch. 14.1 - Prob. 4MP Ch. 14.1 - Prob. 5MP Ch. 14.1 - Prob. 6MP Ch. 14.1 - Prob. 7MP Ch. 14.1 - Prob. 1ED Ch. 14.1 - Prob. 1E Ch. 14.1 - Prob. 2E

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The average total amount of spending for the indicated ranges of the values of x and y .

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To find: The average total amount of spending for the indicated ranges of the values of x and y.

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Chapter 14 Solutions