(a) To determine To show: The total cost in dollars is f ( x , y . z ) = 4000 x y z + 2000 y z subject to the constraint x y + 2 x z = 8 . Explanation Given: An open top box is designed to transport 400 yd 3 of material. The available material is 8 yd 3 . The cost of heavy weight material is $1000 per yd 2 and the costs of each trip is $10. Calculation: Let x , y , and z are the length, width, and height of the box, respectively. Compute the total cost if all of the free material is being used. Here, two sides and bottom of the box can be made from free material. The area of the bottom is xy and area of the two sides of the box is 2 xz . Thus, the area of the two sides and bottom of the box is x y + 2 x z and the free material is 8 yd 3 . That is, the constraint is x y + 2 x z = 8 . The two ends of the box must be made from a heavyweight material. The area of two ends of the box is 2 yz per yd 2 . Since the material cost $1000 per yd 2 , the cost of ends of the box is, c 1 = 2 y z ( 1000 ) = 2000 y z . Need to transport 400 yd 3 of material (b) To determine To find: The dimensions of the box that minimize the transportation cost subject to the constraint by using solver feature on a spreadsheet.

Calculus With Applications, Books a la Carte Plus MyLab Math Package (11th Edition)

11th Edition

ISBN: 9780133886849

Author: Margaret L. Lial, Raymond N. Greenwell, Nathan P. Ritchey

Publisher: PEARSON

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Chapter 9.4, Problem 41E

(a)

To determine

To show: The total cost in dollars is f(x,y.z)=4000xyz+2000yz subject to the constraint xy+2xz=8 .

(b)

To determine

To find: The dimensions of the box that minimize the transportation cost subject to the constraint by using solver feature on a spreadsheet.

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Chapter 9.4, Problem 40E

Chapter 9.4, Problem 42E

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Find the value of the integral: ∬xysin⁡(x)cos⁡(x) dA where the region R lies between the graphs of sine and cosine functions and between 45 and 225 degrees along the xxx-axis. a) Determine the correct limits and write the order of integration that you consider appropriate.b) Solve the integral, providing a detailed step-by-step solution.

Chapter 9 Solutions

Calculus With Applications, Books a la Carte Plus MyLab Math Package (11th Edition)

Ch. 9.1 - YOUR TURN 1 For the function in Example 1, find...Ch. 9.1 - YOUR TURN 2 For the function in Example 3, find...Ch. 9.1 - YOUR TURN 3 Graph x + 2y + 3z = 12 in the first...Ch. 9.1 - YOUR TURN 4 Find the level curve at a production...Ch. 9.1 - Prob. 1WE Ch. 9.1 - Prob. 2WE Ch. 9.1 - Prob. 3WE Ch. 9.1 - Prob. 4WE Ch. 9.1 - Prob. 5WE Ch. 9.1 - Prob. 6WE

Ch. 9.1 - 1. Let f(x, y) = 2x – 3y + 5. Find the...Ch. 9.1 - 2. Let g(x, y) = x2 – 2xy + y3. Find the...Ch. 9.1 - Prob. 3E Ch. 9.1 - 4. Let . Find the following. (a) f(10,...Ch. 9.1 - Prob. 5E Ch. 9.1 - 6. Let f(x, y) = xex+y. Find the...Ch. 9.1 - Prob. 7E Ch. 9.1 - Prob. 8E Ch. 9.1 - Graph the first-octant portion of each...Ch. 9.1 - Graph the first-octant portion of each...Ch. 9.1 - Prob. 11E Ch. 9.1 - Prob. 12E Ch. 9.1 - Prob. 13E Ch. 9.1 - Prob. 14E Ch. 9.1 - Prob. 15E Ch. 9.1 - Graph the level curves in the first quadrant of...Ch. 9.1 - Graph the level curves in the first quadrant of...Ch. 9.1 - Graph the level curves in the first quadrant of...Ch. 9.1 - Prob. 19E Ch. 9.1 - Prob. 20E Ch. 9.1 - Prob. 21E Ch. 9.1 - Prob. 22E Ch. 9.1 - Match each equation in Exercises 23–28 with its...Ch. 9.1 - Prob. 24E Ch. 9.1 - Match each equation in Exercises 23–28 with its...Ch. 9.1 - Prob. 26E Ch. 9.1 - Match each equation in Exercises 23–28 with its...Ch. 9.1 - Match each equation in Exercises 23–28 with its...Ch. 9.1 - 29. Let f(x, y) = 4x2 – 2y2, and find the...Ch. 9.1 - Prob. 30E Ch. 9.1 - Prob. 31E Ch. 9.1 - Prob. 32E Ch. 9.1 - 33. Production Production of a digital camera is...Ch. 9.1 - Production Find the level curve at a production of...Ch. 9.1 - Production Find the level curve at a production of...Ch. 9.1 - Prob. 36E Ch. 9.1 - 37. Cost If labor (x) costs $250 per unit,...Ch. 9.1 - Prob. 38E Ch. 9.1 - Prob. 39E Ch. 9.1 - Prob. 40E Ch. 9.1 - Prob. 41E Ch. 9.1 - 42. Dinosaur Running An article titled “How...Ch. 9.1 - Prob. 43E Ch. 9.1 - 44. Dengue Fever In tropical regions, dengue fever...Ch. 9.1 - Prob. 45E Ch. 9.1 - Prob. 46E Ch. 9.1 - Prob. 47E Ch. 9.1 - Prob. 48E Ch. 9.1 - Prob. 49E Ch. 9.1 - Prob. 50E Ch. 9.1 - 51. Elliptical Templates The holes cut in a roof...Ch. 9.2 - YOUR TURN 1 Let Find and . Ch. 9.2 - Prob. 2YT Ch. 9.2 - Prob. 3YT Ch. 9.2 - Prob. 4YT Ch. 9.2 - Prob. 1WE Ch. 9.2 - Prob. 2WE Ch. 9.2 - Prob. 3WE Ch. 9.2 - Prob. 4WE Ch. 9.2 - Prob. 5WE Ch. 9.2 - Prob. 6WE Ch. 9.2 - Prob. 7WE Ch. 9.2 - Prob. 8WE Ch. 9.2 - Prob. 1E Ch. 9.2 - Prob. 2E Ch. 9.2 - Prob. 3E Ch. 9.2 - In Exercises 3–20, find fx(x, y) and fy(x,y). Then...Ch. 9.2 - In Exercises 3–20, find fx(x, y) and fy(x, y)....Ch. 9.2 - Prob. 6E Ch. 9.2 - Prob. 7E Ch. 9.2 - Prob. 8E Ch. 9.2 - Prob. 9E Ch. 9.2 - Prob. 10E Ch. 9.2 - Prob. 11E Ch. 9.2 - Prob. 12E Ch. 9.2 - In Exercises 3–20, find fx(x, y) and fy(x, y)....Ch. 9.2 - Prob. 14E Ch. 9.2 - Prob. 15E Ch. 9.2 - Prob. 16E Ch. 9.2 - Prob. 17E Ch. 9.2 - Prob. 18E Ch. 9.2 - In Exercises 3–20, find fx(x, y) and fy(x, y)....Ch. 9.2 - Prob. 20E Ch. 9.2 - Prob. 21E Ch. 9.2 - Prob. 22E Ch. 9.2 - Prob. 23E Ch. 9.2 - Prob. 24E Ch. 9.2 - Prob. 25E Ch. 9.2 - Prob. 26E Ch. 9.2 - Prob. 27E Ch. 9.2 - Prob. 28E Ch. 9.2 - Prob. 29E Ch. 9.2 - Prob. 30E Ch. 9.2 - Prob. 31E Ch. 9.2 - Prob. 32E Ch. 9.2 - Prob. 33E Ch. 9.2 - Prob. 34E Ch. 9.2 - For the functions defined as follows, find all...Ch. 9.2 - For the functions defined as follows, find all...Ch. 9.2 - Prob. 37E Ch. 9.2 - Find and for the following. 38. Ch. 9.2 - Prob. 39E Ch. 9.2 - Prob. 40E Ch. 9.2 - Find and for the following. 41. Ch. 9.2 - Find and for the following. 42. Ch. 9.2 - Prob. 43E Ch. 9.2 - Prob. 44E Ch. 9.2 - Business and Economics 45. Manufacturing Cost...Ch. 9.2 - 46. Revenue The revenue from the sale of x units...Ch. 9.2 - Prob. 47E Ch. 9.2 - Prob. 48E Ch. 9.2 - 49. Marginal Productivity A manufacturer estimates...Ch. 9.2 - 50. Marginal Productivity The production function...Ch. 9.2 - Prob. 51E Ch. 9.2 - 52. Marginal Productivity A manufacturer of...Ch. 9.2 - Prob. 53E Ch. 9.2 - Prob. 54E Ch. 9.2 - Prob. 55E Ch. 9.2 - Prob. 56E Ch. 9.2 - Prob. 57E Ch. 9.2 - Prob. 58E Ch. 9.2 - Prob. 59E Ch. 9.2 - 60. Health The body mass index (BMI) is a number...Ch. 9.2 - Prob. 61E Ch. 9.2 - Prob. 62E Ch. 9.2 - 63. Drug Reaction The reaction to x units of a...Ch. 9.2 - Prob. 64E Ch. 9.2 - Prob. 66E Ch. 9.2 - Prob. 67E Ch. 9.2 - Prob. 68E Ch. 9.2 - 69. Gravitational Attraction The gravitational...Ch. 9.2 - Prob. 70E Ch. 9.2 - Prob. 71E Ch. 9.3 - YOUR TURN 1 Find all critical points for Ch. 9.3 - Prob. 2YT Ch. 9.3 - Prob. 1WE Ch. 9.3 - Prob. 2WE Ch. 9.3 - Find all points where the functions have any...Ch. 9.3 - Find all points where the functions have any...Ch. 9.3 - Find all points where the functions have any...Ch. 9.3 - Find all points where the functions have any...Ch. 9.3 - Prob. 5E Ch. 9.3 - Prob. 6E Ch. 9.3 - Prob. 7E Ch. 9.3 - Find all points where the functions have any...Ch. 9.3 - Prob. 9E Ch. 9.3 - Prob. 10E Ch. 9.3 - Prob. 11E Ch. 9.3 - Find all points where the functions have any...Ch. 9.3 - Find all points where the functions have any...Ch. 9.3 - Find all points where the functions have any...Ch. 9.3 - Prob. 15E Ch. 9.3 - Find all points where the functions have any...Ch. 9.3 - Find all points where the functions have any...Ch. 9.3 - Find all points where the functions have any...Ch. 9.3 - Prob. 19E Ch. 9.3 - Prob. 20E Ch. 9.3 - Figures (a)–(f) show the graphs of the functions...Ch. 9.3 - Prob. 22E Ch. 9.3 - Figures (a)–(f) show the graphs of the functions...Ch. 9.3 - Prob. 24E Ch. 9.3 - Prob. 25E Ch. 9.3 - Prob. 26E Ch. 9.3 - 27. Show that f(x, y) = 1 – x4 – y4 has a relative...Ch. 9.3 - 28. Show that D = 0 for f(x, y) = x3 + (x – y)2...Ch. 9.3 - Prob. 29E Ch. 9.3 - Prob. 30E Ch. 9.3 - Prob. 31E Ch. 9.3 - 32. In Exercise 9 of Section 1.3, we found the...Ch. 9.3 - Prob. 33E Ch. 9.3 - 34. Profit Suppose that the profit (in hundreds of...Ch. 9.3 - 35. Labor Costs Suppose the labor cost (in...Ch. 9.3 - 36. Cost The total cost (in dollars) to produce x...Ch. 9.3 - 37. Revenue The total revenue (in hundreds of...Ch. 9.3 - 38. Profit The profit (in thousands of dollars)...Ch. 9.3 - Prob. 39E Ch. 9.3 - 40. Political Science The probability that a...Ch. 9.3 - Prob. 42E Ch. 9.4 - YOUR TURN 1 Find the minimum value of f(x, y) = x2...Ch. 9.4 - Prob. 1WE Ch. 9.4 - Prob. 2WE Ch. 9.4 - Find the relative maxima or minima in Exercises...Ch. 9.4 - Find the relative maxima or minima in Exercises...Ch. 9.4 - Find the relative maxima or minima in Exercises...Ch. 9.4 - Prob. 4E Ch. 9.4 - Find the relative maxima or minima in Exercises...Ch. 9.4 - Prob. 6E Ch. 9.4 - Find the relative maxima or minima in Exercises...Ch. 9.4 - Prob. 8E Ch. 9.4 - Find the relative maxima or minima in Exercises...Ch. 9.4 - Find the relative maxima or minima in Exercises...Ch. 9.4 - 11. Find positive numbers x and y such that x + y...Ch. 9.4 - 12. Find positive numbers x and y such that x + y...Ch. 9.4 - Prob. 13E Ch. 9.4 - 14. Find three positive numbers whose sum is 240...Ch. 9.4 - Prob. 15E Ch. 9.4 - Prob. 16E Ch. 9.4 - Prob. 17E Ch. 9.4 - 18. Show that the function f(x, y) = xy2 in...Ch. 9.4 - 19. Show that the function f(x, y) = 8x2y in...Ch. 9.4 - Prob. 20E Ch. 9.4 - 21. Consider the problem of minimizing f(x, y) =...Ch. 9.4 - Prob. 22E Ch. 9.4 - Business and Economics Utility Maximize each of...Ch. 9.4 - Business and Economics Utility Maximize each of...Ch. 9.4 - Business and Economics Utility Maximize each of...Ch. 9.4 - Prob. 26E Ch. 9.4 - 27. Maximum Area for Fixed Expenditure Because of...Ch. 9.4 - 28. Maximum Area for Fixed Expenditure To enclose...Ch. 9.4 - Prob. 29E Ch. 9.4 - 30. Profit The profit from the sale of x units of...Ch. 9.4 - 31. Production A manufacturing firm estimates that...Ch. 9.4 - Prob. 32E Ch. 9.4 - Prob. 33E Ch. 9.4 - Prob. 34E Ch. 9.4 - Prob. 35E Ch. 9.4 - Prob. 36E Ch. 9.4 - Prob. 37E Ch. 9.4 - Prob. 38E Ch. 9.4 - Prob. 39E Ch. 9.4 - Prob. 40E Ch. 9.4 - 41. Container Construction RD Enterprises is...Ch. 9.4 - Social Sciences 42. Political Science The...Ch. 9.5 - YOUR TURN 1 For the function , find (a) dz, and...Ch. 9.5 - Prob. 2YT Ch. 9.5 - Prob. 3YT Ch. 9.5 - Prob. 1WE Ch. 9.5 - Prob. 2WE Ch. 9.5 - Prob. 3WE Ch. 9.5 - Prob. 4WE Ch. 9.5 - Evaluate dz using the given information. 1. Ch. 9.5 - Evaluate dz using the given information. 2. Ch. 9.5 - Evaluate dz using the given information. 3. Ch. 9.5 - Prob. 4E Ch. 9.5 - Evaluate dz using the given information. 5. Ch. 9.5 - Evaluate dz using the given information. 6. Ch. 9.5 - Prob. 7E Ch. 9.5 - Prob. 8E Ch. 9.5 - Use the total differential to approximate each...Ch. 9.5 - Prob. 10E Ch. 9.5 - Prob. 11E Ch. 9.5 - Prob. 12E Ch. 9.5 - Use the total differential to approximate each...Ch. 9.5 - Use the total differential to approximate each...Ch. 9.5 - Prob. 15E Ch. 9.5 - Prob. 16E Ch. 9.5 - 17. Volume of a Coating An industrial coaling 0.1...Ch. 9.5 - Prob. 18E Ch. 9.5 - Prob. 19E Ch. 9.5 - Prob. 20E Ch. 9.5 - Prob. 21E Ch. 9.5 - Prob. 22E Ch. 9.5 - 23. Blood Volume In Exercise 58 of Section 2 in...Ch. 9.5 - Prob. 24E Ch. 9.5 - Life Span As we saw in Exercise 62 of Section 9.2,...Ch. 9.5 - Prob. 26E Ch. 9.5 - Prob. 27E Ch. 9.5 - Prob. 28E Ch. 9.5 - Prob. 29E Ch. 9.5 - Prob. 30E Ch. 9.5 - Prob. 31E Ch. 9.5 - Prob. 32E Ch. 9.5 - Prob. 33E Ch. 9.5 - Prob. 34E Ch. 9.5 - Prob. 35E Ch. 9.6 - YOUR TURN 1 Evaluate Ch. 9.6 - YOUR TURN 2 Evaluate and then integrate with the...Ch. 9.6 - Prob. 3YT Ch. 9.6 - Prob. 4YT Ch. 9.6 - Prob. 5YT Ch. 9.6 - Prob. 1WE Ch. 9.6 - Prob. 2WE Ch. 9.6 - Prob. 3WE Ch. 9.6 - Prob. 4WE Ch. 9.6 - Prob. 5WE Ch. 9.6 - Prob. 6WE Ch. 9.6 - Prob. 1E Ch. 9.6 - Evaluate each integral. 2. Ch. 9.6 - Prob. 3E Ch. 9.6 - Prob. 4E Ch. 9.6 - Prob. 5E Ch. 9.6 - Evaluate each integral. 6. Ch. 9.6 - Prob. 7E Ch. 9.6 - Prob. 8E Ch. 9.6 - Prob. 9E Ch. 9.6 - Prob. 10E Ch. 9.6 - Evaluate each iterated integral. (Many of these...Ch. 9.6 - Evaluate each iterated integral. (Many of these...Ch. 9.6 - Evaluate each iterated integral. (Many of these...Ch. 9.6 - Prob. 14E Ch. 9.6 - Evaluate each iterated integral. (Many of these...Ch. 9.6 - Prob. 16E Ch. 9.6 - Evaluate each iterated integral. (Many of these...Ch. 9.6 - Prob. 18E Ch. 9.6 - Evaluate each iterated integral. (Many of these...Ch. 9.6 - Evaluate each iterated integral. (Many of these...Ch. 9.6 - Prob. 21E Ch. 9.6 - Find each double integral over the rectangular...Ch. 9.6 - Find each double integral over the rectangular...Ch. 9.6 - Prob. 24E Ch. 9.6 - Find each double integral over the rectangular...Ch. 9.6 - Find each double integral over the rectangular...Ch. 9.6 - Find each double integral over the rectangular...Ch. 9.6 - Prob. 28E Ch. 9.6 - Find the volume under the given surface and above...Ch. 9.6 - Find the volume under the given surface and above...Ch. 9.6 - Prob. 31E Ch. 9.6 - Find the volume under the given surface and above...Ch. 9.6 - Find the volume under the given surface and above...Ch. 9.6 - Prob. 34E Ch. 9.6 - Find the volume under the given surface and above...Ch. 9.6 - Find the volume under the given surface and above...Ch. 9.6 - Prob. 37E Ch. 9.6 - Although it is often true that a double integral...Ch. 9.6 - Prob. 39E Ch. 9.6 - Evaluate each double integral. 40. Ch. 9.6 - Prob. 41E Ch. 9.6 - Prob. 42E Ch. 9.6 - Prob. 43E Ch. 9.6 - Use the region R with the indicated boundaries to...Ch. 9.6 - Prob. 45E Ch. 9.6 - Prob. 46E Ch. 9.6 - Prob. 47E Ch. 9.6 - Use the region R with the indicated boundaries to...Ch. 9.6 - Prob. 49E Ch. 9.6 - Prob. 50E Ch. 9.6 - Prob. 51E Ch. 9.6 - Use the region R with the indicated boundaries to...Ch. 9.6 - Use the region R with the indicated boundaries to...Ch. 9.6 - Use the region R with the indicated boundaries to...Ch. 9.6 - Prob. 55E Ch. 9.6 - Prob. 56E Ch. 9.6 - Evaluate each double integral. If the function...Ch. 9.6 - Prob. 58E Ch. 9.6 - Prob. 59E Ch. 9.6 - Prob. 60E Ch. 9.6 - The idea of the average value of a function,...Ch. 9.6 - Prob. 62E Ch. 9.6 - Prob. 63E Ch. 9.6 - Prob. 64E Ch. 9.6 - 65. Packaging The manufacturer of a fruit juice...Ch. 9.6 - Prob. 66E Ch. 9.6 - 67. Average Production A production function is...Ch. 9.6 - 68. Average Profit The profit (in dollars) from...Ch. 9.6 - 69. Average Revenue A company sells two products....Ch. 9.6 - Prob. 70E Ch. 9.6 - Prob. 71E Ch. 9 - Prob. 1RE Ch. 9 - Prob. 2RE Ch. 9 - Prob. 3RE Ch. 9 - Prob. 4RE Ch. 9 - Prob. 5RE Ch. 9 - Prob. 6RE Ch. 9 - Prob. 7RE Ch. 9 - Prob. 8RE Ch. 9 - Prob. 9RE Ch. 9 - Prob. 10RE Ch. 9 - Prob. 11RE Ch. 9 - Prob. 12RE Ch. 9 - Prob. 13RE Ch. 9 - Prob. 14RE Ch. 9 - Prob. 15RE Ch. 9 - Prob. 16RE Ch. 9 - Prob. 17RE Ch. 9 - Find (–1, 2) and f(6, –3) for the...Ch. 9 - Prob. 19RE Ch. 9 - Prob. 20RE Ch. 9 - Prob. 21RE Ch. 9 - Prob. 22RE Ch. 9 - Prob. 23RE Ch. 9 - Prob. 24RE Ch. 9 - Prob. 25RE Ch. 9 - Prob. 26RE Ch. 9 - Prob. 27RE Ch. 9 - Prob. 28RE Ch. 9 - Prob. 29RE Ch. 9 - Prob. 30RE Ch. 9 - Prob. 31RE Ch. 9 - Prob. 32RE Ch. 9 - Prob. 33RE Ch. 9 - Prob. 34RE Ch. 9 - Prob. 35RE Ch. 9 - Prob. 36RE Ch. 9 - Prob. 37RE Ch. 9 - Prob. 38RE Ch. 9 - Prob. 39RE Ch. 9 - Prob. 40RE Ch. 9 - Prob. 41RE Ch. 9 - Prob. 42RE Ch. 9 - Prob. 43RE Ch. 9 - Prob. 44RE Ch. 9 - Prob. 45RE Ch. 9 - Prob. 46RE Ch. 9 - Prob. 47RE Ch. 9 - Prob. 48RE Ch. 9 - Prob. 49RE Ch. 9 - Prob. 50RE Ch. 9 - Prob. 51RE Ch. 9 - Prob. 52RE Ch. 9 - Prob. 53RE Ch. 9 - Prob. 54RE Ch. 9 - Prob. 55RE Ch. 9 - Prob. 56RE Ch. 9 - Prob. 57RE Ch. 9 - Prob. 58RE Ch. 9 - Prob. 59RE Ch. 9 - Prob. 60RE Ch. 9 - Prob. 61RE Ch. 9 - Prob. 62RE Ch. 9 - Prob. 63RE Ch. 9 - Prob. 64RE Ch. 9 - Prob. 65RE Ch. 9 - Prob. 66RE Ch. 9 - Prob. 67RE Ch. 9 - Prob. 68RE Ch. 9 - Prob. 69RE Ch. 9 - Prob. 70RE Ch. 9 - Prob. 71RE Ch. 9 - Prob. 72RE Ch. 9 - Prob. 73RE Ch. 9 - Prob. 74RE Ch. 9 - Prob. 75RE Ch. 9 - Prob. 76RE Ch. 9 - Prob. 77RE Ch. 9 - Prob. 78RE Ch. 9 - Prob. 79RE Ch. 9 - Prob. 80RE Ch. 9 - Prob. 81RE Ch. 9 - Prob. 82RE Ch. 9 - Prob. 83RE Ch. 9 - Prob. 84RE Ch. 9 - Prob. 85RE Ch. 9 - Prob. 86RE Ch. 9 - Prob. 87RE Ch. 9 - Prob. 88RE Ch. 9 - Prob. 89RE Ch. 9 - Prob. 90RE Ch. 9 - Prob. 91RE Ch. 9 - Prob. 92RE Ch. 9 - Prob. 93RE Ch. 9 - Prob. 94RE Ch. 9 - Prob. 95RE Ch. 9 - Prob. 96RE Ch. 9 - 97. Profit The total profit from 1 acre of a...Ch. 9 - Prob. 98RE Ch. 9 - Prob. 99RE Ch. 9 - Prob. 100RE Ch. 9 - Prob. 101RE Ch. 9 - Prob. 102RE Ch. 9 - Prob. 103RE Ch. 9 - Prob. 104RE Ch. 9 - Prob. 105RE Ch. 9 - Prob. 106RE

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