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6. The average value of f(x, y) over the rectangle R = {(x,y) | a

6. The average value of f(x, y) over the rectangle R = {(x,y) | a

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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5. A rectangular tent is made to have a square base with two partitions inside that divide the tent into four smaller areas, as shown in the figure below. x X Top view x (a) Find an equation for the total surface area of the material to be used to make the tent. (b) If the tent is designed to have a volume of 1,152 cu. ft., find the length, width, and height of the tent to minimize the surface area. (c) Suppose that the material to be used for the sides and partitions cost $5 per sq. ft., and the material used on the top and bottom costs twice as much. Determine the cost of building the tent that minimizes the surface area. 6. The average value of f(x, y) over the rectangle R = {(x, y) | a ≤ x ≤ b, c ≤ y ≤d} is 1 fave = (b − a)(d—c) f(x, y) dA. Find the average value of f(x, y) = xy² x² + 1 over R = = {(x, y) |0 ≤ x ≤ 1, -3 ≤ y ≤ 3}.
Transcribed Image Text:5. A rectangular tent is made to have a square base with two partitions inside that divide the tent into four smaller areas, as shown in the figure below. x X Top view x (a) Find an equation for the total surface area of the material to be used to make the tent. (b) If the tent is designed to have a volume of 1,152 cu. ft., find the length, width, and height of the tent to minimize the surface area. (c) Suppose that the material to be used for the sides and partitions cost $5 per sq. ft., and the material used on the top and bottom costs twice as much. Determine the cost of building the tent that minimizes the surface area. 6. The average value of f(x, y) over the rectangle R = {(x, y) | a ≤ x ≤ b, c ≤ y ≤d} is 1 fave = (b − a)(d—c) f(x, y) dA. Find the average value of f(x, y) = xy² x² + 1 over R = = {(x, y) |0 ≤ x ≤ 1, -3 ≤ y ≤ 3}.
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