#6 handwritten 5. A rectangular tent is made to have a square base with two partitions inside that divide the tentinto four smaller areas, as shown in the figure below.xXTop viewx(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 heightof 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., andthe material used on the top and bottom costs twice as much. Determine the cost ofbuilding 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} is1fave =(b − a)(d—c) f(x, y) dA.Find the average value of f(x, y) =xy²x² + 1over R == {(x, y) |0 ≤ x ≤ 1, -3 ≤ y ≤ 3}.

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

Mathematics For Machine Technology

8th Edition

ISBN:9781337798310

Author:Peterson, John.

Publisher:Peterson, John.

Chapter63: Volumes Of Pyramids And Cones

Section: Chapter Questions

Problem 16A: A piece in the shape of a pyramid with a regular octagon (eight sided) base is machined from a solid...

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Question

#6 handwritten

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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