An open-top box is to be made from a 40 in. by 27 in. piece of cardboard by removing a square from each corner of the box and folding up the flaps on each side. What is the length of the side of the square that should be cut out in order to get a box with the maximum volume? x = inches

Q: The volume of an open box with a square base is 4000 cm3. Find the dimensions of the box if the…

A: Given that volume =4000cm3 find the dimensions of the box that minimize the amount of material used…

Q: A Norman window has the shape of a rectangle surmounted by a semicircle. (Thus the diameter of the…

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Q: An open box is to be made from a 21 ft by 56 ft rectangular piece of sheet metal by cutting out…

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Q: An open box is to be made from a 15 ft by 40 ft rectangular piece of sheet metal by cutting out…

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Q: ) The length of the box is 9 inches more than its width. The height of the box is 1 inch less than…

A: Given: Length is 9 inches more than width. Height is 1 inch less than width. Volume = 72 inch3

Q: An open-top box with a square base is to have a volume of 32 cubic feet. Find the dimensions of the…

A: To determine the dimension of the box which minimize the amount of material used.

Q: What is the maximum area of a rectangle that can be inscribed in a right triangle with a base 8 cm…

A: This question can be solved using the concept of maxima and minima.

Q: 8. Find the dimensions of the rectangular box, open at the top, which has a maximum volume if…

A: Given surface area is 18 square feet.

Q: An оpen box is to be made from a 6 ft by 16 ft rectangular cardboard by cutting out equal squares…

A: We can find the maximum volume of the box as below

Q: An open-top box is to be made from a 36 in. by 27 in. piece of cardboard by removing a square from…

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Q: An open box is to be made of a piece of cardboard 10cm x 16cm by cutting equal squares out of the…

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Q: How tall should the file be to maximize the volume that it can hold?

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Q: Find the dimensions of the rectangle with perimeter 153.6 millimeters with the largest possible…

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Q: A Norman window has the shape of a rectangle surmounted by a semicircle. (Thus the diameter of the…

A: Given: x feet is the width of the rectangular part of the window. Perimeter of the window =8 feet.…

Q: A rancher has 400 feet of fencing with which to enclose two adjacent rectangular corrals (see…

A:

Q: An open box is to be made from a 33 ft by 88 ft rectangular piece of sheet metal by cutting out…

A:

Q: An open box is made from a 16 inch by 16 inch piece of cardboard by cutting equal squares from each…

A: This question is based on application of derivative.

Q: Find the dimensions of the rectangular box of maximum volume if the sum of the length, width, and…

A: To find dimension of the rectangular box of maximum volume  Given sum of length, width and height…

Q: An open box is to be made from a 3-ft by an 8-ft rectangular piece of sheet metal by cutting out…

A: An open box is to be made from a 3-ft by an 8-ft rectangular piece of sheet metal by cutting out…

Q: An open-toped rectangular dumpster that is twice as long as it is wide and can hold 12y cubic yards…

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Q: What is the maximum area of a rectangle that can be inscribed in a right triangle with a base 8 cm…

A: The rectangle which can be inscribed in a right triangle with base 8 cm and height 6  cm.

Q: A cardboard box without a lid is to have a volume of 4000cm3. Find the minimum amount of cardboard…

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Q: If a gun is fired with and a =30o and V0 = 500m/s, whenwill the bullet hit the ground? How far from…

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Q: A Norman window is constructed by adjoining a semicircle to the top of an ordinary rectangular…

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Q: An open rectangular box is to be constructed by cutting square corners out of a 16 by 16 cm piece of…

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Q: A box with an open top is to be constructed from a square piece of cardboard that is 4 feet wide by…

A: Square piece of cardboard of 4 feet wide. Let x feet be cut off from each corner of the square piece…

Q: A rancher has 200 feet of fencing with which to enclose two adjacent rectangular corrals (see…

A: Total fencng = 200 feetTotal fencing = 4x+3y=200 feet  — (i)Area = 2x×yFrom eqn - i - y =200-4x3Area…

Q: An open-top box is to be made from a 37 in. by 27 in. piece of cardboard by removing a square from…

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Q: A rectangular building is to be built on a triangular corner lot with the perpendicular sides equal…

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Q: An open box is to be made from a 33 ft by 88 ft rectangular piece of sheet metal by cutting out…

A: You have asked multiple questions, so we will solve the first question for you. The rest can be…

Q: An open box is to be made from a 21 ft by 56 ft rectangular piece of sheet metal by cutting out…

A:

Q: The perimeter of an isosceles triangle is 42 cm.  Find the maximum area of the isosceles triangle…

A: Let's find.

Q: What is the maximum volume of an open box that can be made from a square piece of cardboard, 10in on…

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Q: An open box is to be made from a 3 ft by 8 ft rectangular piece of sheet metal by cutting out…

A: We need to find maximum volume.

Q: A box is formed by cutting squares from the four corners of a 8"-wide by 10"-long sheet of paper and…

A: Length of the long sheet L = 10'' Width of the long sheet W = 8'' The side of the square cutting…

Q: A Norman window is constructed by adjoining a semicircle to the top of an ordinary rectangular…

A: Given: The total perimeter is 16 feet. The given window is formed by adjoining semicircle to the top…

Q: The size of the rectangle that can be made from 200 cm long wire so that the area is maximum is ….

A: We have to find the maximum area of given rectangle.

Q: (EX) Max wishes to enclose a rectangular garden, using one side of his house as shown below. What is…

A: We use second derivative test to find out dimensions of rectangular garden have maximum area

Q: A manufacturer wants to design an open box having a square base and a surface area of 108 square…

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Q: An open box is to be made from a 3 ft by 8 ft rectangular piece of sheet metal by cutting out…

A: Given: An open box is to be made from a 3 ft by 8 ft rectangular piece of sheet metal by cutting out…

Q: A farmer wants to make a rectangluar enclosure using a wall of a barn as one side and 160 ft of…

A: Let x ,in feet, be the length of side of rectangular enclosure which is along the wall of barn and y…

Q: A rancher has 480 feet of fencing with which to enclose two adjacent rectangular corrals (see…

A: Total fencing needed in that given picture is= x+x+x+x+y+y+y=4x+3y Given that the rancher has 480…

Q: An open box is to be made from a square piece of material by cutting equal squares from each corner…

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Q: A open-top box is to be made from a 24 in by 36 in piece of cardboard by removing a square from each…

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Q: An open box is to be made from a 33 ft by 88 ft rectangular piece of sheet metal by cutting out…

A: Solve the given problem.

Q: A carpenter is building a rectangular room with a fixed perimeter of 116 ft. What dimensions would…

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Q: An open topped box is to be made from a rectangular piece of metal 18cm x 48 cm by cutting off…

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Q: Q1) The base of an open-top rectangular box costs 3$ per square meter to construct, while the sides…

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