1. Find the dimensions of a rectangle with perimeter 1000 meters so that the area of the rectangle is a maximum.

Q: If a rectangle has dimensions x and y, then we must maximize the area A = xy. Since the perimeter is…

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Q: 4. An open-top box with a square bottom and rectangular sides is to have a volume of 256 cubic…

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Q: Suppose we have 45 m^2 of material to build a box with a square bottom and no top. What dimensions…

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Q: 3. Find the dimensions of a open topped box that maximizes the volume with the constraint that the…

A: We need to find dimension of an open box that maximizes the volume.

Q: Consider the following problem: A farmer with 750 ft offencing wants to enclose a rectangular area…

A: Given: A farmer with 750 ft of fencing wants to enclose a rectangular area and then divide it into…

Q: Consider the following problem: A farmer with 950 ft of fencing wants to enclose a rectangular area…

A: Given: A farmer with includes the 950 ft of fencing that results in enclosing the rectangular area…

Q: 12. Show that a rectangle with given perimeter has maximum area when it is a square.

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Q: Show that the rectangle which has maximum area for a given perimeter is a square.

A: This problem can be solved by expressing the area of the rectangle as a function of single variable…

Q: 3. A piece of wire 36 in. is cut into two parts, one of which is bent into the shape of an…

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Q: Find the length L and W (with W(less than or equal to) L) of the rectangle with perimeter 48 that…

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Q: You are to construct an open rectangular box from 12 ft2 of material. What dimensions will result in…

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Q: 2. Helmut, an ostrich farmer, wants to build a rectangular fenced enclosure divided into five…

A: Given that, Total length= 120 m

Q: 3. A farmer has 6000 m of fencing and wishes to create a rectangular field subdivided into four…

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Q: 6. Find the minimum surface area of a box that holds 2 cubic meters.

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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: Your client wants you to construct a rectangular family pool in front of the house with perimeter of…

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Q: Determine the dimensions of the inscribed rectangle of maximum area. y = e¯*

A: Let the point on the curve for the rectangle with maximum area is (x,y) It can be written as: so…

Q: A rectangular garden is to be constructed using a rock wall as one side of the g and wire fencing…

A: We are asked to find dimensions of the rectangle.

Q: Find the dimensions of the rectangle of maximum area that can be inscribed in a circle of radius r =…

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Q: A rectangle is bounded by the x-axis and the semi-circle y = √(36 − x^2). What length and width…

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Q: A box with no top and a square base has to be designed so that its volume must 108 cm³. Find the…

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Q: Two chicken coops are to be built adjacent to one another using 120 ft of fencing. a. What…

A: Total fence needed is: (x+x+x)+y+y+y+y=3x+4y So, 3x+4y=120

Q: Consider the following problem: A farmer with 950 ft of fencing wants to enclose a rectangular area…

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Q: Find the exact maximum and minimum volumes (in cm) of a rectangular box whose surface area is 1,300…

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Q: A rectangle is constructed with its base on the​ x-axis and its upper two vertices on the parabola y…

A: Given informationRectangle base is on x axisTop on parabola

Q: 1. Assuming that one of the sides of a rectangular field is along a river bank and no fencing is…

A: In this question, we want to know the dimensions of the rectangular field that will satisfy the…

Q: Define the livable space of a building to be the volume of space in the building where a person 6…

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Q: A rectangular hole is to be cut in a wall for a vent. If the perimeter of the hole is 48 in. and the…

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Q: A rectangle, R, has length L = 8 and width W = 3. What is the maximum area of the rectangle, Q, that…

A: We need to find maximum area.

Q: The base of an aquarium with given volume V is made of slate and the sides are made of glass. If the…

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Q: Suppose that a pentagon is composed of a rectangle topped by an isosceles triangle. If the length of…

A: We have to find the maximum area.

Q: 1. Find the dimensions of a rectangular box with a square base and no top that has a volume of 100…

A: Solve By minimizing surface area

Q: A poster is to contain 300 cm2 of printed matter with margins of 10 cm at the the top and bottom and…

A: We have, A poster is to contain 300 cm2 of printed matter with margins of 10 cm at the the top and…

Q: 8. A rancher has 200 feet of fencing with which to enclose two adjacent rectangular corrals (see…

A: A rectangular figure is given. Let, the length of parallel side of division be y and the length of…

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: A piece of wire 10 m long is cut into two pieces. One pieceis bent into a square and the other is…

A: To find: The way to use the wire such that the area enclosed by the triangle and square would be…

Q: A rectangular building covering 7000 m² is to be built on a rectangular lot as shown below. If the…

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Q: 3. A divided field is to be constructed with 4000 feet of fence as shown. For what value of z will…

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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: Find the dimensions of a rectangle with area 100 m? whose perimeter is as small as possible? Find…

A: to find:- dimensions of the rectangle. minimum perimeter.

Q: A company that manufactures dog food wishes to pack the food in closed cylindrical tins. What should…

A: Use application of derivative concept. volume of cylinder and total surface area of cylinder…

Q: Consider the following problem: A farmer with 750 ft offencing wants to enclose a rectangular area…

A: Given: The length of the fencing is 750 ft. Let the length of two parallel sides of rectangle be x…

Q: 1. Find the dimensions of closed-top box with the largest volume if the total surface area must be…

A: It is known that perimeter of box is,  2(xy+xz+yz) Given that, 2(xy+xz+yz)=125 So, z=1252-xyx+y The…

Q: Is the rectangle of fixed area whose perimeter is a minimum a square?

A: Given Area of a rectangle =  square units-----(1)   Let length of the rectangle be feet and the…

Q: Consider the following problem: A farmer with 750 ft offencing wants to enclose a rectangular area…

A: Given that, The fencing encloses a rectangular area is 750 ft. The rectangle divides it into four…

Q: Determine the dimensions of the inscribed rectangle of maximum area.

A: Determine the dimensions of the inscribed rectangle of maximumarea.

Q: 1. A closed box, with a rectangular base, whose length is twice its width, is to have a surface of…

A: Topic.- application of derivatives Given: Length is twice the width and the total surface area is…

Q: A poster is to contain 300 m^2 of printed matter with margins of 10 cm at the top and 5 cm at each…

A:

Q: Two chicken coops are to be built adjacent to one another from 144 ft of fencing. Part: 0/ 2 Part 1…

A: Two chicken coops are to be built adjacent to one another from 144 ft of fencing To find dimensions…