If the farmer has 246 feet of fencing, what are the dimensions of the region which enclose the maximal area?

Q: Find the dimensions of the box with square base, surface area 20, and maximal volume.

A: A box with square base has surface area 20we have to find its dimension and maximum volume.

Q: Find the dimensions of a rectangle with perimeter 68 m whose area is as large as possible. Show…

A: Given:Perimeter of a rectangle is 68 m.

Q: A farmer is building a fence to enclose a rectangular area consisting of two separate regions. The…

A: Consider x to be the length and y to be the width of the rectangular region as shown below.

Q: Find the maximum and minimum volumes of a rectangular box whose surface area is 1300 cm2 and whose…

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Q: Find the dimensions of the rectangle of largest area that can be inscribed in a circle of radius r.

A: Consider a rectangle, inscribed in a circle of radius r.Then,

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: Draw an example of a connected region that is not simply-connected.

A: To find the example of connected region that is not simply-connected. That is, to find the example…

Q: Find the dimensions of the isosceles triangle of largest area that can be inscribed in a circle of…

A: Solution:- calculate the value of base by using pythagores therorm.

Q: A poster is to contain 150 in2 of printed matter, surrounded by margins that are 3 in wide on top…

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Q: A rectangular prism has a height of 11.5 inches, a length of 9.6 inches, and a width of 2.10 inches.…

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Q: A piece of wire 10 m long is cut into two pieces. One piece is bent into a 30°-60°-90° triangle and…

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Q: If the farmer has 246 feet of fencing, what are the dimensions of the region which enclose the…

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Q: Is the solution region bounded or unbounded?

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Q: If the dairy uses a rectangle container opti dimensions and the surface area be?

A: Given a dairy sells ice cream in 11.4 L cardboard container.

Q: Find the dimensions of the rectangle with max area that can be inscribed in a circle of radius 10.

A: Find the dimensions of the rectangle with max area that can be inscribed in a circle of radius 10.

Q: what is the minimum possoble perimeter for a rectangle whose area is 100 in^2

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Q: Suppose an airline policy states that all baggage must be​ box-shaped with a sum of​ length, width,…

A: Since the base is square, let the three-dimensional be x, x and y. Since they are lengths x,y,>0…

Q: 2. Find the dimensions of a rectangle with perimeter 100 m whose area is as large as possible? Find…

A: Here we have to find the dimensions of w rectangle with perimeter 100m whose area is as large as…

Q: Find the volume of the maximum volume square prism that can be placed inside a sphere with a radius…

A: Given The radius of sphere 3√2. We find the diameter of sphere

Q: What is the maximum total area of such a corral?

A: Let the length of rectangular corral = LBreadth of rectangular corral = BPerimeter of rectangular…

Q: 2 Find the volume of the parallelepiped whose edges are represented by A =î - 13ĵ+ 4k, B = 3î +2j-7k…

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Q: Find the area of the bounded region

A: Given parabola is y=x2. Given point is 2,4 Differentiating the given curve with respect to x, we get…

Q: Determine the area of the region bounded by y = 2x2 + 10and y = 4x + 16.

A: The area of the region bounded by the functions f(x) and g(x) over the interval [a,b] is:…

Q: Find the maximum and minimum volumes of a rectangular box whose surface area is 1500 cm2 and whose…

A: Find the maximum and minimum volumes of a rectangular box whose surface area is 1500 cm2 and whose…

Q: a

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Q: A farmer wants to enclose a rectangular field with area 1,000 square meters by fencing it into four…

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Q: 8.Show that the rectangular box of maximum volume with a given surface area is a cube

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Q: Determine the area of the region bounded by y= 2x2 +10 and y= 4x +16

A: Please see the diagram below to understand what's going on:

Q: Find the dimensions of the rectangle of greatest area that can be inscribed in a circle of radius a.

A: Let x and y be the length and width of the rectangle inscribe in a circle of radius a. Then the…

Q: How many small cubes with edge of 20 cm each can be just accomodated in a cubical box of 2 m edge

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Q: Find the maximum area of a rectangle that can be circum -scribed about a given rectangle with length…

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Q: Find the area of the region bounded by the graphs of the equations. у 3 7x2 + 5, х %3D 0, х%3D 2, у…

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Q: Find the maximum volume of a rectangular box whose surface area is 1600 cm? and whose total edge…

A: By using lagrange multiplier

Q: What is the largest possible volume of a rectangular box whose diagonal has length L?

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Q: if an open box has a square base and a volume of 256 in^3 and is constructed from a tin sheet.  Find…

A: Given

Q: A farmer has 1200 m of fencing and wishes to enclose a rectangular area and then divide it into 6…

A: Given, A farmer has 1200 m of fencing and wishes to enclose a rectangular area and then divide it…

Q: Determine the dimensions of the rectangle of rectangle of the largest area that can be inscribed in…

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Q: Use double integrad to find the aved of the region R: (4.3) (いり (5,)

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Q: Find the rectangular parallelepiped of fixed total edge length with maximal surface area.

A: The rectangular parallelepiped has all faces in rectangular face. Let a,b,c be the edge lengths for…

Q: What are the dimensions of a rectangle that will maximize the area given its imeter is 100 units?

A: Given: Perimeter of rectangle is 100 units   To Find: Dimensions of a rectangle that will maximize…

Q: If the farmer has 648 feet of fencing, what are the dimensions of the region which enclose the…

A: x = length of the rectangle y = width of the rectangle fencing =648 ft hence 2x + 3y = 648 x…

Q: Of all rectangles with a perimeter of lo meters, which one has the maximum area? (GIve both the…

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Q: Find the dimensions of the rectangle of largest area that can be inscribed in a circle of radius r .

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Q: . A rectangular piece of cardboard measuring 24cm by 30cm is to be made into an open top box by…

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Q: Draw a region that is both vertically simple and horizontally simple

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Q: Sketch a graph and determine the area of the region bounded by y=2x^2+10 , y=4x+16, x=2 , and x=5.

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Q: 2. Among all rectangles that have perimeter of (54+0) ft, find the dimensions of the one with…

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Q: Of all rectangles with area 64, which one has the minimum perimeter?

A: It is required to find the dimensions of rectangle having area 64 units which will have a minimum…

Q: A box with an open top is to be constructed from a square piece of cardboard with dimensions 4 cm x…

A: The dimensions of the box is 4cm×4cm. Let each side of the square cut off from each corner be x cm.…