A rectangular field of fixed area is to be enclosed and divided into five lots by parallel to one of the sides. What should be the relative dimensions of the field to make theamount of fencing minimum

Q: second denivafive method to conclude 1x-21 local minimum at

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Q: A farmer wants to fence in a rectangular field and then divide it in half with a fence parallel to…

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Q: Three equally sized rectangular lots are enclosed by fencing the perimeter of a large rectangular…

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Q: A farmer wants to fence in 80,000m² of land and then divide it into three plots of equal area. Find…

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Q: A piece of wire of length 61 is cut into two pieces. One piece is bent into a square and the other…

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Q: A method for finding the maximum or minimum value of a quantity that is subject to various…

A: Given: A method for finding the maximum and minimum value of a quantity that is subject to various…

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

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Q: A rectangular box is to have a square base and a volume of 16 ft3. If the material for the base…

A: Volume= x2y= 16 So, y= 16/x2   total cost:

Q: A rectangular field of fixed area is to be enclosed and divided into three lots by parallel to one…

A: Given: A rectangular field of the fixed area is to be enclosed and divided into three lots parallel…

Q: Find the dimensions of a rectangular box of maximum volume such that the sum of the lengths of its…

A: According to the question, we have a rectangular box and the sum of the lengths of its 12 edges is…

Q: 13. Of all numbers whose difference is 6, find the two that have the minimum product.

A: Let x and y be such numbers. x-y=6 P=xy. Substitute x=6+y in P=xy and obtain that P=y6+y=6y+y2.

Q: From a tract of land, a developer plans to fence a rectangular region and then divide it into two…

A: Given: Cost of fence on outside = $20 per foot Cost of middle fence = $8 per foot Area of each lot =…

Q: Find two positive numbers with product 256 and whose sum is a minimum

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Q: 2. A rectangular field of fixed area is to be enclosed and divided into five lots by parallel to one…

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Q: A rectangular area of 5000 sq st is to be enclosed by a river on one side. Find the dimensions of…

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Q: A rectangle is constructed with its base on the diameter of a semicircle with radius 30 and with its…

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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: 19. A piece of wire of length 1 meter is cut into two parts, one of which is bent into the shape of…

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Q: A closed three dimensional box is to be constructed in such a way that its volume is 3000 cm³. It is…

A: We have to find the dimensions of the box.

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A: Assuming that the wire is cut in 2 pieces of length x and L-x where the first is used to make a…

Q: A rectangular field is to be covered by 800-meter of hog wire in such a way that one side has a…

A: The Perimeter of rectangular field = 800 m Let length of field = x m Width of field = y m

Q: A book is to contain 36 in² of printed matter per page, with margins of 1 in along the sides and 1…

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Q: A rectangular box is to have a square base and a volume of 40 ft³. If the material for the base…

A: The base of the box is square-shaped. Thus the top part will also be square. Let 'x' be the length…

Q: A city is setting up community garden plots for residents living in apartments. The plots will be…

A: Given area of each plot = 32m2 cost of fencing between lots = $5/m cost of fencing around entire…

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: A piece of wire of length 1 meter is cut into two parts, one of which is bent into the shape of a…

A: A piece of wire of length 1 meter is cut into two parts , one of which is bent the shape of a circle…

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A: Here, the volume of the box is given by: V=lbh Here, for the given box, l=9-2x, w=10-2x,h=x. So,…

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Q: A string of length L is cut into arbitrarily many pieces. Some or all pieces are made to circles and…

A: Let the string is cut into n equal pieces. Then the length of each piece will be Ln. Now, let x…

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Q: A triangle is formed by the positive coordinate axes and a straight line through (6,3) . How large…

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Q: A fencing is limited to 120ft length. What is the maximum rectangular area that can be fenced in…

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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: 1. A rectangular field of fixed area is to be enclosed and divided into three lots by parallels to…

A:

Q: A closed rectangular box with a square base is to be constructed using two different types of wood.…

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Q: From a tract of land, a developer plans to fence a rectangular region and then divide it into two…

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Q: Find a pair of non-negative numbers that have a product of 162 and minimize the sum of two times the…

A: Let the numbers be x,y. Given  x·y=162y=162x The function to be minimized will be Fx=2x+y…

Q: A printed page is to contain 60 cm2 of printed material (not including the margins) with margins (on…

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Q: A food company is constructing an open-top, square-based, rectangular metal tank that will have a…

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Q: A piece of wire of length 69 is cut into two pieces. One piece is bent into a square and the other…

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Q: Find the dimensions of a rectangular box of maximum volume such that the sum of the lengths of its…

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Q: Find two positive numbers with product 256 and whose sum is a minimum.

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Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.