10. A farmer has 400 feet of fencing to enclose two adjacent sheep corrals. What should be the dimensions to maximize the grazing area?

Q: A rectangular field with one side along a river is to be fenced. Suppose that no fence is needed…

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Q: A rectangular corral of 160 square meters is to be fenced off and then divided by a fence into two…

A: Let ,  Length of fence that divides the two corrals = a Length of a side oc the fence perpendicular…

Q: A rectangular lot has a perimeter of 80m. If its lot area is to be maximized, what is its length? *

A: Let the Length of the rectangle be:  x Let the Width of the rectangle be: y It is given that the…

Q: A piece of wire of length L is to be cut into two pieces, one piece to form a square and the other…

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Q: A rancher wants to create two rectangular pens, as shown in the figure, using an existing fence line…

A: The following solution is given below:

Q: A farmer wants to fence an area of 13.5 million square feet in a rectangular field and then divide…

A: Let one side be length P and the other QTotal area = PQ =13.5 million

Q: two cities A and B are 8 km and 12 km, respectively, north of a river which runs due east. City B…

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Q: A piece of wire is with a length of 4 m is cut into two pieces, and the resulting two pieces are…

A: According to given,    Let x be length of the portion that is bent into a circle   Therefore, 4-x=…

Q: A rectangular lot is to be fenced in using two different kinds of fencing. Three sides will be…

A: Given that, Three sides of rectangular land will be fenced using standard fencing that costs $7 per…

Q: a. A rectangular pen is built with one side against a barn. If 2200 m of fencing are used for the…

A: a)find the dimensions maximize the area of the pen

Q: 8. A farmer wants to fence an area of 16000 square feet and then divide it into 4 parts by placing 3…

A: To minimise the cost, the dimensions are to be computed. we have,Area = xy = 16000now,Length of…

Q: 5. Find the length and width of a rectangle that has an area of 32 square feet and a minimum…

A: Given, area A=32 sq.ft Let, x be the length and y be the width. The formula for the area of a…

Q: a. A rectangular pen is built with one side against a barn. If 400 m of fencing are used for the…

A: Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: a. A rectangular pen is built with one side against a barn. If 1500 m of fencing are used for the…

A: a. Let the dimensions of the pen be x m and y m.  Now, the length of the perimeter to be covered by…

Q: A farmer has 1700 m of fencing and wishes to enclose a rectangular area and then divide it into 5…

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Q: 4. You want to enclose a rectangular garden of area 800m². One side will be a brick wall costing…

A:

Q: . A rectangular pen is built with one side against a barn. If 1400 m of fencing are used for the…

A: l+2w=1400; l=1400-2w; l=2(700-w); are=lw ; so, lw=2(700-w)w =(1400w-2w^2);  to maximize,…

Q: A rectangular lot has a perimeter of 80m. If its lot area is to be maximized, what is its length?

A:

Q: 10. Jason has 152 meters of fencing that he wants to enclose a rectangular plot that borders on a…

A: Given: Jason has 152 meters of fencing that he wants to enclose a rectangular plot that borders on a…

Q: a. A rectangular pen is built with one side against a bam. If 1100 m of fencing are used for the…

A: x=width  y=length  perimeter is given by p=2x+y here we have p=1100 1100=2x+y y=1100-2x . the area…

Q: a. A rectangular pen is built with one side against a barn. If 300 m of fencing are used for the…

A: a) Let x represents the width of the pen and y represents the length of the pen. Given that, the…

Q: A farmer has 500 ft of fence for constructing a rectangular corral. One side of the corral will be…

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Q: 9. The backyard of a property is to be fenced off in a rectangular design. Fencing is only needed on…

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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: (2) A rancher wants to construct a rectangular pen by extending an existing 100 ft stone wall by an…

A: Let the length along the stone wall be x. And take the width to be y. Then the length of fencing…

Q: 2 2. A rectangular playing field is to have area 600 m . Fencing is required to enclose the field…

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Q: a. If she walks at 3 mi/hr and rows at 2 mi/hr, at which point on the shore should she land to…

A: Given: A boat on the ocean is 4 mi from the nearest point on a straight shoreline; that point is 6…

Q: Your task is to design a rectangular industrial warehouse consisting of three separate spaces of…

A:

Q: A piece of wire 8 m long is cut into two pieces. One piece is bent into a square and the other is…

A: Since you have posted multiple questions i can do first question as per our company guidelines…

Q: A wire b is cut into two pieces. One piece is bent into an equilateral triangle and the other is…

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Q: 4-Find the length and width of a rectangle with perimeter 100 m that maximize the a

A: I have solved the 4th question for you since you have marked it. As per guidelines, we are supposed…

Q: 9. A student wishes to maximize the amount of poster space for an art exhibit. The requirements are…

A: As per our guidelines we are supposed to answer only one question.Kindly repost other question as…

Q: 19. If the farmer in Exercise 18 wants to enclose 150 square meters of land, what dimensions will…

A: The minimum of a function can be obtained at the point where the slope of the function is 0. The…

Q: Bill is constructing a rectangular corral in his yard. He only has 32 ft of fencing material and…

A: Bill is constructing a rectangular corral in his yard and he has only 32 ft of fencing material. We…

Q: . A rectangular pen is built with one side against a barn. If 2300 m of fencing are used for the…

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Q: You’re building five identical pens adjacent to each other with a total area of 1000 m^2, as shown…

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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: A dog park wants to enclose a rectangular plot of land that borders a lake and hence only requires…

A: Let the length of the plot be x yards and width be y yards. As we have to cover 3 sides of the polt…

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: Find the minimum cost of a rectangular box of volume 100 cm³ whose top and bottom cost 6 cents per…

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Q: 5., You are building TWO identical pens adjacent to each other with a total area of 100 m², as shown…

A: Let's solve 5th question, dimensions for minimize the amount of fencing.

Q: A gardener wants to construct 4 garden areas by first building a fence around a rectangular region,…

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Q: 2. Find the dimensions of a rectangle with an area of 108 square feet that has the minimum…

A: Area of rectangle = (length)*(width) = 108 sq. ft we need to find dimensions of a rectangle with…

Q: 2. A rectangular area is enclosed with fencing on three sides, with the fourth side along a house.…

A: Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: A rancher wants to create two rectangular pens, as shown in the figure, using an existing fence line…

A:

Q: A piece of wire of length 60 is cut, and the resulting two pieces are formed to make a circle and…

A: Let x be the length of the wire cut for the circle then the length of the wire cut for the square.If…

Q: a. A rectangular pen is built with one side against a barn. If 1200 m of fencing are used for the…

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…

Q: 16. A farmer wants to fence an area of 2 million square feet in a rectangular field and then divide…

A: Here first we find the total length of fence in terms of the sides. Now using differentiation we…

Q: 3. Rae plans to build a rectangular pig pen against one of the walls of her barn. If she has 18…

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