A pentagon is formed by placing an isosceles triangle on a rectangle, as shown in the figure. II the pentagon has fixed perimeter P, find the lengths of the sides of the pentagon that maximize the area of the pentagon.

Q: 3. The manager of a department store wants to build a 600-square foot right triangular enclosure on…

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Q: a. A rectangular pen is built with one side against a barn. If 2500 m of fencing are used for the…

A: Let the width of the pen = x ft So length = (2500-2x)ft So area of the pen is: Answer(a):

Q: A rectangular play area is to be fenced using the one side of the school and arranged in to 5…

A: The double derivative test is used to optimize (maximize or minimize) a function. Follow the steps…

Q: A rectangular bird sanctuary is being created with one side along a straight riverbank. The…

A: Let, two sides= x and another side= y So, 2x+y=12  y=12-2x

Q: 4. The bottom of the legs of a three-legged table are the vertices of an isosceles triangle with…

A: In the question 4 it is asked to calculate the minimum wire length required to make a brace of of…

Q: A rectangle has a fixed perimeter of 12. Find the dimensions of the rectangle so that its area is…

A: Let's find.

Q: A rancher is building a horse pen on the corner of her property using 1000 ft of fencing. Because of…

A: Given: A rancher is building a horse pen on the corner of her property using 1000 ft of fencing.…

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

A: Since you have posted multiple questions, we will solve only first question for you. To getremaining…

Q: A rectangular bird sanctuary is being created with one side along a straight riverbank. The…

A:

Q: a. A rectangular pen is built with one side against a barn. If 1700 m of fencing are used for the…

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Q: 5. A farmer wants to build a fence around and across a rectangular field as shown below. The fencing…

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Q: 31. Cost In redecorating an office, the cost for new carpeting is $40 per square meter and the cost…

A: Concept: The Lagrange multiplier method: The Lagrange multiplier method is a method for determining…

Q: 7. A Norman window has the outline of a semicircle on top of a rectangle, as shown in the figure.…

A: The available wood trim is 8+π. The window the of the shapes semi-circle and rectangle.

Q: 55. A cardboard box without a lid is to have a volume of 32,000 cm³. Find the dimensions that…

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Q: 24) you are designing a rectangular poster continue to contain 27 in.² of printing with a 3 inch…

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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: e) A farmer wishes to enclose three pens with fencing, as shown. If the farmer has 700 feet of…

A: 700 feet of fencing to work .

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: A vertical dashed line divides a rectangle into two pieces as show in the figure. Find the value of…

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Q: Two triangular pens are built against a barn. Two hundred twenty  meters of fencing are to be used…

A: Given the perimeter of the fencing for the two triangular pens. fencing available for 220 meters…

Q: You want to make 3 pairs of earrings that are in the shape of isosceles triangles. Each earring will…

A: perimeter is sum of all sides of triangle

Q: A covered box is to be made from a rectangular sheet of cardboard measuring 10 inches by 16 inches.…

A: Volume of the box=x.y.z —1                                   height*lenth*width    2x+z=10  —2…

Q: 7. A Norman window has the outline of a semicircle on top of a rectangle, as shown in the figure.…

A: The solution of the problem is given in the next steps.

Q: 3. The manager of a department store wants to build a 600-square foot right triangular enclosure on…

A:

Q: 1. (. A box is to be made from a rectangular sheet of paper by cutting out squares from the corners…

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Q: Your College is building a new running track. It is to be the perimeter of a region obtained by…

A: a Let the length of the rectangle be x and its breadth be y Then perimeter =2x+πy2+πy2…

Q: An advertisement consist of a rectangular printed region plus 1-inch margins at the topand botton.…

A: Given that, advertisement consist of a rectangular printed region plus 1-inch margins at the top and…

Q: your college is building a new running track. It is to be the perimeter of a region obtained by…

A: Given: The perimeter of the track is 440 yards.

Q: 4. The bottom of the legs of a three-legged table are the vertices of an isosceles triangle with…

A: According to the question, we need to determine the minimum length of wire needed to make a brace of…

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 manufacturer wants to use 108 square inches of material to make an open topped box with a…

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Q: 6. Eva wants to fence two rectangular plots of land. Both plots must have the same dimensions and…

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Q: 5. A two-pen corral is to be built. The outline of the corral forms two identical adjoining…

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Q: ONotes Evaiuate A box with an open top is to be constructed out of a rectangular piece of cardboard…

A: topic - application of derivatives

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 the width of the pen be x ft.  So, length is y=300-2x feet. Then, the area of the pen is,…

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

A:

Q: You have an 8 inch by 10 inch piece of cardboard and you want to make an open topped box. To do this…

A: Given carboard,let size of square be x inchfor critical points,…

Q: 2. A 27-in gutter is bent on two sides as shown. Find the r and o values that will maximize the area…

A: From the given diagram:The cross-sectional area…

Q: 6. An entry window consisting of a rectangle topped with a semi-circle is to have a perimeter of 20…

A: Given: Perimeter of semi circlep=20 feet. Objective is to find radius of semicircle if the area of…

Q: 15. A rancher will use 600 m of fencing to build a corral in the shape of a semicircle on top of a…

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Q: 3. Packaging From a 9-inch by 9-inch piece of cardboard, Souare corners are cut out so that the…

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Q: 18. A farmer intends to make four identical rectangular pens each with an area of 100 m² as shown in…

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

A: According to the given problem , A piece of wire L m long is cut into two pieces and let first piece…

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

A: Note: Since you have posted multiple questions we will solve the first question for you. If you want…

Q: .A Norman window has the outline of a semicircle on top of a rectangle, as shown in the figure.…

A:

Q: 6. A family wants to build a fence in their backyard for their dogs, Charlie and Linus. The enclosed…

A: Let x and y be the dimensions of the rectangular field. According to given , Area(A)= xy= 4000…

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…