A 100 cm piece of wire is going to be cut in two pieces. One will be bent into a square, and the other will be bent into a circle. How long should each piece of wire be so the area enclosed by the two wire shapes is minimized?

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A: Given that , Total length of the sheet = 18 inches find width across the top will give the greatest…

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Q: A piece of wire 16m long is cut into two pieces. One piece is bent into a square and the other is…

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

A: Let the length of square is x. Then each side of the square will be x4. The circumference of the…

Q: A rectangle having area 392 m2 is twice as long as it is wide.Find its dimensions.

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Q: A farmer has a 100 ft roll of fencing with which to fence a rectangular grazing field for her new…

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Q: . The sides of a cube are found to be 6 feet in length with a possible error of no more than 1.5…

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Q: A wire of length 12 m is divided into two pieces and the pieces are bent into a square and a circle.…

A: Let the circle will have x m and the square will have (12-x) m So the circumference of the circle =…

Q: A semi-elliptical goblet has a depth of 4 inches and its round opening has a width of 3 inches. It…

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Q: The sum of the sides of an isosceles triangle is 24ft. find the lengths of the sides that maximize…

A: Given:              Let ΔABC be an isosceles triangle with AB=AC.Let AD be the altitude of the…

Q: A long rectangular sheet of metal 30 inches wide is to be made into a gutter by turning up strips…

A: Let the length of the vertical strips along the tow sides is x inches. Then the length of the base…

Q: a rectange is 4 inches longer than it is wide. numerically its area exceeds its perimeter by 17.…

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Q: Two vertical poles, one 8 m high and the other 16 m high, stand 45 m apart on a flat field. A worker…

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Q: A farmer wants to construct a rectangular pigpen using [ 100 ] ft of fencing. The pen will be built…

A: Given data: The total length of fencing is 100 ft. Consider the length of AB=x. Consider the length…

Q: A rectangular field is four times as long as it is wide. If the perimeter of the field is 500 yards,…

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Q: a wire measuring 12 ft long is cut into two pieces. once piece is to be bent into a square and the…

A: The perimeter of a square is: Perimeter=4a Area of a square is: Area=a2 Where a is the edge of the…

Q: The letters of "FALCONS" should be evenly spaced across a 47-inch-wide banner, with no margins. Each…

A: Note that, the word "FALCONS" has 7 letters which should be evenly spaced across a 47-inch-wide…

Q: The maximum possible volume of a rectangular box with the sum of its twelve edges 60 cm is

A: Given 12 edges sum is 60, let C=60So, 4x+4y+4z=CV=xyz    =xy(14C-x-y)    =14Cxy-x2y-xy2 for x>0,…

Q: Two vertical poles, one 16 ft high and the other 24 ft high, stand 30 feet apart on a flat field. A…

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

Q: Two vertical poles, 8 ft and 16 ft high, stand 18 ft apart on a flat field. A worker wants to…

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Q: The length of a rectangular garden is 4 ft longer than its width. The garden has a wall along one…

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Q: A builder must fence all sides of 3 adjacent rectangular lots, each having 168 m2 of area. Front…

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Q: Find the dimensions of a rectangle with area 1000m2 whose perimeter is as small as possible.

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Q: Three equally sized corrals are constructed next to a river. if the area to be enclosed is 19600…

A: Use concept of minimizing of fencing

Q: A farmer wants to fence an area of 37.5 million square feet in a rectangular field and then divide…

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Q: The sides of a cube are found to be 6 feet in length with a possible error of no more than 1.5…

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Q: A rectangular field is three times as long as it is wide. If the perimeter of the field is 400…

A: Suppose that the width of a rectangular field is x then the length of the rectangular field is 3x.

Q: The length of a rectangle is 2 m longer than its width. If the perimeter of the rectangle is 24 m,…

A: Let w be the width of the rectangle. Now since the length is 2 m longer than the width, therefore…

Q: A 1000 square yard rectangular lot along a highway is to be fenced off such that one side of the…

A: Area of the rectangular yard:= 1000 square yard;         Fencing cost around the highway:=…

Q: Two posts, one 8 meters high and the other 12 meters high, stand 15 meters apart. They are to be…

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Q: A Normal window is in the shape of a rectangle surmounted by a semi-circle. What is the ratio of the…

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Q: A piece of wire 14 m long is cut into two pieces. One piece is bent into a square and the other is…

A: the total length of a wire is 14m  let the length of a square be x m so, the length of a circle will…

Q: In order to properly feed her animals, a rancher needs to enclose a total area of 4704 square feet…

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Q: An aquarium with rectangular sides and bottom (and no top) is to hold 5 gal. Find its proportions so…

A: Let the dimensions of a rectangular aquarium is Length =l Width=w Height=h Now, The volume is,…

Q: . A 1000 square yard rectangular lot along a highway is to be fenced off such that one side of the…

A: Explanation of the answer is as follows

Q: The length of a rectangle is 4 m longer than its width. If the perimeter of the rectangle is 32 m,…

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Q: A 4-pen kennel of 1,440 square feet is to be constructed as shown. The cost is $20 per foot for the…

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Q: A trapezoidal gutter is to be made, from a strip of metal 22 inches wide by bending up the edges. If…

A: Solution is here

Q: A cardboard box must have a volume of 144m3 and two vertical sides should be square. If the material…

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Q: 2 ends

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Q: A rectangular garden length is 2ft longer than its width has an area of 65ft. Find the dimensions of…

A: Let x be the width of the rectangular garden.Given, length is 2ft longer than its width and the area…

Q: A gutter with trapezoidal cross section is to be made from a long sheet of tin that is 15 inches…

A: Trapezoidal  and geometrical area

Q: A piece of wire 15 m long is cut into two pieces. One piece is bent into a square and the other is…

A: Given A piece of wire 15 m long is cut into two pieces. One piece is bent into a square and the…

Q: A rectangular tile has a length of 4X cm and width (x+3) cm. The area of a reactangle is less than…

A: Area of rectangle

Q: Two posts, one 8ft. high and the other 12ft high, stand 15ft. Apart. They are to be stayed by wires…

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Q: The top and bottom margins of a poster are each 15 cm and the side margins are each 10 cm. If the…

A: Let a be the width and b be the height of the poster. Let the area of the poster to be minimized be…

Q: Three of the sides will require fencing and the fourth wall already exists.If the farmer has 132…

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Q: The top and bottom margin of a poster are 6 cm and side margins are each 4cm. If the area of the…

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Q: The base of a rectangular prism shaped aquarium without a lid is made of slate and the sides are…

A: Here the size of the Aquarium be: l=x b=y h=z. Area of base=xy Volume=96=xyz  ...(1) Cost of slate…

Q: A farmer wants to fence an area of 37.5 million square feet in a rectangular field and then divide…

A: Consider the given information.