piece of wire 10 m long is cut into two pieces. One piece is bent into a square and the other is bent into an equilateral triangle. How should the wire be cut so that the total area enclosed is (a) A minimum?

Q: A closed rectangular box has volume 60 cm³. What are the lengths of the edges giving the minimum…

A:

Q: A box with a square base and open top must have a volume of 62,500 cm. Find the dimensions of the…

A: Topic- Application of Derivative

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A:

Q: A fence must be built in a large field to enclose a rectangular area of 25,600 m?. One side of the…

A: Let x be the length of the two end sides and  y be the length of side which has fence already.…

Q: Find the minimum cost of a rectangular box that is three times as long as it is wide and which holds…

A: Given  that length is three times as long as width so let width be x then length will be 3x  let…

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A:

Q: A farmer uses 2000 feet of fence to enclose a rectangular region and also to subdivide the region…

A: Let the width of the fence be:  w Let the length of the fence be:  l

Q: what are the dimensions of the right hexagonal prism of minimum surface whose volume is 36 cubic…

A: This is a problem of optimization.

Q: A square piece of cardboard of side a is used to make an open-top box by cutting out a small square…

A: Since, a square piece of cardboard of side 'a' is used to make an open-top box by cutting out a…

Q: You are to construct an open rectangular box from 12 ft2 of material. What dimensions will result in…

A:

Q: A box with a square base and open top must have a volume of 32 000 cm³. Find th dimensions of the…

A: Given: The Volume of square box =32000cm3 To find its dimention

Q: A piece of wire 10 m long is cut into two pieces. One piece is bent into a square and the other is…

A:

Q: 2. Helmut, an ostrich farmer, wants to build a rectangular fenced enclosure divided into five…

A: Given that, Total length= 120 m

Q: A rectangular sheet of metal having dimensions 20cm by 12cm has squares removed from each of the…

A: A rectangular sheet of metal having dimensions 20cm by 12cm has squares removed from each of the…

Q: How do you solve for the minimum surface area of a sphere that circumscribes a cone in which that…

A: Let R be radius of inner sphere and r be radius of cone. and let h be the height of cone.

Q: Of all boxes with square base and a volume of 512 cm, which one has the minimum surface area? (Give…

A:

Q: A wire of length L is available for making a circle and a square. How should the wire be divided…

A: In the question we have to find the length of wire where it should be divided to maximize the area…

Q: A landowner wishes to use 2 miles of fencing to enclose a rectangular region of maximum area. 1.…

A:

Q: A rectangular lot having an area of 5000 sq meters is to be fenced on three sides Find the minimum…

A:

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: 4. The volume of an open box with square base is 256 cu. in. Find the dimension if the material used…

A: Lets assume  length of base = x in width = x in ( as it is square base ) height of box = y

Q: (1 point) A closed rectangular box has volume 26 cm³. What are the lengths of the edges giving the…

A: let length x and width y  and height z of the box the total surface Area S=2xy+xz+yz  -----(1) Given…

Q: A piece of wires 10 m long is cut into two pieces. One piece is bent into a square and the other is…

A: Let the square be cut =yThen the equilateral triangle will be =10-yTotal area=Area of square+Area of…

Q: A cylinder with no top is to have a volume of 100π cubic centimeters. Find the minimum possible…

A: To find the minimum possible surface area of the given type of cylinder.

Q: A cylindrical can has a volume of 1024r cm. What dimensions yield the minimum surface area?

A:

Q: A poster of area 6000 cm2 has blank margins of 10 cm wide on the top and bottom and 6 cm wide on the…

A: SOLUTION-

Q: Find the dimensions of a rectangle of maximum area inscribed in a circle of radius 4. (Must show…

A: Let ABCD be the rectangle inscribed in the circle of radius 4. AC and BD are the diameters of length…

Q: A metal wire of length 80 cm is cut into two parts such that one part is 4k cm long. Each part of…

A:

Q: A rectangular tank with a square​ base, an open​ top, and a volume of 37,044 ft3 is to be…

A: Given,Volume of the rectangular tank = 37044 ft3

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…

Q: Two poles, one 6 meters tall and one 15 meters tall, are 20 meters apart. A length of wire is…

A:

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

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,…

Q: A piece of wiren 10 m long is cut into two pieces. One piece is bent into a square and the other is…

A: Length of the wire is 10 m. Let the length used for the square be x. Thus, the length used for…

Q: A tube of lip balm has a height of 2.75 inches and a diameter of 0.75inches.  a. if the cap on the…

A: Part (a):Diameter of the lip balm tube, d = 0.75 inches. Thus, the radius of the tube is r = d/2 =…

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

A:

Q: A poster is to contain 300 cm2 of printed matter with margins of 10 cm at the the top and bottom and…

A: We have, A poster is to contain 300 cm2 of printed matter with margins of 10 cm at the the top and…

Q: A rectangular tank with a square base, an open top, and a volume of 8788 ft 3 is to be constructed…

A: A rectangular tank has square base Let x be the base of the tank  and y be the height  x is the…

Q: A closed rectangular box has volume 22 cm3. What are the lengths of the edges giving the minimum…

A: Minimization problem

Q: A piece of wire 10 m long is cut into two pieces. One pieceis bent into a square and the other is…

A: To find: The way to use the wire such that the area enclosed by the triangle and square would be…

Q: Find the minimum cost of a rectangular box of volume 200 cm³ whose to

A:

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

A: to find:- dimensions of the rectangle. minimum perimeter.

Q: A open-top box is to be made from a 24 in by 36 in piece of cardboard by removing a square from each…

A:

Q: A rectangular  box has a square base with edges at least 10cm long.  It has no top, and the total…

A: Given: let's side of base of rectangular box is x+10cm, x+10cm and height is h cm

Q: A 60 m long pipe of metal is cut into two pieces. One piece is used to form a square and the other…

A: Perimeter of square =4a 4a=x Perimeter of triangle =3b 3b=60-x b=(60-x)/3

Q: Brittany needs to construct a cylinder from a single sheet of metal with a perimeter of 2,148 mm.…

A: Given that a single sheet with perimeter 2148 mm.

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

A:

Q: A rectangular tank that is 1372 ft° with a square base and open top is to be constructed of sheet…

A: The tank with minimum weight is the one with minimum surface area. Since the base is square, its…