An LPG tank is to hold x cubic meter. It is constructed of a cylinder capped on top by a hemisphere. Find the dimensions of the most economical tank if the cylindrical part cost P100.00 per square centimeters to build while the hemisphere cost P150.00 per square centimeters.

Q: a worker has 750ft of fencing and he wants to build a fence enclosing a rectangular region and the…

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Q: A piece of wire 40 cm long is to be cut into two pieces . One piece wil bent to form a circle, the…

A: The total length of the wire is 40 cm and one piece is to be formed into a circle and another one is…

Q: 2. Your senior project is to design the most economical tomato soup can. The can must hold 400 cm³.…

A: Assume the height of the can be h and radius be r. Find the cost function C(r) for the can. Volume…

Q: If to produce 1 kg of mix A costs $12.50, 1 kg of mix B costs $12.40 and 1 kg of mix C costs $11.70,…

A: Given: Cost of 1 kg of mixture A=$12.50=$125 hundred of grams, Cost of 1 kg of mix B =$12.40=$124…

Q: manufacturer needs a piece of plastic shape of a right triangle with one leg 2cm longer than the…

A: Given query is to find the perimeter of the triangle.

Q: A fence is to be built to enclose a rectangular area of 280 square feet. The fence along three sides…

A: Area of rectangular place = 280 square feet.

Q: A playground with a rectangle shape with a 500 m^2 area is to be surrounded by a fence, with an…

A: topic - optimization

Q: You wish to cross the 11 m x 10 m courtyard without being detected by the two guards and escape…

A: Given: S=FD2             →(1)   for guard 1 &   S=116            →(2)  for guard 2 To calculate…

Q: Farmer Jones, and his wife, Dr. Jones, decide to build a fence in their field, to keep the sheep…

A:

Q: - The sum of the perimeters of an equilateral triangle and a square is 10. Determine the dimensions…

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Q: You want to install a 13.5 feet deep in-ground pool in your backyard but you are concerned about the…

A: The pool must be 13.5 deep. We can install a circular poor with a diameter of 10 feet i.e. radius of…

Q: You wish to cross the 11 m x 10 m courtyard without being detected by the two guards and escape…

A:

Q: If the nuts vendor has a fixed cost of $550 and every pack of nuts cost him $2.50 to produced. By…

A: Given problem is  :

Q: What is true when two chords intersect inside of a circle? Their intersection MUST go through the…

A: Consider a circle with two chord which intersect each other:

Q: A company needs to manufacture cylindrical cans out of tin, each of which must have both a bottom…

A: Solve by minimizing surface area

Q: A company needs to manufacture cylindrical cans out of tin, each of which must have both a bottom…

A:

Q: The sum of the lengths of all edges of a cube is 84 cm. 1.Find the volume V (in cubic centimeters)…

A: Solution: The objective is to find the volume and surface area of the cube

Q: 1. A 12-meter wire is cut into two pieces so that x meters will be used to form a circle and the…

A:

Q: Mary is sowing wildflower seeds in a rectangular flowerbed with length 10 yards and width 6 yards.…

A: Rectangular flowerbed: length = 10 yards  width =  6 yards Area of the rectangular flowerbed =…

Q: A firmer needs to protect his land of area 14400 square feet. He wants to use two types of fencing…

A: The area of the land is 14400 square feet. Now the land is in the form of a rectangle and the…

Q: You are the owner of a printing business and to support your preferred presidential candidate for…

A:

Q: n aluminum wire with a length of 2m will be cut into two pieces. One of the two pieces will be bent…

A: Given that: Total length of wire = 2m

Q: You wish to cross the 11 m x 10 m courtyard without being detected by the two guards and escape…

A: Red dot for gaurd 2 =(3,3)

Q: 2) Find the length of the legs of a right triangle whose hypotenuse is 26 cm and whose area is 120…

A:

Q: 2. During the planning of a birthday party, it is decided that the souvenir will be enclosed in a 80…

A: We will find cost function in terms of a single variable and then minimize it  For relative maximum…

Q: The cost of phone plan Q is $10 per month plus &0.14 per minute.phone plan R costs $7 per month plus…

A: Let x  denotes the number of minutes. Then cost of plan Q is  Qx=10+0.14x ⇒Q70=10+0.1470⇒Q70=19.8…

Q: 4. A 12-meter string is cut into two pieces so that x meters will be used to form a circle and the…

A:

Q: 4) An ice cream company is designing fancy glass containers for their ice cream. The containers will…

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Q: 2. Find the length and width of a rectangle that has an area of 64 square feet and a minimum…

A: Find the length and width of the rectangle

Q: The fencing of the left border costs $5 per foot, while the fencing of the lower border costs $1 per…

A: Find  left border ft = bottom border ft = garden area ft2.

Q: 2. Your senior project is to design the most economical tomato soup can. The can must hold 400 cm3.…

A: A round cylinder is a cylinder with a circular base and top. The volume is given by the expression…

Q: 1. A candy factory needs a box with a volume of 420 cubic inches. The height should be 2 inches less…

A: We have to find the dimensions of the box with a volume of 420 cubic inches.

Q: Some airlines have restrictions on the size of items of luggage that passengers are allowed to take…

A:

Q: Joe wants to make a right square pyramid tent and is considering two sizes. He will either make one…

A: Solve the following

Q: According to the shipping regulation of a company, the girth plus the length of a parcel sent by…

A:

Q: A farmer needs to enclose two different breads of animals in a rectangular area. The two breads are…

A: Note that, 3 widths and 1 length is required. Also, given that the perimeter of the fence is 185…

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 container manufacturer plans to make rectangular boxes whose bottom and top measure x by 3x. The…

A: We need to find height.

Q: fence is to be built to enclose a rectangular area of 280 square feet. The fence along three sides…

A: Rectangular area=280 square feet   Let the length of rectangle=x   Let the width of rectangle…

Q: the two endpoints of a bench measure 4/3x centimeters and 2/3x centimeters, then the midpoint is ___…

A: Given query is to find the midpoint, perimeter and the side  of the different shapes.

Q: $24 is available to make a rectangular storage container with a square base and open top. If the…

A:

Q: A gardener with 600 meters of available fencing wishes to enclose a rectangular field and then…

A: Given problem:- A gardener with 600 meters of available fencing wishes to enclose a rectangular…

Q: Suppose a company has fixed costs of $57,600 and variable costs of 4 9 x + 222 dollars per unit,…

A: Given that, Fixed cost =$57600 Variable cost =49x+222 Selling price =2054-59x

Q: 3 4 5 What is true when two chords intersect inside of a circle? The sum of the two lengths of one…

A:

Q: 2. Suppose Kim can run at 8 miles per hour and swim at 2 miles per hour. As shown in the figure…

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Q: 4. Find the dimensions of the least expensive rectangular box which is three times as long as it is…

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Q: A 4-pen kennel of 1,960 square feet is to be constructed as shown. The cost is $20 per foot for the…

A: The area of the rectangular land is 1800 sq feet. let the side parallel to divider be y and the side…

Q: 2. A rectangular lot adjacent to a highway is to be enclosed by a fence. If the fencing costs P250…

A: The rectangular plot has length x  and width y cost of the fence is 250(length along highway )…

Q: 5. The area of the rectangular banner should be 6.75 square meters. If the length is to be thrice…

A: