9. (a) Given the perimeter of a rectangle is 100 meters. What dimensions should be to get the maximum area? (b) Given the area of a rectangle is 64 meters. What dimensions should be to get the minimum perimeter? square

Q: 15. You want to put a fence around a rectangular field and then subdivide the field into 4 smaller…

A: Let's find.

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. A three-sided fence is to be built next to a straight section of river, which forms the fourth…

A:

Q: 2. An orange grower has 400 crates of fruit ready for market and will have 20 m day the grower…

A: We will create function and use derivative to maximize it

Q: 2. What is the minimum product of two numbers that differ by 15? What are the two numbers?

A: Let one number be x and another number be x+15 So their product=x(x+15)=x2 + 15x =f(x) (say)

Q: 3. An architect is asked to design a game room in the shape of an isosceles trapezoid, where the non…

A: I am attaching image so that you understand each and every step.

Q: 1. The sum of two positive numbers is 10. Find these numbers if the sum of their squares is a…

A:

Q: A company has determined that when x hundred dulcimers are​ built, the average cost per dulcimer can…

A: The average cost per duclimer  can be estimated by the following function…

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A:

Q: How do I find the minimum number for the upper quarter of the time to pass a kidney stone  .…

A: Obtain the minimum number for the upper quarter of the time to pass a kidney stone. The minimum…

Q: Suppose you have a 2.5 grade point average in 3 courses. What is the minimum average you can have in…

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Q: 1000 7. If a rectangular fence is supposed to have 3 pens, and in total enclose feet find the…

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Q: 5. A farmer wants to fence an area of 9600 square feet in a rectangular field and then divide it in…

A:

Q: 5. An open rectangular box with a square base is to contain 500 m³ . What is the minimum cost if the…

A: A open rectangular box with a square base contain 500 m^3

Q: 8. The area of a rectangle whose perimeter is a fixed 80 feet is given by A 40w – w² , where w is…

A: Perimeter of rectangle is 80 feet p=80 2(l+w)=80 l+w=40l=40-w Area of rectangle:- A=lw =(40-w)w…

Q: 3. If the sum of two numbers is C, find the minimum value of the sum of their squares.

A:

Q: If the price for smoothie supplies which is $35 increases by 5%, what is the minimum price that a…

A: Price of smoothie=$35 After 5% increase in price = 35+35×5100=$36.75

Q: An open box is to be made from a piece of cardboard, 15 inches by 15 inches, by cutting equal…

A:

Q: A box is to be constructed from a sheet of cardboard that is 20 cm by 60 cm by cutting out squares…

A: Volume of the cuboid , V= (length)(Breadth)(height)

Q: A courier service will deliver a package only if the length plus girth does not exceed 96 inches.…

A: NOTE: Refresh your page if you can't see any equations. . length L=x width W=x height H=y the…

Q: 9. A box with square bottom and no top is to contain 32 cubic inches Find the dimensions that will…

A: Recall the following. The volume of box with square base of side length x and height of length l is…

Q: A courier service will deliver a package only if the length plus girth does not exceed 96 inches.…

A: As per given  We have to determine dimension of rectangle box

Q: 8. The area of a rectangle whose perimeter is a fixed 80 feet is given by A= 40w– w² , where w is…

A:

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

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

Q: 19. A piece of wire of length 1 meter is cut into two parts, one of which is bent into the shape of…

A:

Q: 1. Find 2 numbers whose sum is 23 and whose product is a maximum. 2. Find the dimension of a…

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Q: If an open box is to be made using a square sheet of tin, 20 inches by 20 inches, by cutting a…

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Q: 4. A rectangular box is to be made from a piece of cardboard 15cm by 24 cm by cutting equal squares…

A: A rectangular box is to be made from a piece of cardboard 15 cm by 24 cm by cutting equal squares…

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: A wire of length L is cut into pieces, one being bent to form a square and the other form an…

A: Assuming that the wire is cut in 2 pieces of length x and L-x where the first is used to make a…

Q: manufacturer estimates that the cost (C) of production of (x) units of a certain item is ? = 40? −…

A: Given query is to find the production level for minimum cost.

Q: 6. A square sheet of cardboard of side 12 in. square is used to make an open box by cutting out…

A:

Q: 6. The sum of two numbers is k. Find the minimum value of the sum of their cubes.

A: Minimum value of the sum of their cubes is

Q: Karl benedict, the president of mathematics club, proposed a project to put up a rectangular math…

A: We have to maximize the area of rectangle.

Q: A sheet of paper for a poster contains 18 cm² of area. Tha margins at the top bottom are 0.75 cm and…

A: Let dimensions of paper piece  are x cm and y cm.

Q: An open box of maximum volume is to be made from a square piece of material, 24 inches on a side, by…

A:

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: 1. A rectangular page is to contain 24 square inches of print. The margins at the top and bottom of…

A: The solution is given in the next steps.

Q: 4. A home improvement contractor is painting the walls and ceiling of a rectangular room. The volume…

A:

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: What should the dimensions of the poster be so that the least amount of poster is used?

A: Assume that, x = length of the printed space y = height of the printed space Then, Length of the…

Q: b) We are going to fence in a rectangular field. If we look at the field from above the cost of the…

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Q: 6) A rectangular page is to contain 24 square inches of print. The margins at the top and bottom of…

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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: Solve the given item on a separate sheet of paper. A rectangular box with open top and has a square…

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Q: 2. The sum of two positive real numbers x and y is 120. Find the values of x and y that will…

A:

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

A:

Q: A farmer wants to fence in an area of 1.5 million square feet in a rectangular field and then divide…

A: Note:- We’ll answer the first question since the exact one wasn’t specified. Please submit a new…

Q: A management company is going to build a new apartment complex. They know that if the complex…

A: To find the number of apartments for which the cost is minimum and also find the minimum cost.

Q: The cables on a suspension bridge can be modeled by h = 0.0076s2 − 0.76s + 40, where h is the height…

A: