Constructing cages One thousand feet of chain-link fence is to be used to construct six ahimal cages, as shown in the figure. (a) Express the width y as a function of the length x. (b) Express the total enclosed area A of the cages as a func- tion of x. (c) Find the dimensions that maximize the enclosed area.

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A: Given that, A rectangle has one vertex on the line y=10-x, x>0, another at the origin, one of the…

Q: 64. Making a Rain Gutter A rain gutter is formed by bending up the sides of a 30-in.-wide…

A: Let the measure of other 2 sides be x inches each . Since , the sheet metal is 30 inch wide , the…

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A: Note: As per the honor code, only one question can be answered at a time. Please post another…

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Q: The reproduction function for a sardine is  f(p) = −0.0004p2 + 2p, where p and  f(p)  are in hundred…

A: For the maximum sustainable yield f'(p)=0 We differentiate both sides with respect to p.

Q: A rain gutter is formed by bending up the sides of a 38-in.-wide rectangular metal sheet as shown in…

A: Width of the gutter is 38 inches. Let w be the width in the middle.From the diagram , find the width

Q: The reproduction function for king salmon in a sea is f(p) = −1/4p2 + 4.5p, where p and f(p)are in…

A:

Q: 2. A Norman window is constructed by adjoining a semicircle to the top of an ordinary rectangular…

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Q: In the problem you are asked to find a function that models a real life-life situation and then use…

A: (a) To find: The function that model the length of the the fencing required: Given: The Area of the…

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A: Here we use the application of derivative to find the solution

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A: Given a piece of cardboard which dimensions has 10 inch by 16 inch

Q: 11. A horse breeder plans to construct a corral next to a horse barn that is 50 feet long, using all…

A: Given :- A horse breeder plans to construct a corral next to a horse barn that is 50 feet long,…

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A: Consider the provided question, The hourly number of units y produced after t hours of production is…

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A: Given

Q: Analysis of daily output of a factory during a 8-hour shift shows that the hourly number of units y…

A:

Q: A school wishes to form three sides of a rectangular playground using 360 meters of fencing. The…

A: As shown in the figure below, Let ABCD is the ground of the school, where AB=CD=x and AB+BC+CD=360…

Q: 8. Suppose that a family wants to fence in an arca of their yard for a vegetable garden to keep out…

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A: The base of the box is a square with side length x. The height of the box is given as h. The Surface…

Q: The reproduction function for a sardine is f(p) = -0.0005p2 + 2p, where p and f(p) are in hundred…

A: Given function :

Q: 79. Minimum Average Cost The average cost per hour in dollars, C, of producing x riding lawn mowers…

A: Given data: a.) Given function is C¯(x) = 0.3x2+21x-251 + 2500x,  which represents average cost per…

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Q: In exercises 7 - 8, find a formula for the described function and state its domain. 7. The area of a…

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Q: Analysis of daily output of a factory during a 8-hour shift shows that the hourly number of units y…

A: The output of the factory is given by- y=140t+12t2-t3,0≤t≤8 To maximize the hourly units- dydt=0

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A: Find your answer below

Q: 1. 1500 feet of chain link fence are to be used to construct six animal cages as the following…

A: Let the animal cages be in the form of square as seen in the figure. Apply the properties of square…

Q: A school wishes to enclose its rectangular playground using 320 meters of fencing. Suppose that a…

A: This question related to application of derivatives.

Q: 89. Volume of a Box An open box is to be constructed from a piece of cardboard 20 cm by 40 cm by…

A: Given Length of cardboard =40cm Width of cardboard=20cm

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A: To find out the function that models the amount of fencing required.

Q: The reproduction function for king salmon in a sea is f(p)=p² + 7.5p, where p and f(p) are in…

A:

Q: A farmer wants to enclose a rectangular area with 400 feet of fence. In order to maximize the area…

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Q: A rectangular frame of uniform depth for a shadow box is to be made from a 36-in. piece of wood. a.…

A: a) Length =y and width=x So perimeter= 2(x+y) Given perimeter=36 in So,

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A: Answer(a)

Q: Maximizing the Volume of a Box An open-top box is to be made from a 30 in. by 40 in. piece of…

A: Let's solve given maximizing volume of a box problem.

Q: (a) Use a graph to estimate the absolute maximum andminimum values of the function to two decimal…

A:

Q: Making a Rain Gutter A rain gutter is formed by bending up the sides of a 30-in.-wide rectangular…

A:

Q: Analysis of daily output of a factory during a 8-hour shift shows that the hourly number of units y…

A:

Q: Making a Rain Gutter A rain gutter is formed by bending up the sides of a30-in.-wide rectangular…

A: Solution:GivenA rain gutter is formed by bending up the sides of a 30-in widerectangular metal…

Q: A school wishes to enclose its rectangular playground using 160 meters of fencing. Suppose that a…

A: Use derivative and property of rectangle.

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A: Given,

Q: 15. A farmer wishes to enclose a rectangular region. He has 500 feet of fencing and plans to use his…

A: (a) The length of the fencing is 500 feet that is the perimeter of the region. Consider the…

Q: The figure shows a rectangle with two vertices on a semicircle of radius 3 and two vertices on the…

A: The figure shows a rectangle with two vertices on a semicircle of radius 3 and two vertices on the…

Q: a) A farmer plans to fence a rectangular pasture adjacent to a river. The pasture must contain…

A: Given: a) A farmer plans to fence a rectangular pasture adjacent to a river. The pasture must…

Q: Dianna has available 120 yards of fencing and wishes to enclose a rectangular area. ​(a) Express the…

A: a) Diana has available 120 yards of fencing and wishes to enclose a rectangular area. Let the length…