Carlos wants to build a rectangular enclosure for his animals. One side of the pen will be against thebarn, so he needs no fence on that side. The other three sides will be enclosed with wire fencing. IfCarlos has 400 feet of fencing, you can find the dimensions that maximize the area of the enclosure.a. Let w be the width of the enclosure (perpendicular to the barn) and let I be the length of theenclosure (parallel to the barn). Write a function for the area A of the enclosure in terms of w.A(w) =b. What width w would maximize the area?w =ftc. What is the maximum area?A =square feetQuestion Help: D Post to forumSubmit QuestionescG Search or type URL@#2$24QWEtabD FくO

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Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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A taxi company charges for rides according to the following. The cost for every ride starts at $3.50, then the cost increases by $0.50 every quarter-mile of the taxi ride. i) Write a function for the cost C of the ride, in terms of the distance d of the taxi ride. ii) If it is 13 miles to the airport, how much will it cost to take a taxi there? iii) How far can you travel for $16.00?
A salesperson is paid a base salary of $2000 a month plus a 4% commission on their sales of x dollars. Write a linear function P(x) that represents the salesperson's total monthly pay, P (in dollars) in terms of their sales x. Then use that linear function to determine the value of x that will result in a monthly pay of $3120. Enter just the value of x that will result in a monthly pay of $3120 in the answer box. x=? dollars
A rectangular parcel of land has width, w feet. The length of the diagonal, d, between opposite corners is 18 feet more than the length of the parcel. Note that d is lowercase. (a) Express the length, L, of the parcel as a function of d. (b) Express the width, w, of the parcel as a function of d. (c) Express the area, A, of the parcel as a function of d. L = W = A = (d) Suppose a fence is to be built around the perimeter of the rectangular parcel of land. The fencing material will cost $25 per foot. Express the total cost, C, of fencing the parcel as a function of d. C =
A packaging company will only accept packages for shipment if the sum of its height and perimeter of the base is not more than 300 inches. Write a function to represent the volume, V, of a box with a square base, with sum of the height and perimeter of the base equal to 300 inches.
According to the postal service in the United States, first class mail is used for personal and business correspondence. Any item that is sent by mail, could be sent first class. Includes postcards, letters, large envelopes, and small packages. Maximum weight is 13 ounces. The following function is used to calculate the cost of mailing a first class letter, where x is the weight of the package in ounces. Calculate the cost in dollars of shipping a package first class for the following weights: A letter weighing 4.3 ounces: ____ dollarsA postcard that weighs 0.4 ounces: ____ dollarsA package weighing 12.2 ounces: ____ dollars
A party planner needs to figure out how much it will cost her client to rent a space and pay person for meals. If the cost of the rental space is 40,000and the price per person for food is 500. Construct a function that shows the total cost for any number of people in attendance.
Jeff delivers pizza for Papa Jim’s Pizza. Papa Jim’s pays Jeff $6.75 per hour. In addition to this hourly rate, Jeff earns $0.65 for every pizza he delivers. Write the function that describes Jeff’s wages, where x represents the number of pizzas he delivers during a 8-hour shift. If Jeff works a 8-hour shift and delivers 67 pizzas during his shift, how much money will he earn?
A 1000-square-foot rectangular plot of land is going to be divided into three equal-sized, adjacent playgrounds (see diagram). Find the number of feet of fencing required as a function of x. (Note: there is only one fence between the playgrounds, not two.) Answer:
Each horse you own eats 4 bales of hay per month. Each bale of hay costs $15. a. Create a function called f whose input is the number of horses you own and whose output is the number of bales of hay eaten per month. Use x as your input variable. b. Create a function called g whose input is the number of bales of hay eaten per month and whose output is the total cost. Use x as your input variable. c. Create a function called / whose input is the number of horses you own and whose output is the total cost. Use x as your input variable. d. If you own 5 horses, use your functions f, g and h to find out how many bales of hay are eaten per month and how much money this will cost. e. Draw a diagram of the three functions f, g, and h. Show the input and output of each function, and their relationship.
Fill in the blanks outside the table showing the changes in the x- and y-values. Then, answer the questions. 1) a. Is it a linear function? b. Why/Why not? -3 1. -2 -1 3 4 1 5 2) a. Is it a linear function? b. Why/Why not? -5 2 1. -2 4 -1 6 1. 2 8 1. 10 3) -10 a. Is it a linear function? 1. -5 b. Why/Why not? 4 2 5 1. 10 -3 4) y a. Is it a linear function? b. Why/Why not? -1 -9 ]. -4 1. 1 1. 3 7 11 1. 11 15
The cost of renting a canoe is $20 for the first 4 hours and $4 per hour for additional hours. Write a piecewise function that represents the cost of renting a canoe for 0 to 8 hours.

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