In this problem you are asked to find a function that models a real-life situation and then use the model to answer questions about the situation. Use the quldellnes onpage 237 to help you.A wire 18 cm long is cut Into two pleces, one of length x and the other of length 18 - x, as shown In the figure. Each piece is bent Into the shape of a square.18 cm18 x(a) Find a function that models the total area A enclosed by the two squares in terms of x.A(x) =(b) Find the value of x that minimizes the total area of the two squares.X =cmNeed Help?Read It

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Answered: A wire 18 cm long is cut Into two…

College Algebra

7th Edition

ISBN:9781305115545

Author:James Stewart, Lothar Redlin, Saleem Watson

Publisher:James Stewart, Lothar Redlin, Saleem Watson

Chapter2: Functions

Section: Chapter Questions

Problem 26P

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In this problem you are asked to find a function that models in real life situation and then use the model to answer questions about the guidelines on page 273 to help you. Minimizing Time A man stands at a point A on the bank of a straight river, 2 mi wide. To reach point B, 7 mi downstream on the opposite bank, he first rows his boat to point Pon the opposite bank and then walks the remaining distances x to B, as shown in the figure. He can row at a speed or 2 mi/h and walk as a speed of mi/h (a) Find a function that models the time needed for the trip. (b) Where should he land so that he reaches B as soon as possible?
How do the graphs of the functions f(x)=x2 and f(x)=x21 differ? We graphed them at the start of this section. What is the difference between their graphs? How are their graphs the same?
Use your schools library, the Internet, or some other reference source to find real-life applications of approximations of functions.
Suppose you have a job that pays $8.50 per hour and you work anywhere from 10 to 40 hours per week. a. Write an equation, with a restriction on the variable x, that gives the amount of money, y, you will earn for working x hours in one week. b. Use the function rule you have written in part (a) to complete Table 4. c. Construct a line graph from the information in Table 4. d. State the domain and range of this function.
When examining the formula of a function that is the result of multiple transformations, how can you tell a horizontal shift from a vertical shift?
In this problem you are asked to find a function that models in real life situation and then use the model to answer questions about the guidelines on page 273 to help you. Bird Flight A bird is released from point A on an island. 5 mi from the nearest point Bon a straight shoreline. The bird flies to a point C on the shoreline and then flies along the shoreline to its nesting area D (see the figure). Suppose the bird requires 10 Kcal/mi of energy to fly over land md 14 kcal/mi to fly over water. a) Use the fact that energy used = energy per mile X miles flown to show that the total energy used by the bird is modeled by the function E(x)=14x2+25+10(12x) (b) If the bird instinctively chooses a path that minimizes its energy expenditure, to whatpoint does it fly?
What is the difference between the input and the output of a function?
Describe why the horizontal line test is an effective way to determine whether a function is one-to-one?
When examining the formula of a function that is the result of multiple transformations, how can you tell a horizontal stretch from a vertical stretch?
When examining the formula of a function that is the result of multiple transformations, how can you tell a reflection with respect to the x-axis from a reflection with respect to the y-axis?
How do you find the domain for the composition of two functions, fg ?
In these problems you are asked to find a function that models a real-life situation. Use the principals of modeling described in this Focus to help you. Distance They ships leave port at the same time. One sails south at 15 mi/h, and the other sails east at 20 mi/h. Find a function that models the distance D between the ships in terms of the time t (in hours) elapsed since their departure.

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