A graphing calculator is recommended.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 guidelines on page 237 to help you.A box with an open top is to be constructed from a rectangular piece of cardboard with dimensions 14 in. by 20 in. by cutting out equal squares of side x at each corner and then folding up the sides(see the figure)20 in.ххх14 inхXX(a) Find a function that models the volume V of the box280x 32x24x3XV(x)(b) Find the values of x for which the volume is greater than 230 in3. (Round your answers to three decimal places. Enter your answer using interval notation.)(c) Find the largest volume that such a box can have. (Round your answer to three decimal places.)in3

(a) Obtain the function that models the volume of the box as follows.

Answered: A graphing calculator is recommended.…

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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Similar questions

In these problems 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 guidelines on page 273 to help you. Minimizing Costs A rancher wants to build a rectangular pen with an area of 100m2 . (a) Find a funtions that models the lenghth of fencing required. (b) Find the pen dimensions that require the minimum amount of fencing.
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?
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?
Use your schools library, the Internet, or some other reference source to find real-life applications of approximations of functions.
In these problems you are asked to find a function that model a real-life situation and then use the model to answer questions about the situation. Use the guidelines on page 273 to help you. Dividing a Pen A rancher with 750 ft of fencing wants to enclose a rectangular area and then divide it into four pens with fencing parallel Lo one side of the rectangle (see the figure). (a) Find a function that models the total area of the tour pens. (b) Find the largest possible total area of the four pens.
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.
In these problems you are asked to find a function that models a real-life situation and use the model to answer question about the situation. Use the guidelines on page 273 to help you. Fencing a Garden plot A property owner wants to fence a garden plot adjacent to a road. As shown in the figure. The fencing next to the road must be studier and costs $5 per foot, but the other fencing costs just $3 per foot. The garden is to have an area of 1200ft2 . (a) Find a function that models the cost of fencing the garden. (b) Find the garden dimensions that minimize the cost of fencing. (c) If the owner has at most $600 to spend of fencing, find the range of length he can fence along the road.
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?

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