Concept explainers
To find:
A function that models area in terms of width.
Answer to Problem 1P
Solution:
The area of the building modeled by the function
Explanation of Solution
The model we want is a function that gives the area of the rectangular building.
For the rectangular building,
There are two varying quantities: Length and Width.
But the function we want depends on the width w.
We must express the length in terms of its width w. Because the length of the building is three times as long as it is wide. If we let length be l, then we have,
The model is the function A that gives the area of the rectangular building for any width w.
Thus, the area of the building modeled by the function
Final statement:
The area of the building modeled by the function
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Chapter 2 Solutions
Algebra and Trigonometry (MindTap Course List)
- 19-32 In these problems you are asked to find a function that models a real life situations and then use the model to answer questions 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 sturdier and costs 5 per foot, but the other fencing costs just 3 per foot. The garden is to have an area of 1200 ft2. 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 on fencing, find the range of lengths he can fence along the road.arrow_forwardIn 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.arrow_forwardIn 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.arrow_forward
- In these problem you are asked to find a function that models a real-life situation. Use the principles of modeling described in this Focus to help you. Area A rectangular building lot is threetimes as long as it is wide. Find a function that models its area A in terms of its width w.arrow_forwardIn these problem you are asked to find a function that models a real-life situation. Use the principles of modeling described in this Focus to help you. Area An isosceles triangle has a perimeter of 8 cm. Find a function that models its area A in term of the length of its base b.arrow_forwardIn 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.arrow_forward
- Algebra and Trigonometry (MindTap Course List)AlgebraISBN:9781305071742Author:James Stewart, Lothar Redlin, Saleem WatsonPublisher:Cengage LearningCollege AlgebraAlgebraISBN:9781305115545Author:James Stewart, Lothar Redlin, Saleem WatsonPublisher:Cengage Learning