SOLUTION: Application Assignment #1
Polynomials
Application Practice
Answer the following questions. Use Equation Editor to write mathematical expressions and equations. First, save
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Polynomials
Application Practice
Answer the following questions. Use Equation Editor to write mathematical expressions and equations. First, save
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Question 259594: Application Assignment #1
Polynomials
Application Practice
Answer the following questions. Use Equation Editor to write mathematical expressions and equations. First, save this file to your hard drive by selecting Save As from the File menu. Click the white space below each question to maintain proper formatting.
Part One
1. You are employed by Fences R Us, an aluminum fencing company that specializes in building fenced enclosures. Your job is to build these enclosures on your clients properties. One client has purchased a certain length of fencing and wants to enclose the largest possible area in her yard. All gates are included in the fencing.
a. Suppose that the client needs 100 feet of fencing. Choose several values for the width of the rectangle and determine the corresponding lengths and areas of the rectangle.
Width (in feet) Length (in feet) Area (in sq. feet)
20 30 600sq
10 40 400sq
35 15 525sq
25 25 625sq
What is the relationship between the length and width of rectangles with a perimeter of 100 feet?
p=2 (l + w)
So, the perimeter is 100 feet
b. Determine whether there is a rectangle enclosed by 100 feet of fencing that has the following areas:
400 square feet h x w=a 10*40=400
500 square feet h * w = a
700 square feet
c. Let c represent the length of a rectangle enclosed by 100 feet of fencing. Write an expression for the width of the rectangle in terms of c.
d. Express the area A of a rectangle with perimeter 100 feet as a function of the length c of one of its sides.
e. Simplify this function so that it reads as a quadratic equation.
2. If you were to sketch the graph of the function in 1e, where the x-axis is labeled as your length (in feet) and the y-axis is labeled as your area (in square feet), you will see that it has the shape of a parabola.
Use the graph to determine the dimensions of a rectangle with perimeter 100 feet and the following two areas:
o 400 square feet & 500 square feet
Explain how 700 square feet is not a possible area in this situation.
3. Use the function in 1e to algebraically determine the length c of a rectangle with perimeter 100 feet. and the following areas:
400 square feet
500 square feet
4. Use the function in 1e to algebraically support the conclusion that 700 square feet is not a possible area in this situation.
5. What is the maximum value of the function in 1e? Explain how you arrived at this conclusion and what does the maximum value represent.
6. What is the corresponding length c of the rectangle? Explain how you arrived at this conclusion.
7. What is the most specific name for the rectangle with perimeter 100 feet and length c found in #6?
You can put this solution on YOUR website! Can you do some editing and ask questions where you need help instead of cutting and pasting your entire assignment? THe tutors are willing to help but don't want to do your entire assignment for you. Thanks!
