8. Enclosing a Field You have 16 miles of fence that you will use to enclose a rectangular field. a. Draw a picture to show that you can arrange the 16 miles of fence into a rectangle of width 3 miles and length 5 miles. What is the area of this rectangle? b. Draw a picture to show that you can arrange the 16 miles of fence into a rectangle of width 2 miles and length 6 miles. What is the area of this rectangle? c. The first two parts of this exercise are designed to show you that you can get different areas for rectangles of the same perimeter, 16 miles. In general, if you arrange the 16 miles of fence into a rectangle of width w miles, then it will enclose an area of A = w(8 – w) square miles. i. Make a graph of the area enclosed as a function of w, and explain what the graph is showing.

8. Enclosing a Field You have 16 miles of fence that you will use to enclose a rectangular field. a. Draw a picture to show that you can arrange the 16 miles of fence into a rectangle of width 3 miles and length 5 miles. What is the area of this rectangle? b. Draw a picture to show that you can arrange the 16 miles of fence into a rectangle of width 2 miles and length 6 miles. What is the area of this rectangle? c. The first two parts of this exercise are designed to show you that you can get different areas for rectangles of the same perimeter, 16 miles. In general, if you arrange the 16 miles of fence into a rectangle of width w miles, then it will enclose an area of A = w(8 – w) square miles. i. Make a graph of the area enclosed as a function of w, and explain what the graph is showing.

Algebra and Trigonometry (6th Edition)

6th Edition

ISBN:9780134463216

Author:Robert F. Blitzer

Publisher:Robert F. Blitzer

ChapterP: Prerequisites: Fundamental Concepts Of Algebra

Section: Chapter Questions

Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...

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Question

8. Enclosing a Field You have 16 miles of fence that
you will use to enclose a rectangular field.
a. Draw a picture to show that you can arrange
the 16 miles of fence into a rectangle of width
3 miles and length 5 miles. What is the area
this rectangle?
b. Draw a picture to show that you can arrange
the 16 miles of fence into a rectangle of width
2 miles and length 6 miles. What is the area
this rectangle?
c. The first two parts of this exercise are designed
to show you that you can get different areas for
rectangles of the same perimeter, 16 miles. In
general, if you arrange the 16 miles of fence into
a rectangle of width w miles, then it will enclose
an area of A = w(8 – w) square miles.
i. Make a graph of the area enclosed as a
function of w, and explain what the graph is
showing.

ii. What width w should you use to enclose the
most area?
iii. What is the length of the maximum-area
rectangle that you have made, and what kind
of figure do you have?

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