8) A decade from now, you reach your early twenties, decide you have an unignorable passion for milk, and go off into the country to start a dairy farm. The cows will be housed in a large rectangular pen divided in half into two smaller pens by a piece of fencing (to keep rival cows separated), as shown below. You have a total of 100 feet of fencing to use for the large rectangular pen and its dividing fence. Let the dimensions of each of the two smaller pens be l and w, as shown. a) Write a function A(w) that gives the total area A of the pens in terms of w. b) Without using your graphing calculator or Desmos, determine the exact dimensions l and w that maximize the total area of the pens for the cows. Show your work.
8) A decade from now, you reach your early twenties, decide you have an unignorable passion for milk, and go off into the country to start a dairy farm. The cows will be housed in a large rectangular pen divided in half into two smaller pens by a piece of fencing (to keep rival cows separated), as shown below. You have a total of 100 feet of fencing to use for the large rectangular pen and its dividing fence. Let the dimensions of each of the two smaller pens be l and w, as shown. a) Write a function A(w) that gives the total area A of the pens in terms of w. b) Without using your graphing calculator or Desmos, determine the exact dimensions l and w that maximize the total area of the pens for the cows. Show your work.
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,...
Related questions
Topic Video
Question
8.0 refer to image
Transcribed Image Text:8) A decade from now, you reach your early twenties, decide you have an unignorable passion for
milk, and go off into the country to start a dairy farm. The cows will be housed in a large rectangular
pen divided in half into two smaller pens by a piece of fencing (to keep rival cows separated), as
shown below. You have a total of 100 feet of fencing to use for the large rectangular pen and its
dividing fence. Let the dimensions of each of the two smaller pens be l and w, as shown.
a) Write a function A(w) that gives the total area A of the pens in terms of w.
b) Without using your graphing calculator or Desmos, determine the exact dimensions l and w
that maximize the total area of the pens for the cows. Show your work.
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 6 steps
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, algebra and related others by exploring similar questions and additional content below.Recommended textbooks for you
Algebra and Trigonometry (6th Edition)
Algebra
ISBN:
9780134463216
Author:
Robert F. Blitzer
Publisher:
PEARSON
Contemporary Abstract Algebra
Algebra
ISBN:
9781305657960
Author:
Joseph Gallian
Publisher:
Cengage Learning
Linear Algebra: A Modern Introduction
Algebra
ISBN:
9781285463247
Author:
David Poole
Publisher:
Cengage Learning
Algebra and Trigonometry (6th Edition)
Algebra
ISBN:
9780134463216
Author:
Robert F. Blitzer
Publisher:
PEARSON
Contemporary Abstract Algebra
Algebra
ISBN:
9781305657960
Author:
Joseph Gallian
Publisher:
Cengage Learning
Linear Algebra: A Modern Introduction
Algebra
ISBN:
9781285463247
Author:
David Poole
Publisher:
Cengage Learning
Algebra And Trigonometry (11th Edition)
Algebra
ISBN:
9780135163078
Author:
Michael Sullivan
Publisher:
PEARSON
Introduction to Linear Algebra, Fifth Edition
Algebra
ISBN:
9780980232776
Author:
Gilbert Strang
Publisher:
Wellesley-Cambridge Press
College Algebra (Collegiate Math)
Algebra
ISBN:
9780077836344
Author:
Julie Miller, Donna Gerken
Publisher:
McGraw-Hill Education