Calculus 10th Edition

Published by Brooks Cole
ISBN 10: 1-28505-709-0
ISBN 13: 978-1-28505-709-5

Chapter P - Problem Solving - Page 39: 5

Answer

a) $A=x(\frac{100-x}{2})$ b) (graph is shown in the image below) let the y-axis becomes the Area and the x-axis as the length in x. Based on the graph shown, the length of 50 meters will yield the maximum amount of area for the pasture. c) dimensions: 25x50 m

Work Step by Step

a) $2y+x=100$ $2y=100-x$ $y=\frac{100-x}{2}$ $A=xy$ $A=x(\frac{100-x}{2})$ ------------------------------ b) (graph is shown in the image below) let the y-axis becomes the Area and the x-axis as the length in x. Based on the graph shown, the length of 50 meters will yield the maximum amount of area for the pasture. ------------------------------ c) $A=x(\frac{100-x}{2})$ $=-x^2+50x$ $A=-\frac{1}{2}(x^2-100x+2500)+1250$ $A=-\frac{1}{2}(x-50)^2+1250$ $x=5 m$ $y=\frac{100-50}{2}$ $=25 m$ dimensions: 25x50 m
Update this answer!

You can help us out by revising, improving and updating this answer.

Update this answer

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.