Lesson 3.1 Quadratic Functions and Models
Discuss Problems 76 and 78 on page 192
posted by Mrs. S. at 7:55 AM
Monday, December 04, 2006
Discuss Problems 76 and 78 on page 192
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- Name: Mrs. S.
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I teach AP Calculus, Pre AP Precalculus, and Advanced Algebra/Trigonometry at Muscle Shoals High School. In my spare time, I enjoy spending time with my family and granddaughters. My husband and I like to travel and visited Germany and France last summer. I also enjoy reading, art and music. Last spring, I read The Other Boleyn Girl by Philippa Gregory. I am currently reading the Constant Princess (by the same author). I love "anything about England". "SUGGESTED READING LIST" The Mathematical Traveler. It is a great book that combines history and interesting facts about famous mathematicians. See me if you want to "check it out".
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1 Comments:
3.1 #76 ) 76. A farmer with 10,000 meters of fencing wants to enclose a rectangular field and then divide it into two plots with a fence prallel to one of the sides (see the figure on pg. 192). What is the largest area that can be enclosed???
The wording of this problem confused me. I did not understand what the question was asking. I took it as the area of both parts totaled. First, you know that 10,000=3x+2y. You also know that the area is still going to be = to xy (Area=xy). To express the area in terms of a single variable, you must solve the first equation for y and substitute the answer into the A= xy equation.
5000-(3/2)x=y
A=(x)(5000-(3/2)x)
A= (-3/2)x²+ 5000x
Now that you have a quadratic function, you can find the maximum point, which is the maximum value of A, by finding -b/2a. ( This is where the value occurs at, not the actual value.)
= 5000/3
The maximum value = A = (-3/2)(5000/3)²+ 5000(5000/3)
= 4166666.667
Taylor McClanahan
5:22 PM
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