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Question 156634: PLEASE PLEASE PLEASE HELP ME! IT'S DUE IN 5 HOURS ONLINE! THANKS!
A rancher with 900 ft of fencing wants to enclose a rectangular area and then divide it into four pens with fencing parallel to one side of the rectangle.
(a) Find a function that models the total area of the four pens. (Use w to represent the width of the field, and write the function A in terms of w.)
A(w)=
(b) Find the largest possible total area of the four pens.
______ square feet.
Answer by Alan3354(69443)   (Show Source):
You can put this solution on YOUR website! A rancher with 900 ft of fencing wants to enclose a rectangular area and then divide it into four pens with fencing parallel to one side of the rectangle.
(a) Find a function that models the total area of the four pens. (Use w to represent the width of the field, and write the function A in terms of w.)
A(w)=
(b) Find the largest possible total area of the four pens.
______ square feet.
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The perimeter will be 2w + 2l (L = length)
The fencing used with 3 dividers will be 2w + 2L + 3L = 900
2w + 5L = 900
L = (900 - 2w)/5
A = wL = w*(900-2w)/5
A = (900w-2w^2)/5
A = 180w - (2/5)w^2 That's the function of A in terms of w
To find the max, set the 1st derivative to 0
180 - 4w/5 = 0
4w = 900
w = 225 ft
L = (900-450)/5
L = 90 feet
A = wL = 225*90
A = 20,250 sq ft
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