<PRE><B>Question 816302</B>
72 = 2L + 2w
a = Lw
L = a/w
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72 = 2L + 2w
72 = 2a/w + 2w
2a/w + 2ww/w - 72 = 0
2a/w + 2ww/w - 72w/w = 0
2a + 2ww - 72w = 0w
2a = 0 - 2ww + 72w
a(w) = -(2/2)w^2 + (72/2)w
a(w) = -w^2 + 36w
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the above quadratic equation is in standard form, with a=-1, b=36, and c=0
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to solve the quadratic equation, plug this:
-1 36 0
into this: https://sooeet.com/math/quadratic-equation-solver.php
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the quadratic vertex is a maximum at: ( w= 18, a(w)= 324 )
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Answer:
w = 18 ft
L = 18 ft
a(w)= 324 sq.ft
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Number of alpacas that fit comfortably in the pen: 324/30 = 10 alpacas 
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Calculate and graph the linear regression of any data set:
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