anonymous
  • anonymous
Suppose that 320 feet of fencing are available to enclose a rectangular field and that one side of the field must be given double fencing. What are the dimensions of the field of maximum area?
Mathematics
  • Stacey Warren - Expert brainly.com
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schrodinger
  • schrodinger
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darthsid
  • darthsid
Let one side be x, and the other side be y. Now, let the side with double fencing be x. So, the perimeter is 3x + 2y, which is given to be 320. We need to maximize the area, which is xy. From the perimeter, y = 160-3/2x so, area = xy = 160x - 3/2(x^2) now, using differentiation, find points where d(area)/dx has maxima.
anonymous
  • anonymous
How is differentiation to be used?
anonymous
  • anonymous
Do you mean like ax^2+bc+c=0

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anonymous
  • anonymous
Please help
darthsid
  • darthsid
Yeah, just like that. Find out values of x where d(area)/dx is zero. You can differentiate the area expression the same way you would differentiate a generic quadratic expression like ax^2+bx+c. The area expression I mentioned above can be written like ax^2 + bx + c, where a = -3/2 b = 160 c = 0
anonymous
  • anonymous
Suppose that a rectangular area is to be fenced, except one side must be fenced twice because it runs along a river.  If the amount of fencing is 320 yards in length, what is the maximum area that can be fenced? I see this question answered below, but We need to maximize the area, which is xy. From the perimeter, y = 160-3/2x so, area = xy = 160x - 3/2(x^2) - why is this x squared? and once you derive the ax^2+bx+c=0 formula, how do you maximize the area?

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