anonymous
  • anonymous
optimization problem: a physical fitness room consists of a rectangular region with a semicircle on each end. if the perimeter of the room is to be a 200 meter running track, find the dimensions that will make the are of the rectangular region as large as possible
Mathematics
jamiebookeater
  • jamiebookeater
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anonymous
  • anonymous
Do you know how to find the largest area possible?
anonymous
  • anonymous
Draw a picture
anonymous
  • anonymous
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anonymous
  • anonymous
lol
anonymous
  • anonymous
That's fine lol
anonymous
  • anonymous
c=2piR and 200=4r+2x (x being the base of the rectangle) this is how i set it up
anonymous
  • anonymous
i think you have the perimeter wrong
anonymous
  • anonymous
how?
anonymous
  • anonymous
You're not accounting for the circumference of the circle. Your equation only includes the area of the rectangle.
anonymous
  • anonymous
You would need it to be \(2x + c = 200\)
anonymous
  • anonymous
c is the circumference right
anonymous
  • anonymous
Yes, and that's right (\(2 \pi r\)).
anonymous
  • anonymous
okay and then differentiate that equation correct?
anonymous
  • anonymous
You would need to differentiate the area, not the perimeter.
anonymous
  • anonymous
So, can you first determine a formula for the area of your diagram?
anonymous
  • anonymous
pir^2+2rx
anonymous
  • anonymous
Yeah, that looks good.
anonymous
  • anonymous
should i substitute r or x
anonymous
  • anonymous
Whichever one you want
anonymous
  • anonymous
100/3pi = r seem right?

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