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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
 one year ago
 one year ago
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
 one year ago
 one year ago

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geoffbBest ResponseYou've already chosen the best response.2
Do you know how to find the largest area possible?
 one year ago

math>philosophyBest ResponseYou've already chosen the best response.0
Draw a picture
 one year ago

finaynayBest ResponseYou've already chosen the best response.0
dw:1353735822700:dw
 one year ago

math>philosophyBest ResponseYou've already chosen the best response.0
That's fine lol
 one year ago

finaynayBest ResponseYou've already chosen the best response.0
c=2piR and 200=4r+2x (x being the base of the rectangle) this is how i set it up
 one year ago

math>philosophyBest ResponseYou've already chosen the best response.0
i think you have the perimeter wrong
 one year ago

geoffbBest ResponseYou've already chosen the best response.2
You're not accounting for the circumference of the circle. Your equation only includes the area of the rectangle.
 one year ago

geoffbBest ResponseYou've already chosen the best response.2
You would need it to be \(2x + c = 200\)
 one year ago

finaynayBest ResponseYou've already chosen the best response.0
c is the circumference right
 one year ago

geoffbBest ResponseYou've already chosen the best response.2
Yes, and that's right (\(2 \pi r\)).
 one year ago

finaynayBest ResponseYou've already chosen the best response.0
okay and then differentiate that equation correct?
 one year ago

geoffbBest ResponseYou've already chosen the best response.2
You would need to differentiate the area, not the perimeter.
 one year ago

geoffbBest ResponseYou've already chosen the best response.2
So, can you first determine a formula for the area of your diagram?
 one year ago

finaynayBest ResponseYou've already chosen the best response.0
should i substitute r or x
 one year ago

math>philosophyBest ResponseYou've already chosen the best response.0
Whichever one you want
 one year ago

finaynayBest ResponseYou've already chosen the best response.0
100/3pi = r seem right?
 one year ago
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