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finaynay
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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
 2 years ago
 2 years ago
finaynay Group Title
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
 2 years ago
 2 years ago

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geoffb Group TitleBest ResponseYou've already chosen the best response.2
Do you know how to find the largest area possible?
 2 years ago

math>philosophy Group TitleBest ResponseYou've already chosen the best response.0
Draw a picture
 2 years ago

finaynay Group TitleBest ResponseYou've already chosen the best response.0
dw:1353735822700:dw
 2 years ago

math>philosophy Group TitleBest ResponseYou've already chosen the best response.0
That's fine lol
 2 years ago

finaynay Group TitleBest 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
 2 years ago

math>philosophy Group TitleBest ResponseYou've already chosen the best response.0
i think you have the perimeter wrong
 2 years ago

geoffb Group TitleBest 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.
 2 years ago

geoffb Group TitleBest ResponseYou've already chosen the best response.2
You would need it to be \(2x + c = 200\)
 2 years ago

finaynay Group TitleBest ResponseYou've already chosen the best response.0
c is the circumference right
 2 years ago

geoffb Group TitleBest ResponseYou've already chosen the best response.2
Yes, and that's right (\(2 \pi r\)).
 2 years ago

finaynay Group TitleBest ResponseYou've already chosen the best response.0
okay and then differentiate that equation correct?
 2 years ago

geoffb Group TitleBest ResponseYou've already chosen the best response.2
You would need to differentiate the area, not the perimeter.
 2 years ago

geoffb Group TitleBest ResponseYou've already chosen the best response.2
So, can you first determine a formula for the area of your diagram?
 2 years ago

geoffb Group TitleBest ResponseYou've already chosen the best response.2
Yeah, that looks good.
 2 years ago

finaynay Group TitleBest ResponseYou've already chosen the best response.0
should i substitute r or x
 2 years ago

math>philosophy Group TitleBest ResponseYou've already chosen the best response.0
Whichever one you want
 2 years ago

finaynay Group TitleBest ResponseYou've already chosen the best response.0
100/3pi = r seem right?
 2 years ago
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