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finaynay
 2 years 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
finaynay
 2 years 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

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

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

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

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

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

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

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

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

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

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

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

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

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

finaynay
 2 years ago
Best ResponseYou've already chosen the best response.0100/3pi = r seem right?
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