finaynay
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
Delete
Share
This Question is Closed
geoffb
Best Response
You've already chosen the best response.
2
Do you know how to find the largest area possible?
math>philosophy
Best Response
You've already chosen the best response.
0
Draw a picture
finaynay
Best Response
You've already chosen the best response.
0
|dw:1353735822700:dw|
finaynay
Best Response
You've already chosen the best response.
0
lol
math>philosophy
Best Response
You've already chosen the best response.
0
That's fine lol
finaynay
Best Response
You'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
math>philosophy
Best Response
You've already chosen the best response.
0
i think you have the perimeter wrong
finaynay
Best Response
You've already chosen the best response.
0
how?
geoffb
Best Response
You'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.
geoffb
Best Response
You've already chosen the best response.
2
You would need it to be \(2x + c = 200\)
finaynay
Best Response
You've already chosen the best response.
0
c is the circumference right
geoffb
Best Response
You've already chosen the best response.
2
Yes, and that's right (\(2 \pi r\)).
finaynay
Best Response
You've already chosen the best response.
0
okay and then differentiate that equation correct?
geoffb
Best Response
You've already chosen the best response.
2
You would need to differentiate the area, not the perimeter.
geoffb
Best Response
You've already chosen the best response.
2
So, can you first determine a formula for the area of your diagram?
finaynay
Best Response
You've already chosen the best response.
0
pir^2+2rx
geoffb
Best Response
You've already chosen the best response.
2
Yeah, that looks good.
finaynay
Best Response
You've already chosen the best response.
0
should i substitute r or x
math>philosophy
Best Response
You've already chosen the best response.
0
Whichever one you want
finaynay
Best Response
You've already chosen the best response.
0
100/3pi = r seem right?