ok so if an athletic field is build in the shape of a rectangle with X as it's length and the rectangle is capped by a semicircles at both ends with a radius R. the field is bounded by a 400meter track. What value of X and R will give the rectangle the largest possible area?
IM NOT LOOKING FOR AN ANSWER, I JUST NEED TO KNOW HOW TO START THE PROBLEM...
2007-11-11 07:53:37 · 2 answers · asked by broken_monkey08 2 in Science & Mathematics ➔ Mathematics
Work out a formula for the area in terms of X and R, e.g.
Area = something with X and R in it
Then work out how X and R are related to the 400 metre total length.
Rearrange to get R = something with X and 400 in it
Substitute in your area formula, so that it only contains X and not R
Differentiate your area formula, then set the derivative to zero (which will correspond to the maximum or minimum), then solve for X, then substitute back in your R = something with X and 400 in it.
Make sense?
2007-11-11 08:06:05 · answer #1 · answered by Anonymous · 0⤊ 0⤋
The 400 meter track is length 2x + 2pi*r
The area of the rectangle is x * 2r
Given x + pi*r = 200
Maximize 2xr
x = 200 - pi*r
Maximize 2(200-pi*r)r
Maximize 400r - 2pi*r^2
Maximize 200r - pi*r^2
Is that a good start for you?
2007-11-11 16:08:10 · answer #2 · answered by Steve A 7 · 0⤊ 0⤋