The distance around the whole circle is .
I need to determine the radius of the semicircular ends of the room in terms of Y. The perimeter of the room is to be a 200-meter single-lane running track.
As well as finding the radius, I need to find the distance (in terms of Y) of the 2 semicircular parts of the track.
Once those things are done, I have to take the radius and write an equation (in terms of x & y) for the distance traveled in one lap around the track.
THEN I have to solve for Y. I then take that answer and write the area A of the rectangular region as a function of X.
And FINALLY, I have to figure out t he dimensions that will produce a maximum area of the rectangle (x & y).
I have absolutely no idea how to do any of this. Can't find this crap anywhere in the damn book.
Hello, BeSweeet!
Come on!
I'm sure you already know everything necessary to solve this problem.
We have a 200-meter running track.
The center is an -by- rectangle with semicircles on the ends.
(a) Find the radius of the semicircular ends of the track in terms of
The diameter of the semicircle is
. . The radius is half of that: .
The two semicircles make up one circle.(b) Find the distance (in terms of ) of the 2 semicircular parts of the track.
Circumference of a circle: .
. . Therefore: .
(c) Write an equation (in terms of & ) for the distance around the track.
. .
(d) Solve for
Since , we have: .
. . Therefore: . .[1]
(e) Write the area of the rectangular region as a function of
The area of a rectangle is: .
So we have: .
Substitute [1]: .
Solve(f) Find the dimensions that will produce a maximum area of the rectangle.
. . Therefore: .