Answer:
[tex]x^2 + (y-60)^2 = 30,625[/tex]
Step-by-step explanation:
There are 42 carts, so there is 42 spaces in between them; if one of those spaces are 25pi/3 feet long, then 42 of them would be 25*42*pi/3 = 350pi (Perfect! no fractions)
350pi is the circumference. Now if we plug that into the circumference equation we get:
C = 2pi*r
350pi = 2pi*r
Divide both sides by pi to get rid of it
350 = 2r
Divide both sides by 2
r = 175 feet
So the new equation to graph it is:
x^2+y^2 = 175^2 = 30,625
We also know that the center of the Ferris wheel has to be at least 60 feet from the ground. Since the radius is more than that, a good bit of the Ferris wheel has to be underground OR we can make it higher (keyword: at least) if we want it to be above ground. I'll do the equation for underground since it more closely represents the question.
subtracting a number from y, shifts the graph up that much so:
[tex]x^2 + (y-60)^2 = 30,625[/tex]
I can't really draw it electronically but I can graph it:
