A rope is swinging in such a way that the length of the arc is decreasing geometrically. If the first arc is 18 feet long and the third arc is 8 feet long, what is the length of the second arc?
a. 12 feet
b. 10 feet
c. 5 feet
d. 72 feet
We can find the common ratio, thusly
18* r^2 = 8 rearrange as
r^2 = 8/18
r^2 = 4/9 take the positive root of both sides
r = 2/3
So.........the length of the second arc = 18 (2/3) = 12 ft
