Question

LAST RADIANS AND ARC LENGTH PLZ HELP

Answer 1

The full circumference is given by:
S = 2 * pi * r
The given circumference is:
S '= (5/6) * pi * r
The fraction will be:
S '/ S = ((5/6) * pi * r) / (2 * pi * r)
Rewriting we have:
S '/ S = ((5/6)) / (2)
S '/ S = 5/12
Answer:
The fraction represented by the arc shown is:
S '/ S = 5/12

Answer 2

We have that the arc and the angle that it subtends are proportional in a circle. In plain words, if the angle is doubled, the arclength is also doubled. We know that 2π is the total amount of radians in a circle and it corresponds to the whole circumference. Suppose that x is the fraction of the circumference that 5π/6 radians subtend. By proportionality, we have the following equation:

`(1circumf. )/(2\pi) = (x)/((5\pi)/(6))`.
Multiplying both sides with 5pi/6 we get:

`(5\pi)/(6) * (1)/(2\pi) =x`

Hence, x=5/12