Question

LAST RADIANS AND ARC LENGTH PLZ HELP

Answer 1

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:
$\frac{1circumf. }{2\pi} = \frac{x}{\frac{5\pi}{6}}$.
Multiplying both sides with 5pi/6 we get:
$\frac{5\pi}{6} * \frac{1}{2\pi} =x$

Hence, x=5/12

Answer 2

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