For 13 and 14, the conversion factor is
180° = π radians
13. (105°)*(π radians)/180° = 7π/12 radians
14. 5π/6 radians * 180°/(π radians) = 150°
15. (The geometry shown cannot actually exist. The total of subtended arcs on any linked sprockets must be 360°.)
a.
The arc length on the smaller sprocket is (12 in)*(160/360) = 5 1/3 in.
The arc length on the larger sprocket is (20 in)*(185/360) = 10 5/18 in.
The total chain length is 5 6/18 +10 + 10 5/18 + 10 = 35 11/18 in. Rounded to the nearest tenth inch, the chain length is 10.3 inches.
b.
10.3/0.5 ≈ 20.6 ≈ 21
The chain has about 21 links. (There are no "teeth" on a chain.)
1. The radius can be found by looking at the distance between the origin and the line 8x+6y-48=0. That distance is |-48|/√(8²+6²) = 4.8.
Since the radius of the circle is 4.8, so its circumference is ...
9.6π cm, about 30.159 cm.
2. s = rθ
s = (12 cm)(π/3 radians) = 4π cm
The length of arc AB is 4π cm, about 12.566 cm.