Final answer:
The arc length for a 160-degree angle on a circular curve of radius r is found by taking a fraction of the circle's circumference, which is (160/360) × 2πr, corresponding to choice b).
Step-by-step explanation:
The student's question revolves around finding the length of an arc when a car is traveling along a circular curve. The radius of the curve is r, and the angle subtended by the arc is 160 degrees. To determine the arc length, we use the fact that for one complete revolution (360 degrees), the arc length is equal to the circumference of the circle, which is 2πr.
Since we are only dealing with 160 degrees, we take the fraction of the circumference that corresponds to this angle, which is (160/360). Therefore, the correct formula to find the length of the arc is (160/360) × 2πr, which simplifies to (4/9) × 2πr. This matches choice b).