Final answer:
The tires will rotate through approximately 41,024 radians within the full warranty length.
Step-by-step explanation:
To calculate the number of radians the tires will rotate through within the full warranty length, we need to find the circumference of the tires. The formula to calculate the circumference of a circle is C = 2πr, where r is the radius. Since the diameter is given, we can find the radius by dividing the diameter by 2. In this case, the radius is 28.6/2 = 14.3 inches. Since the warranty length is given in miles, we need to convert the radius from inches to miles. 1 mile is equal to 63,360 inches, so the radius in miles is 14.3/63,360 = 0.000225 miles. Now we can calculate the circumference of the tires by using the formula C = 2πr. Substituting the value of r, we get C ≈ 2π * 0.000225 ≈ 0.001413 miles. Finally, to find the number of radians the tires will rotate through within the full warranty length, we divide the warranty length in miles by the circumference of the tires. 58,000 miles / 0.001413 miles ≈ 41,024 radians.