if a car were to travel exactly one mile ,one of its tires would make 830 revolutions.Find the radius of the tire in inches.

1 mile = 5280 feet or 63360 inches

so
830(2πr) = 63360
r = 63360/(2π(830)) = 12.15

An isosceles triangle has a perimeter of 147 inches.Each of the two equal lenghts is three times as long as the base.find the length of the base

To find the radius of the tire in inches, we need to understand the relationship between the number of revolutions made by the tire and the distance it travels.

The circumference of a circle (such as a tire) is given by the formula:
Circumference = 2 * π * Radius

In this case, we're given that the car travels exactly one mile, which is equivalent to 5,280 feet or 63,360 inches. We also know that one tire makes 830 revolutions.

To find the distance traveled by one tire, we can multiply the circumference of the tire by the number of revolutions:
Distance = Circumference * Number of Revolutions

Therefore, we can set up the following equation:
63,360 inches = 2 * π * Radius * 830 revolutions

To find the radius of the tire, we can rearrange the equation:
Radius = 63,360 inches / (2 * π * 830 revolutions)

Now, let's calculate the radius using the given information:
Radius = 63,360 inches / (2 * π * 830 revolutions)
Radius ≈ 4.83 inches

Therefore, the radius of the tire is approximately 4.83 inches.