A wheel with a 22 inch diameter is turning at the rate of 31 revolutions per minute. What is the

linear speed of a point on the rim, measured to the nearest inch per minute?

To find the linear speed of a point on the rim, we need to calculate the distance traveled by the point in one minute.

First, we need to convert the diameter of the wheel into the radius. The diameter is given as 22 inches, so the radius (r) is half of the diameter, which is 22/2 = 11 inches.

Next, we need to find the circumference of the wheel. The circumference of a circle is given by the formula C = 2πr, where C is the circumference and r is the radius. Plugging in the value of the radius (11 inches), we get C = 2π(11) = 22π inches.

Since the wheel makes 31 revolutions per minute, we can multiply the circumference by the number of revolutions to find the distance traveled in one minute. Therefore, the distance traveled in one minute is 31 * 22π inches.

To find the linear speed to the nearest inch per minute, we round the distance traveled to the nearest whole number. So, the linear speed of a point on the rim of the wheel, measured in inches per minute, is approximately 683 inches per minute.