A ceiling fan has 15-Inch blades (so the radius of the circular fan is 15 inches)Suppose the fan turns at a rate of 68 revolutions per minute. (a) Find the angular speed of the fan In radians per minute. (b) Find the linear speed of the tip of a blade in Inches per minute. Do not round any Intermediate computations, and round your answer to the nearest whole number. (a) Angular speed:radians per minute square (b) Linear speed: square inches per mi

(a) To find the angular speed of the fan in radians per minute, we need to convert the given revolutions per minute to radians per minute.<br /><br />1 revolution = 2π radians<br /><br />Given that the fan turns at a rate of 68 revolutions per minute, we can calculate the angular speed as follows:<br /><br />Angular speed = 68 revolutions/minute * 2π radians/revolution<br /><br />Angular speed = 136π radians/minute<br /><br />Therefore, the angular speed of the fan is 136π radians per minute.<br /><br />(b) To find the linear speed of the tip of a blade in inches per minute, we need to use the formula:<br /><br />Linear speed = Angular speed * Radius<br /><br />Given that the radius of the circular fan is 15 inches and the angular speed is 136π radians per minute, we can calculate the linear speed as follows:<br /><br />Linear speed = 136π radians/minute * 15 inches<br /><br />Linear speed = 2040π inches/minute<br /><br />Rounding to the nearest whole number, the linear speed of the tip of a blade is approximately 6420 inches per minute.