To find the speed of the ladybug in cm/sec, we need to calculate the linear speed at which the ladybug is moving on the spinning record. Here's how we can do it:
1. First, we need to convert the record's rotation rate from revolutions per minute (rpm) to revolutions per second (rps). Since 1 minute is equal to 60 seconds, we divide 19 rpm by 60 to get the rate in revolutions per second.
2. Next, we calculate the circumference of the circular path the ladybug travels as the record spins. The formula for the circumference of a circle is C = 2πr, where r is the distance from the center of the record to the ladybug (11 cm in this case).
3. Substituting the value of r into the formula, we get the circumference of the circular path in terms of π.
4. To find the speed of the ladybug, we multiply the circumference of the circular path by the rate of revolution in rps. This gives us the speed of the ladybug in cm/sec, leaving the answer in terms of π.
By following these steps and calculations, you can determine the speed of the ladybug as it sits 11 cm from the center of the spinning record.
