A record is spinning at the rate of 37 rpm. If a ladybug is sitting 8 cm from the center of the record, find and exact answer for each of the following. a) What is the angular velocity of the ladybug? (in radians/sec)
b) What is the speed of the ladybug? (in cm/sec) c) After 17 seconds, how far has the ladybug traveled? (in cm)

The angular velocity of the ladybug is the same as the angular velocity of

the record.

Correct responses (approximate values):

a)  3.875 rad/s

b) 31 cm/s

c) 527 cm

The rate at which the record is spinning = 37 rpm

Location of the ladybug on the record = 8 cm from the center

a) The angular velocity of the ladybug is given as follows;

1 revolution = 2·π radians

1 minute = 60 seconds

Therefore;

b) Linear speed, v = Radius, r × Angular speed, ω

The radius with the ladybug rotates, r = 8 cm

Angular velocity of the ladybug = ω ≈ 3.875 rad/s

Therefore;

c) Distance, d = Speed, v × Time, t

After 17 seconds, we have;

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f(x) has value 150 at x= 0

and 0 at x= 3

so d(f(x))/dt = slope = -150/3 = -50