MATH SOLVE

5 months ago

Q:
# Tammy is at the dentist's office waiting on her appointment. She notices that the 6-inch-long minute hand is rotating around the clock and marking off time like degrees on a unit circle. Part 1: How many radians does the minute hand move from 1:20 to 1:55? (Hint: Find the number of degrees per minute first.) Part 2: How far does the tip of the minute hand travel during that time? You must show all of your work.

Accepted Solution

A:

There are 12 five minutes in one hour and 1 hour correspond to 360°, then each 5 minutes represents 360/12 = 30°

From 1:20 to 1: 55 we have 35 minutes or 7 x 5 minutes or

7 x 30° = 210°

To convert degree into radian, we apply the following formula:

degree/180° = radian/π

210/180 = r/π or (cross multiplication) →Radian = (π x 210/180

→ Radian = 7π/6 (simplify by 30)

From 1:20 to 1: 55 we have 35 minutes or 7 x 5 minutes or

7 x 30° = 210°

To convert degree into radian, we apply the following formula:

degree/180° = radian/π

210/180 = r/π or (cross multiplication) →Radian = (π x 210/180

→ Radian = 7π/6 (simplify by 30)