Celia is staring at the clock waiting for school to end so that she can go to track practice. She notices that the 4-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 1:25 to 1:50? (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. (10 points)

Part 1: 5pi/6. Part 2: 10pi/3

Step-by-step explanation:

There are 60 minutes in an hour, and there are 360⁰ in a circle, so for every one minute that passes that is 6⁰ being passed.

From the time 25 to 50 is 25 minutes, which is also 150⁰.

To convert from degrees to radians you have to multiply 150⁰ by pi/180⁰ this turns into 5pi/6.

To find how far the tip of the clock moved you have to use arc length, which is arc length=radius×angle in radians.

we know that radius is 4, because thats the length of the minute hand times the degrees in radians which is 5pi/6.

4×5pi/6=20pi/6

this reduces to

10pi/3 which is how far the minute hand traveled.

step-by-step explanation:

4  

25

5258y

54.

t5

5r

54

5856

542

5458

86

.8558.65

565

565

55898

786

8/95

5896

8656265

556478