Question

I will fan and medal.

Freddie is at chess practice waiting on his opponent's next move. He 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 3:35 to 3:55? (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.

Answer 1

how many minutes in an hour?

Answer 2

60

Answer 3

and how many degrees in a circle?

Answer 4

360

Answer 5

so how may degrees per minute?

Answer 6

6

Answer 7

actually since your question is given in radians, we can forget about degrees

Answer 8

or, now that you have 6 degrees, we can convert the 6 degrees to radians
do you know how to do that?

Answer 9

i dont know how to do that

Answer 10

put it over \(180\) and multply by \(\pi\) i.e.. \[6^\circ=\frac{6\pi}{180}\] which you can reduce

Answer 11

i mean reduce the fraction, leave the \(\pi\) there

Answer 12

so for number 1 its 30?

Answer 13

no

Answer 14

on minute is \[\frac{\pi}{30}\] radians

Answer 15

for 20 minutes, multiply that by 20

Answer 16

im confused what i multiply by 20

Answer 17

lets go slow

Answer 18

is it clear that from 3:35 to 3:55 is 20 minutes?

Answer 19

yes

Answer 20

and it is also clear that 20 minutes is one third of an hour?

Answer 21

yes

Answer 22

and do you know that the entire circle, one complete rotation, is an angle of \(2\pi\)?

Answer 23

yes

Answer 24

so your 20 minutes is one third of that

Answer 25

so what should i type for the first one? I put there is 20 minutes in between

Answer 26

i have no idea what you should type in for what
the answer to the first question
"How many radians does the minute hand move from 3:35 to 3:55? " is \[\large \frac{2\pi}{3}\]

Answer 27

ok

Answer 28

since twenty minutes is one third of 60 minutes, and two pi divided by 3 is what i wrote above

Answer 29

thank you. i will be right back let me type this up in my own words

Answer 30

How far does the tip of the minute hand travel during that time?
the hand if 4 inches long
multiply the result above by 4

Answer 31

ok im back.

Answer 32

ok we are done right?

Answer 33

need help for the second please

Answer 34

i wrote the answer above `

Answer 35

4 inches long?

Answer 36

the angle is actually defined by the arc length over the radius
your radius is 4 and your angle is \(\frac{2\pi}{3}\) therefore the arc length is the product of those two numbers

Answer 37

divide 2pi/3 by 4 to get the arc length?

Answer 38

"product"

Answer 39

aka multiply

Answer 40

8.37?

Answer 41

i would just write \[4\times \frac{2\pi}{3}=\frac{8\pi}{3}\] and leave it at that

Answer 42

thank you so much i understand now

Answer 43

yw