anonymous
  • anonymous
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? Part 3: How many radians on the unit circle would the minute hand travel from 0 degrees if it were to move 3pi inches? Part 4: What is the coordinate point associated with this radian measure?
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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chestercat
  • chestercat
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anonymous
  • anonymous
I got the first part I just need help on the second. The answer for the first part is 2π/3 radians
anonymous
  • anonymous
@jim_thompson5910 ?
jim_thompson5910
  • jim_thompson5910
I'm getting 2pi/3 as well

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jim_thompson5910
  • jim_thompson5910
what is the circumference of the entire circle?
anonymous
  • anonymous
360°
jim_thompson5910
  • jim_thompson5910
that's the number of degrees in a full rotation
jim_thompson5910
  • jim_thompson5910
I want the perimeter of the circle
anonymous
  • anonymous
It doesn't give one. I can only think of 360
jim_thompson5910
  • jim_thompson5910
formula C = 2*pi*r
anonymous
  • anonymous
This is the circle
1 Attachment
jim_thompson5910
  • jim_thompson5910
the clock's minute hand has a length of 4 so r = 4
jim_thompson5910
  • jim_thompson5910
I'm talking about the minute hand's circle, not the unit circle
anonymous
  • anonymous
I got 25.12
jim_thompson5910
  • jim_thompson5910
good
jim_thompson5910
  • jim_thompson5910
that's the distance around the whole circle
jim_thompson5910
  • jim_thompson5910
but we only want a piece of that circle (from 35 min to 55 min)
anonymous
  • anonymous
Okay how would we find that?
jim_thompson5910
  • jim_thompson5910
how did you find 2pi/3 from the previous part?
anonymous
  • anonymous
\[360\div60=6\] \[6\times20=120\] so 120° on the circle has 2π/3 radians
jim_thompson5910
  • jim_thompson5910
good, so 120 degrees is 120/360 = 1/3 of the full circle
jim_thompson5910
  • jim_thompson5910
multiply 1/3 by the circumference to get the distance just from 35 to 55
anonymous
  • anonymous
I got 8.37 (rounded)
jim_thompson5910
  • jim_thompson5910
me too
jim_thompson5910
  • jim_thompson5910
that's the approximate distance around the circle edge from 35 to 55
anonymous
  • anonymous
Okay thank you :) could you help me with part three too?
jim_thompson5910
  • jim_thompson5910
sure
jim_thompson5910
  • jim_thompson5910
The exact circumference is C = 2*pi*4 = 8pi agreed?
anonymous
  • anonymous
Yes
jim_thompson5910
  • jim_thompson5910
8pi inches is a full circle the minute hand travels 3pi inches what fraction of the circle does it travel?
anonymous
  • anonymous
8pi/3pi?
jim_thompson5910
  • jim_thompson5910
it's the other way around 3pi/8pi = 3/8
jim_thompson5910
  • jim_thompson5910
so it travels 3/8 around the circle
jim_thompson5910
  • jim_thompson5910
3/8 of 2pi radians = ???
anonymous
  • anonymous
\[\frac{ 2π }{ 1 }\times \frac{ 3 }{ 8 }?\] \[\frac{ 6π }{ 8 }=\frac{ 3π }{ 4 }?\]
jim_thompson5910
  • jim_thompson5910
that is the radian measure
anonymous
  • anonymous
Oh and the points would be\[(\frac{ -√2 }{ 2 }, \frac{ √2 }{ 2 })\]
jim_thompson5910
  • jim_thompson5910
very close
jim_thompson5910
  • jim_thompson5910
keep in mind that the radius is not 1 it's 4
anonymous
  • anonymous
I thought we were looking for the radian measure. The next part is the points of that radian measure.
jim_thompson5910
  • jim_thompson5910
yes it's points on a circle with radius 4

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