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anonymous

  • one year ago

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?

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  1. anonymous
    • one year ago
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    I got the first part I just need help on the second. The answer for the first part is 2π/3 radians

  2. anonymous
    • one year ago
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    @jim_thompson5910 ?

  3. jim_thompson5910
    • one year ago
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    I'm getting 2pi/3 as well

  4. jim_thompson5910
    • one year ago
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    what is the circumference of the entire circle?

  5. anonymous
    • one year ago
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    360°

  6. jim_thompson5910
    • one year ago
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    that's the number of degrees in a full rotation

  7. jim_thompson5910
    • one year ago
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    I want the perimeter of the circle

  8. anonymous
    • one year ago
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    It doesn't give one. I can only think of 360

  9. jim_thompson5910
    • one year ago
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    formula C = 2*pi*r

  10. anonymous
    • one year ago
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    This is the circle

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  11. jim_thompson5910
    • one year ago
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    the clock's minute hand has a length of 4 so r = 4

  12. jim_thompson5910
    • one year ago
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    I'm talking about the minute hand's circle, not the unit circle

  13. anonymous
    • one year ago
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    I got 25.12

  14. jim_thompson5910
    • one year ago
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    good

  15. jim_thompson5910
    • one year ago
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    that's the distance around the whole circle

  16. jim_thompson5910
    • one year ago
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    but we only want a piece of that circle (from 35 min to 55 min)

  17. anonymous
    • one year ago
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    Okay how would we find that?

  18. jim_thompson5910
    • one year ago
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    how did you find 2pi/3 from the previous part?

  19. anonymous
    • one year ago
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    \[360\div60=6\] \[6\times20=120\] so 120° on the circle has 2π/3 radians

  20. jim_thompson5910
    • one year ago
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    good, so 120 degrees is 120/360 = 1/3 of the full circle

  21. jim_thompson5910
    • one year ago
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    multiply 1/3 by the circumference to get the distance just from 35 to 55

  22. anonymous
    • one year ago
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    I got 8.37 (rounded)

  23. jim_thompson5910
    • one year ago
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    me too

  24. jim_thompson5910
    • one year ago
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    that's the approximate distance around the circle edge from 35 to 55

  25. anonymous
    • one year ago
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    Okay thank you :) could you help me with part three too?

  26. jim_thompson5910
    • one year ago
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    sure

  27. jim_thompson5910
    • one year ago
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    The exact circumference is C = 2*pi*4 = 8pi agreed?

  28. anonymous
    • one year ago
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    Yes

  29. jim_thompson5910
    • one year ago
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    8pi inches is a full circle the minute hand travels 3pi inches what fraction of the circle does it travel?

  30. anonymous
    • one year ago
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    8pi/3pi?

  31. jim_thompson5910
    • one year ago
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    it's the other way around 3pi/8pi = 3/8

  32. jim_thompson5910
    • one year ago
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    so it travels 3/8 around the circle

  33. jim_thompson5910
    • one year ago
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    3/8 of 2pi radians = ???

  34. anonymous
    • one year ago
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    \[\frac{ 2π }{ 1 }\times \frac{ 3 }{ 8 }?\] \[\frac{ 6π }{ 8 }=\frac{ 3π }{ 4 }?\]

  35. jim_thompson5910
    • one year ago
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    that is the radian measure

  36. anonymous
    • one year ago
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    Oh and the points would be\[(\frac{ -√2 }{ 2 }, \frac{ √2 }{ 2 })\]

  37. jim_thompson5910
    • one year ago
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    very close

  38. jim_thompson5910
    • one year ago
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    keep in mind that the radius is not 1 it's 4

  39. anonymous
    • one year ago
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    I thought we were looking for the radian measure. The next part is the points of that radian measure.

  40. jim_thompson5910
    • one year ago
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    yes it's points on a circle with radius 4

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