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anonymous

  • one year ago

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? Part 3: How many radians on the unit circle would the minute hand travel from 0° if it were to move 3π 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 just need to know if I'm right. To find the degree you would divide the degrees of a circle by the number of minutes in an hour which would be 360/60=6. So six per minute you would multiply by 5 and get 30° in 5 minutes. Now we need to find the radians by dividing 30 by 180 like this 30/180 which would give you 1/6 and the radian measure is π/6. I'm not exactly sure what to do now

  2. anonymous
    • one year ago
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    @texaschic101 can you help?

  3. anonymous
    • one year ago
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    @Michele_Laino can you help? Please.

  4. anonymous
    • one year ago
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    Can someone help?

  5. Michele_Laino
    • one year ago
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    the angular velocity of the 4-inch hand is 2*pi/60= pi/30 radians/min

  6. anonymous
    • one year ago
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    I'm confused..

  7. Michele_Laino
    • one year ago
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    since the long minute hand travels one complete turn every 60 minutes

  8. Michele_Laino
    • one year ago
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    so we can write this condition: \[2\pi R = \omega R\Delta t\] where \Delta t = 60 minutes and R = 4 inches

  9. Michele_Laino
    • one year ago
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    \[2\pi R = \omega R60\] dividing by 60, we get: \[\omega = \frac{{2\pi }}{{60}} = \frac{\pi }{{30}}\]

  10. Michele_Laino
    • one year ago
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    so the answer for part 1, is: \[\alpha = \frac{\pi }{{30}} \times 20\]

  11. Michele_Laino
    • one year ago
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    since from 3.35 to 3.55 there are 20 minutes

  12. Michele_Laino
    • one year ago
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    so, after a simplification, we get: \[\alpha = \frac{{2\pi }}{3}\]

  13. Michele_Laino
    • one year ago
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    oops.. \[\alpha = \frac{{2\pi }}{3}\;radians\]

  14. anonymous
    • one year ago
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    Sorry my computer froze. I think I am understanding a bit more

  15. Michele_Laino
    • one year ago
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    now, part 2 the requested distance L, is given by the subsequent computation: \[\Large L = R\alpha = R\frac{{2\pi }}{3}\] where R = 4 inches

  16. anonymous
    • one year ago
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    The part I need help with is part 4 now

  17. Michele_Laino
    • one year ago
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    part 3) the requested angle is: \[\Large \beta = \frac{{3\pi }}{R}\]

  18. Michele_Laino
    • one year ago
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    and the requested coordinates are: \[\Large \left( {R,\frac{{3\pi }}{2}} \right)\] |dw:1433448393972:dw|

  19. anonymous
    • one year ago
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    That is confusing^

  20. Michele_Laino
    • one year ago
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    the long-minute hand travels for a distance 3pi long, right?

  21. anonymous
    • one year ago
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    Yes

  22. Michele_Laino
    • one year ago
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    so the final position is: |dw:1433449752947:dw|

  23. Michele_Laino
    • one year ago
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    at the final position correspond an angle of 3*pi/2 radians, so the polar coordinates are: (R, 3*pi/2) being R the length of the long minute hand

  24. Michele_Laino
    • one year ago
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    |dw:1433450239850:dw|

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