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anonymous

  • one year ago

I'm not fully understanding this and need help. Points A and B lie on a circle centered at point O. If length of own AB/radius=π/10, what is the ratio of the area of sector AOB to the area of the circle? A.) 1/10 B.) π/10 C.) 1/20 D.) π/20 I already know B isn't the answer. I'm thinking A is.

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  1. phi
    • one year ago
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    when you say "own AB" do you mean "arc AB" ?

  2. anonymous
    • one year ago
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    I believe so

  3. phi
    • one year ago
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    there is an expression \[ r \theta = s\] which means radius times the angle (in radians) = the length of the arc

  4. phi
    • one year ago
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    for your problem, where we use arc AB instead of "s" \[ r \theta = arc AB \] if we divide both sides by r we get \[ \theta = \frac{arc\ AB}{r} \] the question says that is pi/10 \[ \theta = \frac{arc\ AB}{r} = \frac{\pi}{10}\]

  5. anonymous
    • one year ago
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    I'm following

  6. phi
    • one year ago
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    I think you want the ratio of theta (the angle of the sector) divided by 2pi (the angle of the whole circle)

  7. phi
    • one year ago
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    or instead of dividing theta by 2pi, multiply by 1/(2pi)

  8. phi
    • one year ago
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    the idea is the angle of sector / 2pi is the fraction of the whole circle we want to know \[ \frac{\pi}{10} \cdot \frac{1}{2 \pi} \]

  9. anonymous
    • one year ago
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    So I would solve that?

  10. phi
    • one year ago
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    strictly speaking you only solve equations (which have = signs) in this case, you simplify. notice you have a pi "up top" and "down below" which means pi/pi = 1 (i.e. it cancels) to multiply the fraction, you multiply top time top and bottom times bottom (and of course simplify pi/pi to 1)

  11. anonymous
    • one year ago
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    So replace both pi with 1 (I'm trying to fully understand ^^;)

  12. phi
    • one year ago
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    it works the same way as with numbers. for example if you had 6/3 (which we know is 2) but we write it as \[ \frac{3\cdot 2}{3} = \frac{3}{3} \cdot 2 = 1 \cdot 2 = 2\]

  13. phi
    • one year ago
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    think of the pi as the "3" in that example \[ \frac{\pi}{10} \cdot \frac{1}{2 \pi} = \frac{\pi}{\pi} \cdot \frac{1}{10 \cdot 2} \]

  14. phi
    • one year ago
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    2pi means 2 * pi so the top is 1*pi the bottom is 2*10*pi and the pi's cancel

  15. anonymous
    • one year ago
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    Oh I understand it now. The pi would cancel out and then the answer would pretty much be right in front of you. (As you just said)

  16. phi
    • one year ago
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    the top simplifies to 1 the bottom to 2*10 which (I assume) you know is 20

  17. anonymous
    • one year ago
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    Thank you so much

  18. phi
    • one year ago
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    yw

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