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metalslayer

  • one year ago

A regular n-gon is inscribed in the unit circle. What is the perimeter for each n below? a.3 b.5 c.6 d.10 e.57 f.542 g. n h. The perimeter in part f should be close to what number? How close is it?

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  1. anonymous
    • one year ago
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    Aye, mate. I may be of some assistance. But first, I need a favor from ye. Tell me when the observatory is.

  2. metalslayer
    • one year ago
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    What observatory?

  3. metalslayer
    • one year ago
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    I really need help on this

  4. geerky42
    • one year ago
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    Do you know Trigonometry? Or at least Law of Cosines?

  5. geerky42
    • one year ago
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    If so, this site may helps: http://mathcentral.uregina.ca/QQ/database/QQ.09.07/h/lindsay2.html

  6. metalslayer
    • one year ago
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    I've been on that website. I just don't get it. Can you please just solve for A and show the steps so I could do the rest? Thanks.

  7. metalslayer
    • one year ago
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    I do know trig and law of cosines and sines

  8. geerky42
    • one year ago
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    What A?

  9. metalslayer
    • one year ago
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    a.3 b.5 c.6 d.10 e.57 f.542 g. n h. The perimeter in part f should be close to what number? How close is it?

  10. metalslayer
    • one year ago
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    Please show me how to answer some of them with the steps. Thank You.

  11. metalslayer
    • one year ago
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    By A i meant n=3

  12. geerky42
    • one year ago
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    From site, our equation would be \(P = nc = n\sqrt{2-2\cos\left(\dfrac{360^\text o}{n}\right)}\)

  13. geerky42
    • one year ago
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    Do you understand how this equation was derived?

  14. metalslayer
    • one year ago
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    P is perimeter, n is the n-gon, what is c?

  15. geerky42
    • one year ago
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    c is side.

  16. metalslayer
    • one year ago
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    How do I find the side? I am only given the n.

  17. geerky42
    • one year ago
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    You can use law of cosines to find the length of sides:|dw:1436579931950:dw|

  18. geerky42
    • one year ago
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    n-gon is inscribed in unit circle, which has radius of 1.

  19. metalslayer
    • one year ago
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    So lets try to solve a.) n=3. I will plug in n into 360/n so it will equal 120 degrees. Then I have no idea lol.

  20. geerky42
    • one year ago
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    Yes, Plugging in n=3, you would have \(P = 3\sqrt{2-2\cos\left(120^\text o\right)}\)

  21. geerky42
    • one year ago
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    You can just use calculator.

  22. metalslayer
    • one year ago
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    p=5.2?

  23. geerky42
    • one year ago
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    Yeah I got approximately that.

  24. metalslayer
    • one year ago
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    So first I divide 360 by n, and then plug it into the formula?

  25. geerky42
    • one year ago
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    Actually, you just plug in whether value of n, then calculate.

  26. geerky42
    • one year ago
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    For case of n=3, you just plug in n=3 and calculate \(P = 3\sqrt{2-2\cos\left(\dfrac{360^\text o}{3}\right)}\)

  27. metalslayer
    • one year ago
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    Oh I see. Thank you. What about if n = 542?

  28. geerky42
    • one year ago
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    Same. Plug in n=542 then calculate \(P = \textbf{542}\sqrt{2-2\cos\left(\dfrac{360^\text o}{\textbf{542}}\right)}\)

  29. metalslayer
    • one year ago
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    Great, thanks. And lastly could you please explain part h.

  30. metalslayer
    • one year ago
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    h. The perimeter in part f should be close to what number? How close is it?

  31. geerky42
    • one year ago
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    Well, imagine if n goes to infinity, what would n-gon become into?

  32. metalslayer
    • one year ago
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    a circle

  33. geerky42
    • one year ago
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    Right. Saying we have case of \(n=\infty\). How can we find perimeter?

  34. geerky42
    • one year ago
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    Or should I say "circumference"?

  35. metalslayer
    • one year ago
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    \[\pi radius squared\]

  36. metalslayer
    • one year ago
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    pi radius squared

  37. geerky42
    • one year ago
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    That's area of circle. We want circumference.

  38. metalslayer
    • one year ago
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    2pi*r

  39. metalslayer
    • one year ago
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    so what is the radius?

  40. geerky42
    • one year ago
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    Yeah. Here, we have UNIT circle, so radius is 1. So part f should be close to \(2\pi\)

  41. metalslayer
    • one year ago
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    So that's my answer? Thank You. You are so helpful.

  42. geerky42
    • one year ago
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    Yeah. Though I am not sure how to answer "How close is it?" I guess subtract part f from \(2\pi\).

  43. geerky42
    • one year ago
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    But I think you did your job good enough lol...

  44. metalslayer
    • one year ago
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    Thank you. This helped me so much.

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