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Posers and Puzzles

Posers and Puzzles

  1. 30 Jul '05 08:09
    The length of a pendulum is 20cm. If the tip of the pendulum swings through an angle of 86 degrees, find :

    a) The arc length ABC (the distance through which the tip travels)
    b) The area of triangle OAC.
    c) The area of the sector.
    d) The area of the minor segment.
    e) The length BX.
  2. 30 Jul '05 08:11
    Where are A, B, C, O and X? I picture would be nice
  3. 30 Jul '05 11:24 / 1 edit
    Assuming O is the center of the movement (where the pendulum is attached), A and C are the extremes, B is in the middle, and O is the intersection of AC and OB, I get (approximately):
    a) 30 cm
    b) 200 cm² (199.5...)
    c) 300 cm²
    d) 100 cm² (100.5..)
    e) 5.4 cm

    miscalcs are very realistic though.
  4. 30 Jul '05 15:41
    Do your own homework.
  5. 31 Jul '05 01:51
    Originally posted by THUDandBLUNDER
    Do your own homework.
    T'n'B, you are wrong.

    The answers provided are right.

    a) arc ABC = 20[86*(pi/180)]
    b) (1/2)(20)(20)sin(86deg)
    c) (1/2)(20)(30)
    d) 300 -199.5
    e) 20 -20cos(43deg)
  6. 31 Jul '05 03:02
    what's with your profile phgao ?
  7. 31 Jul '05 03:22 / 1 edit
    Originally posted by phgao
    T'n'B, you are wrong.
    Maybe, but it doesn't seem like a puzzle to me. Just straightforward school maths.
  8. 31 Jul '05 03:30
    i like math
  9. 31 Jul '05 08:53
    Originally posted by THUDandBLUNDER
    Maybe, but it doesn't seem like a puzzle to me. Just straightforward school maths.
    40 years after school, straightforward math looks like a puzzle
  10. 31 Jul '05 15:51
    Originally posted by Mephisto2
    40 years after school, straightforward math looks like a puzzle

    my rec.

    If only I could remember how to get the square root of a number using only paper and pencil... :'(


  11. 31 Jul '05 15:59
    Originally posted by LittleBear

    If only I could remember how to get the square root of a number using only paper and pencil... :'(
    Check this
    http://www.bbc.co.uk/dna/h2g2/A827453

  12. Subscriber sonhouse
    Fast and Curious
    01 Aug '05 17:47
    Originally posted by ilywrin
    Check this
    http://www.bbc.co.uk/dna/h2g2/A827453

    wow, that brings back memories, learned that one when I was in
    grade school at the First Lutheran School in El Monte California.
    Wonder how you would do it for cube roots? can this method be
    generalized for Nth roots?
  13. 01 Aug '05 18:27
    Originally posted by sonhouse
    wow, that brings back memories, learned that one when I was in
    grade school at the First Lutheran School in El Monte California.
    Wonder how you would do it for cube roots? can this method be
    generalized for Nth roots?
    Well i just did a little googling and found this generalization
    http://en.wikipedia.org/wiki/Shifting_nth-root_algorithm

  14. Subscriber sonhouse
    Fast and Curious
    02 Aug '05 02:14
    Originally posted by ilywrin
    Well i just did a little googling and found this generalization
    http://en.wikipedia.org/wiki/Shifting_nth-root_algorithm

    wow, lets hope we don't lose our calculators!
  15. 02 Aug '05 03:03
    Originally posted by LittleBear

    my rec.

    If only I could remember how to get the square root of a number using only paper and pencil... :'(


    For square root, I recommend using the "Divide and Average" algorithm. It has quadratic convergence (ie, it smokes), and it can be generalized for nth root. From what I see in the algorithms presented here, they seem to have linear convergence (ie, they're slow).

    Here's Divide and Average.

    Say you want to find the square root of the number k.

    Set X(0) to be a guess of the square root of k.

    Now, set X(n+1) = (1/2)*(X(n)+(k/(X(n))).

    Another good thing about Divide and Average is that if you make a mistake, your mistake gets smaller, and smaller with every iteration. With linear convergence methods, if you make a mistake, your results are worthless, regardless of how far you carry the calculation after your mistake. With Divide and Average, you can make a mistake at every step, and each mistake gets damped more and more, as you iterate, so you always approach the answer you are interested in.