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Thread: The Maths Thread

  1. #181
    International Vice-Captain Redbacks's Avatar
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    Quote Originally Posted by blahblahblah View Post
    cool stuff redbacks..

    u got any problems u willing to share?

    u r welcome =)
    I uncovered some old 'comp maths' books we were given at uni so I have hundreds of puzzles for you to enjoy

    a) Just after three o'clock the school fire alarm rings for exactly 10 minutes. If the angle between the minute hand and hour hands was three times bigger when the alarm started than when it finished, when exactly did the bell start ringing. (draw a diagram )

    b) Prove that if p and q are odd numbers then p^2 - q^2 is divisible by 8.

  2. #182
    The Wheel is Forever silentstriker's Avatar
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    Quote Originally Posted by Redbacks View Post
    I uncovered some old 'comp maths' books we were given at uni so I have hundreds of puzzles for you to enjoy

    a) Just after three o'clock the school fire alarm rings for exactly 10 minutes. If the angle between the minute hand and hour hands was three times bigger when the alarm started than when it finished, when exactly did the bell start ringing. (draw a diagram )

    b) Prove that if p and q are odd numbers then p^2 - q^2 is divisible by 8.
    A. 3pm. At 3pm, you have a 90 degree angle. at 3:10pm, you have a 30 degree angle.

    B. I've done this problem before, so it's unfair . Hint: Factor!
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  3. #183
    International Vice-Captain Redbacks's Avatar
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    in (a) you have to take into account that the hour hand moves also.

  4. #184
    Global Moderator Spark's Avatar
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    b), on a piece of little paper.

    Let q = 2a-1, b= 2b-1, a,b in N*
    p^2-q^2 = 4(a-b)(a+b-1)

    Case a-b is even: a-b = 2n, n in N*, hence p^2-q^2 = 8n(a+b-1) | 8 as required
    a-b odd: a+b is odd (=(a-b)+2b, odd+even = odd), hence a+b-1 is even ie a+b-1=2n etc.as above

    QED

    Here's one from an exam today that gave me the ****s

    Find an element x (or prove there does not exist one) of S5 such that when a is conjugated by x it gives b, where a = (15)(243) and b = (135)(24)

    And no I don't know the answer.
    Last edited by Spark; 18-11-2010 at 06:25 AM.
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  5. #185
    Cricket Web: All-Time Legend Uppercut's Avatar
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    Quote Originally Posted by silentstriker View Post
    A. 3pm. At 3pm, you have a 90 degree angle. at 3:10pm, you have a 30 degree angle.
    The hour hand moves too in that ten minutes so it's not exactly 3pm. The hour hand moves 1/12th of the speed of the minute hand.

    Letting M be the number of minutes that have passed since 3pm, H be the position of the hour hand and x be the number of minutes past 3 the clock originally was, we can derive three equations:

    H=15+M/12
    M=x+10
    H-M=(H-x)/3

    so
    x=M-10,
    x=3M-2(15+M/12)=17M/6-30

    17M/6-30=M-10, M+20=17M/6, 6M+120=17M, 11M=120, M=10.9090..

    But we actually want x, which is M-10. So unless I've yet again ballsed up the algebra at some point, the alarm went off at exactly 0.90r minutes past 3.
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    The Filth have comfortably the better bowling. But the Gash have the batting. Might be quite good to watch.

  6. #186
    The Wheel is Forever silentstriker's Avatar
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    Ah, right. Of course .

  7. #187
    International Vice-Captain Redbacks's Avatar
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    The answer is slightly out, H will move also during the 10 mins but appears to be given equivalent in the 3rd equation
    Last edited by Redbacks; 18-11-2010 at 07:46 AM.

  8. #188
    International Vice-Captain Redbacks's Avatar
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    Here is how I attacked the problem + the uppercut method which give the same results
    Attached Images Attached Images

  9. #189
    The Wheel is Forever silentstriker's Avatar
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    Love your hand writing. Very mathematician-esque.

  10. #190
    International Coach PhoenixFire's Avatar
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    ∫e^(x^2) dx

    Came across this in a homework and have no idea how to do it, any help?
    Quote Originally Posted by Top_Cat View Post
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  11. #191
    Cricket Web: All-Time Legend Uppercut's Avatar
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    You can differentiate that, right? Integrating it is just doing the opposite. Divide by the factors you'd multiply by when differentiating, keep constant what you'd keep constant when differentiating.

  12. #192
    International Coach PhoenixFire's Avatar
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    Well yeah I can differentiate it and I can integrate lots of other ones like that, but I can't do that specific one.

  13. #193
    Cricket Web: All-Time Legend Uppercut's Avatar
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    Maybe I'm missing something... why not?

  14. #194
    International Coach PhoenixFire's Avatar
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    Lack of something like x or 2x before the e term...

    Try if you can get an answer for it..

  15. #195
    Cricket Web: All-Time Legend Uppercut's Avatar
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    The coefficient of e is 1.

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