Current Year 12 Thread Mark VI

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  1. paranoid_android2's Avatar
    421 02-05-2012  21:59
    • Vengeful, Imperial Overlord of The Student Room
    Re: Current Year 12 Thread Mark VI
    (Original post by Heptapus)
    Woohooo! I am so busy now - I have 3 pieces of music to arrange. :lolwut:

    Yep! Wooo

    Okay. First question. Find G - Okay easy enough

    Second question find the sum to this G^2(H-h) <- something like that - WHAT H!? I HAVE NO H ON MY PAPER! :nooo:
    :eek:
    Good luck! :console:

    Oh no, I hate it when stuff like that happens in an exam! :console: :console:
  2. Heptapus's Avatar
    422 02-05-2012  22:08
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    Re: Current Year 12 Thread Mark VI
    (Original post by --emma--)
    :eek:
    Good luck! :console:

    Oh no, I hate it when stuff like that happens in an exam! :console: :console:
    I will do them after exams - I am just far too busy.
    Thanks.

    I found H.
  3. Maths_Lover's Avatar
    423 02-05-2012  22:21
    • TSR Legend
    Re: Current Year 12 Thread Mark VI
    (Original post by Heptapus)
    I do, for chat. :ninja:
    :lol:

    (Original post by chickenonsteroids)
    :yawn: maths is boring me now
    Maths is never boring. :sogood:
  4. Maths_Lover's Avatar
    424 02-05-2012  22:22
    • TSR Legend
    Re: Current Year 12 Thread Mark VI
    Guys... are you still working on the inequalities question? I hope that I challenged you significantly. :ahee:
  5. chickenonsteroids's Avatar
    425 02-05-2012  22:24
    • TSR Demigod
    • Posts: 6,675
    Re: Current Year 12 Thread Mark VI
    (Original post by Maths_Lover)
    Maths is never boring. :sogood:
    I started with C1 and :yawn: I think i'm just being lazy. Although some of the things i'm clueless about like integration :lol:

    Maths ... be interesting again. otherwise I'll just work on physics instead
  6. Maths_Lover's Avatar
    426 02-05-2012  22:31
    • TSR Legend
    Re: Current Year 12 Thread Mark VI
    (Original post by chickenonsteroids)
    I started with C1 and :yawn: I think i'm just being lazy. Although some of the things i'm clueless about like integration :lol:

    Maths ... be interesting again. otherwise I'll just work on physics instead
    Hang in there... the awesomeness will come with thinking deeply about the maths you learn.
  7. 4mar_ar5en4l's Avatar
    427 02-05-2012  22:32
    • Overlord in Training
    • Location: Leicester
    • Posts: 3,384
    Re: Current Year 12 Thread Mark VI
    (Original post by Maths_Lover)
    Of course! I'm sorry. Here it is:

    http://www.shoup.net/ntb/ntb-v1.pdf

    Proceed armed with patience and willpower. These books do not explain things as fully as I did the other day - you have to figure it out for yourself (which makes it all the more fun, of course).
    Thanks

    Yes I will need a LOT of patience and even more willpower!

    That is where the fun lies, but only if you have all the time in the world to learn it properly - I guess this'll have to wait for summer.
  8. Maths_Lover's Avatar
    428 02-05-2012  22:35
    • TSR Legend
    Re: Current Year 12 Thread Mark VI
    (Original post by 4mar_ar5en4l)
    Thanks

    Yes I will need a LOT of patience and even more willpower!

    That is where the fun lies, but only if you have all the time in the world to learn it properly - I guess this'll have to wait for summer.
    No problemo.

    Indeed... like I have said, it took me a while to really get into Number Theory but once I got going, I couldn't stop. :lol: It's so much fun. :cute:

    This summer is going to be epic... filled with maths and physics. :sogood:

    I can't wait until exams are over.
  9. Heptapus's Avatar
    429 02-05-2012  22:37
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    Re: Current Year 12 Thread Mark VI
    (Original post by Maths_Lover)
    :lol:
    :ninja:
    I am not on it now though.
  10. Maths_Lover's Avatar
    430 02-05-2012  22:42
    • TSR Legend
    Re: Current Year 12 Thread Mark VI
    Show that, if p&gt;m&gt;0, then

    \displaystyle \frac{p-m}{p+m} \leq \frac{x^2-2mx+p^2}{x^2+2mx+p^2} \leq \frac{p+m}{p-m}, \ \forall x \in \mathbb{R}

    By the way... NO CALCULUS ALLOWED!!!

    Hint:

    Spoiler:
    Show

    Let \displaystyle y = \frac{x^2-2mx+p^2}{x^2+2mx+p^2} .

    What can you say about the resulting quadratic in x, \displaystyle \forall x \in \mathbb{R} ?

    Last edited by Maths_Lover; 02-05-2012 at 22:44.
  11. Maths_Lover's Avatar
    431 02-05-2012  22:45
    • TSR Legend
    Re: Current Year 12 Thread Mark VI
    (Original post by Heptapus)
    :ninja:
    I am not on it now though.
    Good.
  12. Llewellyn's Avatar
    432 02-05-2012  23:11
    • Section Moderator
    • Astray anyway
    Re: Current Year 12 Thread Mark VI
    (Original post by Maths_Lover)
    Show that, if p&gt;m&gt;0, then

    \displaystyle \frac{p-m}{p+m} \leq \frac{x^2-2mx+p^2}{x^2+2mx+p^2} \leq \frac{p+m}{p-m}, \ \forall x \in \mathbb{R}

    By the way... NO CALCULUS ALLOWED!!!

    Hint:

    Spoiler:
    Show

    Let \displaystyle y = \frac{x^2-2mx+p^2}{x^2+2mx+p^2} .

    What can you say about the resulting quadratic in x, \displaystyle \forall x \in \mathbb{R} ?

    Hmm, I just considered very basic cases such as (x-p)^2, and then say if p=m, then obviously the situation holds. The tricky part was proving the degree of difference for (1) compared to (2), showing in particular that this was not 1. I think there are a few flaws in my argument because it became "obviously this" and "this" followed by a few expansions and "let the opposite be true", etc.

    In hindsight, I think it may have been better to either square everything and equate various terms using the fact that p,m > 0, or to just use proof by contradiction.

    Edit: I put x^2 + 2px + p^2 > x^2 + 2mx + p^2 in my workings. :facepalm: (before I defined x)
    eh, 11pm maths, not the greatest idea ever.
    Last edited by Llewellyn; 02-05-2012 at 23:17.
  13. Heptapus's Avatar
    433 02-05-2012  23:15
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    Re: Current Year 12 Thread Mark VI
    (Original post by Maths_Lover)
    Good.
    Going on it now though.
  14. bananarama2's Avatar
    434 03-05-2012  17:34
    • TSR Legend
    Re: Current Year 12 Thread Mark VI
    (Original post by Maths_Lover)
    Show that, if p&gt;m&gt;0, then

    \displaystyle \frac{p-m}{p+m} \leq \frac{x^2-2mx+p^2}{x^2+2mx+p^2} \leq \frac{p+m}{p-m}, \ \forall x \in \mathbb{R}

    By the way... NO CALCULUS ALLOWED!!!

    Hint:

    Spoiler:
    Show

    Let \displaystyle y = \frac{x^2-2mx+p^2}{x^2+2mx+p^2} .

    What can you say about the resulting quadratic in x, \displaystyle \forall x \in \mathbb{R} ?

    Is is something to do with the fact the minimum value of the middle bit is 1? So the LHS is clearly always less that one as p-m < P+m
  15. Maths_Lover's Avatar
    435 03-05-2012  17:44
    • TSR Legend
    Re: Current Year 12 Thread Mark VI
    (Original post by wcp100)
    Is is something to do with the fact the minimum value of the middle bit is 1? So the LHS is clearly always less that one as p-m < P+m
    You are on the right track... What is the inequality actually telling us?

    Consider this:

    If you let \displaystyle y = \frac{x^2-2mx+p^2}{x^2+2mx+p^2} and then multiply through by the denominator and do some simplification and shuffling around of terms, what do you get?
  16. Maths_Lover's Avatar
    436 03-05-2012  17:46
    • TSR Legend
    Re: Current Year 12 Thread Mark VI
    (Original post by Llewellyn)
    Hmm, I just considered very basic cases such as (x-p)^2, and then say if p=m, then obviously the situation holds. The tricky part was proving the degree of difference for (1) compared to (2), showing in particular that this was not 1. I think there are a few flaws in my argument because it became "obviously this" and "this" followed by a few expansions and "let the opposite be true", etc.

    In hindsight, I think it may have been better to either square everything and equate various terms using the fact that p,m > 0, or to just use proof by contradiction.

    Edit: I put x^2 + 2px + p^2 > x^2 + 2mx + p^2 in my workings. :facepalm: (before I defined x)
    eh, 11pm maths, not the greatest idea ever.
    See what I have said to wcp.

    You may be over-complicating it a little.

    :lol: There is plenty of room for error and missing things when doing late night maths.
  17. Maths_Lover's Avatar
    437 03-05-2012  17:47
    • TSR Legend
    Re: Current Year 12 Thread Mark VI
    (Original post by Heptapus)
    Going on it now though.


    Not a good idea.
  18. Maths_Lover's Avatar
    438 03-05-2012  17:48
    • TSR Legend
    Re: Current Year 12 Thread Mark VI
    Hyperphysics is amazing. :love:
    Post rating:
    1
  19. blueray's Avatar
    439 03-05-2012  17:58
    • TSR Legend
    • Location: United States of Nippon
    Re: Current Year 12 Thread Mark VI
    Can any one doing biology help me on this simple question on biogas? Thanks!

    http://www.thestudentroom.co.uk/show...4#post37387274
  20. paranoid_android2's Avatar
    440 03-05-2012  18:04
    • Vengeful, Imperial Overlord of The Student Room
    Re: Current Year 12 Thread Mark VI
    (Original post by Heptapus)
    I will do them after exams - I am just far too busy.
    Thanks.

    I found H.
    Good idea.

    Oh, well done! :woo:
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