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  1. sonofdot's Avatar
    1261 26-01-2009  22:36
    • Peer Of The TSR Realm
    • Location: Cambridge
    • Posts: 1,656
    Re: Official TSR Mathematical Society
    (Original post by Swayum)
    Yes, that works. Now what does 1/sinx equal?
    so then I would get xcosecx which I could do by parts, but I can't be bothered to do that now :p:
  2. SimonM's Avatar
    1262 26-01-2009  22:38
    • TSR Idol
    • Posts: 9,193
    Re: Official TSR Mathematical Society
    Hmm... I think this is one of that \displaystyle \int_0^a f(x) dx = \int_0^a f(a-x) dx jobs

    (Original post by sonofdot)
    so then I would get xcosecx which I could do by parts, but I can't be bothered to do that now :p:
    Kinda tough integral though, doesn't evaluate in elementary functions
  3. Zhen Lin's Avatar
    1263 27-01-2009  00:12
    • Vengeful, Imperial Overlord of The Student Room
    • Posts: 4,791
    Re: Official TSR Mathematical Society
    (Original post by SimonM)
    A little easy again

    Spoiler:
    Show

    Based on two basic theorems

    \displaystyle \sum_{k=0}^{\infty} x^k = \frac{1}{1-x}
    and
    \displaystyle \sum_{k=0}^{\infty} kx^k = \frac{x}{(1-x)^2}

    Combining these we get

    \displaystyle \frac{a}{b} + \frac{a+c}{bd} + \frac{a+2c}{bd^2} + \frac{a+3c}{bd^3} + \cdots = \frac{a}{b} \sum_{k=0}^{\infty} \left ( \frac{1}{d} \right )^k + \frac{c}{b} \sum_{k=0}^{\infty} k \left ( \frac{1}{d} \right)^k = \frac{a}{b} \frac{1}{1-\frac{1}{d}} + \frac{c}{b} \frac{\frac{1}{d}}{(1-\frac{1}{d})^2} = \boxed{ \frac{ad}{b(d-1)} + \frac{c}{b} \frac{d}{(d-1)^2}}


    Random trivia: \begin{pmatrix} a \\ b \end{pmatrix} is not the same thing as \displaystyle \left( \frac{a}{b} \right). The latter is something called the Jacobi symbol.
    Post rating:
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  4. The Bachelor's Avatar
    1264 27-01-2009  04:43
    • TSR Demigod
    • Posts: 5,614
    Re: Official TSR Mathematical Society
    (Original post by Zhen Lin)
    Random trivia: \begin{pmatrix} a \\ b \end{pmatrix} is not the same thing as \displaystyle \left( \frac{a}{b} \right).
    Doh
  5. Horizontal 8's Avatar
    1265 27-01-2009  17:04
    • Benevolent Member
    • Location: London
    • Posts: 733
    Re: Official TSR Mathematical Society
    (Original post by SimonM)
    Hmm... I think this is one of that \displaystyle \int_0^a f(x) dx = \int_0^a f(a-x) dx jobs



    Kinda tough integral though, doesn't evaluate in elementary functions

    Yep that's the way forward (that's how the teacher expected us to do it atleast)
  6. Unbounded's Avatar
    1266 27-01-2009  18:40
    • TSR Demigod
    Re: Official TSR Mathematical Society
    (Original post by SimonM)
    Hmm... I think this is one of that \displaystyle \int_0^a f(x) dx = \int_0^a f(a-x) dx jobs
    I must be being absolutely stupid, but isn't it:

    \displaystyle \int_0^a f(x) dx = - \int_0^a f(a-x) dx ?
  7. SimonM's Avatar
    1267 27-01-2009  18:47
    • TSR Idol
    • Posts: 9,193
    Re: Official TSR Mathematical Society
    (Original post by GHOSH-5)
    I must be being absolutely stupid, but isn't it:

    \displaystyle \int_0^a f(x) dx = - \int_0^a f(a-x) dx ?
    Nope
  8. Hancock orbital's Avatar
    1268 27-01-2009  18:54
    • Full Member
    • Location: Scotland
    • Posts: 118
    Re: Official TSR Mathematical Society
    (Original post by GHOSH-5)
    I must be being absolutely stupid, but isn't it:

    \displaystyle \int_0^a f(x) dx = - \int_0^a f(a-x) dx ?
    Consider the substitution y = a - x and the fact that \int_0^a f(x) dx = - \int_a^0 f(x) dx
  9. Unbounded's Avatar
    1269 27-01-2009  18:56
    • TSR Demigod
    Re: Official TSR Mathematical Society
    (Original post by Hancock orbital)
    Consider the substitution y = a - x and the fact that \int_0^a f(x) dx = - \int_a^0 f(x) dx
    im an idiot. thank you.
  10. Unbounded's Avatar
    1270 27-01-2009  18:56
    • TSR Demigod
    Re: Official TSR Mathematical Society
    (Original post by Hancock orbital)
    Consider the substitution y = a - x and the fact that \int_0^a f(x) dx = - \int_a^0 f(x) dx
    im an idiot. thank you.
  11. ~|Shock|~'s Avatar
    1271 27-01-2009  19:12
    • Exalted and Worshipped Member
    • Location: Dagenham/Essex
    • Posts: 1,272
    Re: Official TSR Mathematical Society
    [joke]
    if we define "one" as "two" and "two as "one" does that gives "two plus two equals one"?
    [/]

    anyway, join request on the way
  12. Hancock orbital's Avatar
    1272 27-01-2009  19:26
    • Full Member
    • Location: Scotland
    • Posts: 118
    Re: Official TSR Mathematical Society
    (Original post by ~|Shock|~)
    [joke]
    if we define "one" as "two" and "two as "one" does that gives "two plus two equals one"?
    [/]

    anyway, join request on the way
    NO
  13. The Muon's Avatar
    1273 28-01-2009  19:14
    • Overlord in Training
    Re: Official TSR Mathematical Society
    (Original post by Ekpyrotic)
    Ok, I understand it's customary to post a problem. Might be a little old but it's a good 'un.

    ABC is isosceles.

    AB=BC

    AB= \sqrt 5

    AC=2

    Find a way to cut the triangle into 4 pieces so that they can be constructed to form a regular square.
    I must be some sort of idoit but can someone put a hint?


    Another problem, though not very mathys:

    A farmer has the following three fields and he has 4 sons and 4 daughters. He wants to leave them with land when he passes away and to be fair they all have to have the same size plot and same shape plot. How can this be achieved?

    Attached Thumbnails
    Click image for larger version.  Name: untitled.JPG  Views: 142  Size: 3.6 KB  ID: 64324  
    Last edited by The Muon; 28-01-2009 at 19:24.
  14. JohnnySPal's Avatar
    1274 28-01-2009  23:25
    • Overlord in Training
    Re: Official TSR Mathematical Society
    (Original post by The Muon)
    A farmer has the following three fields and he has 4 sons and 4 daughters. He wants to leave them with land when he passes away and to be fair they all have to have the same size plot and same shape plot. How can this be achieved?
    Does the solution involve molesting his eldest daughter to acquire a ninth child? It's plausible; you know what farmers are like :jiggy:. I think. *ahem*.
  15. Mathematician!'s Avatar
    1275 29-01-2009  18:38
    • Overlord in Training
    • Location: In a house :D
    • Posts: 2,997
    Re: Official TSR Mathematical Society
    (Original post by The Muon)
    I must be some sort of idoit but can someone put a hint?


    Another problem, though not very mathys:

    A farmer has the following three fields and he has 4 sons and 4 daughters. He wants to leave them with land when he passes away and to be fair they all have to have the same size plot and same shape plot. How can this be achieved?

    How about leaving one field for animals to graze upon, and dividing the remaining two fields into equally sized squares and give them to his children?
    Last edited by Mathematician!; 29-01-2009 at 18:53.
  16. The Muon's Avatar
    1276 29-01-2009  18:46
    • Overlord in Training
    Re: Official TSR Mathematical Society
    (Original post by Mathematician!)
    How about leaving one field for animals to graze upon, and diving the remaining two fields into equally sized squares and give them to his children?
    I do not know the answer, it's on the wall at college and I can never figure it out.
  17. Mathematician!'s Avatar
    1277 29-01-2009  18:50
    • Overlord in Training
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    Re: Official TSR Mathematical Society
    (Original post by The Muon)
    I do not know the answer, it's on the wall at college and I can never figure it out.
    Well this is plausible, as it doesn't say you can't leave a field for animals :p:
  18. Mathematician!'s Avatar
    1278 29-01-2009  20:24
    • Overlord in Training
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    • Posts: 2,997
    Re: Official TSR Mathematical Society
    (Original post by DeanK22)
    Have not drawn this out just thought about in my head but;

    Spoiler:
    Show
    24 \div 3 = 8 and 24 \times 3 = 72

    72 \div 8 = 9


    Spoiler:
    Show
    Chop each square into 24 rectangles allocating 2 rectangles from the big square and 1 from the square beneath, alternating this pattern. Consider the rectangle at the left with nothing above or below. Give three rectangles to one person.


    Should do it - everbody gets 9 rectangles.
    Off topic, but did DeanK2 get a perm. ban?
  19. Mathematician!'s Avatar
    1279 29-01-2009  20:28
    • Overlord in Training
    • Location: In a house :D
    • Posts: 2,997
    Re: Official TSR Mathematical Society
    (Original post by DeanK22)
    This is the same person :rolleyes: ...
    No really? :rolleyes:

    What I meant is did your other account get a perm. ban?
  20. Mathematician!'s Avatar
    1280 29-01-2009  20:32
    • Overlord in Training
    • Location: In a house :D
    • Posts: 2,997
    Re: Official TSR Mathematical Society
    (Original post by DeanK22)
    I requested such a ban due to spending too much time on TSR - the irony.
    Lol! Why did you start a new account then? :eyeball:
    Changed your mind?
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