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Let's discuss Mathematics

Discussion in 'Science & Technology' started by ParadigmShifter, Mar 16, 2009.

  1. CKS

    CKS Deity

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    I would solve this differently. I'm using * for times.

    Problem 1:
    We have (1-x)e2 + (1-x)e3, which is (1-x)e2 + {(1-x)e2 * (1-x)}. Each term has (1-x)e2 in it, so I factor it out to get (1-x)e2 * {1 + (1-x)} or (1-x)e2 * (2-x). (Notice that Harv dropped a minus sign - F and A are opposites of each other.)

    Problem 2:
    (π - 4)e2 + π - 4 has n-4 in each term. Factor it out to get (n-4) * {(n-4) + 1}, so we have (n-4)* (n-3).
     
  2. Harv

    Harv Emperor

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    Yes, this is simpler. My mentality has been to find a brute-force solution first, and a simpler solution second.

    This is correct. I re-constructed the formula based on the roots and I was only thinking of rewriting the formula f(x)=-f(x)=0. I will edit in a correction.
     
  3. sanabas

    sanabas Psycho Bunny Hall of Fame Staff

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    Not factor theorem. Just basic finding the common factor. i.e. x^2y + xy^2, common factor is xy, so you get xy(x+y). Or 8x^2 + 6x, common factor is 2x, so 2x(4x+3).

    These questions are the next step from that, because the common factor isn't just xy or 2x, but is in the form (a+b), which makes it a bit trickier to divide each term by the common factor.

    So (1-x)^2 + (1-x)^3, common factor is (1-x)^2. So you get [(1-x)^2](1 + (1-x)) = (2-x)(1-x)^2

    (n-4)^2 + (n-4), common factor is (n-4), so (n-4)((n-4)+1) = (n-4)(n-3)

    *edit* and already answered over the page. oops. */edit*
     
  4. Robert FIN

    Robert FIN Monty n' Roll

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    ^^ Whoah, thanks to 3 of you! Makes sense now. Those example "problems" were really difficult to my level. Thanks.

    And those are absolutely correct, checked the answers. I will send you more if there will be more weird examples in the future. Thanks.
     
  5. Robert FIN

    Robert FIN Monty n' Roll

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    Hey, here's a new problem:

    Have a pair of equations (I hope this is the right term...) but I don't know how to solve it the smart way (this one is easy to count without any smart ways too).

    x + y = 20
    x * y = 91

    If I multiply another one with negative number, it makes everything to go zero... Is this even possible to do? And is it even right to have * marks in that kinda problem?
     
  6. dutchfire

    dutchfire Deity Retired Moderator

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    x = 20-y
    (20-y)*y = 91
    -y^2+ 20y - 91 =0
    y=7 or y=13
    x=13 or x=7
     
  7. Robert FIN

    Robert FIN Monty n' Roll

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    ^ Yes, cool.

    The first move was the thing I was missing. Thanks.

    And the answer is right.
     
  8. bhavv

    bhavv Glorious World Dictator

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    Math sounds terrible you darn Americans.

    Its maths, for the simple reason that the full term is mathematics, not mathematic.

    Lern 2 English.
     
  9. Harv

    Harv Emperor

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    I looked at the last two pages and I think Americans are in the minority.
     
  10. Robert Can't

    Robert Can't Éponine

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    Do any of you have much experience using LaTeX?

    Just started looking into it as I'm going to need to use it in an internship over next Summer.
     
  11. dutchfire

    dutchfire Deity Retired Moderator

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    Yes. I think it is pretty much unavoidable for mathematics/theoretical physics writing and publishing.
     
  12. Silv Something

    Silv Something Pi(e) Loving Maniac

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    Somewhere over the rainbow . . .


    EDIT: I mean, just look at that font.
     
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  13. Robert Can't

    Robert Can't Éponine

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    It is truly something of beauty
     
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  14. Atticus

    Atticus Deity Retired Moderator

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    It can be a bit overwhelming first, but the best way is usually to dive straight into it: copy the settings from someone and start to write.

    Here's what I usually use for short stuff. I wrote some nonsense there so you can pick some of the most usual things:
    Spoiler :

    Code:
    \documentclass[a4paper,10pt]{article}
    \usepackage[utf8]{inputenc}
    \usepackage{amsfonts}
    %\usepackage{cases}
    \usepackage{amsmath}
    \usepackage{booktabs}
    \usepackage{graphicx}
    \usepackage{enumerate}
    \usepackage[parfill]{parskip}
    
    \begin{document}
    \global\let\newpagegood\newpagegood
    \title{Type Title Here}
    \author{Type Author Here}
    \maketitle
    
    Type inline formulae inside single dollars: $\Delta \alpha \int f \, dx$. (Backslash-comma is just a space). Formulae on their own row inside twi dollars:
    $$\sum_{k=0}^{\infty} \int_{0}^1 f_k \, dx \neq  \lim_{x\to 0} x \le 1.$$
    
    If you want to align the rows, use this:
    \begin{align*}
    1 &= 2\\
       &= 3\\
       &= 4.
    \end{align*} 
    Here et-symbol sets tabs and two backslashes changes the line.
    
    \textbf{Bold text.} \emph{Emphasize,}
    \end{document}     
    


    Use some IDE for writing, like MikTex for Windows or Kile for Linux.

    EDIT: % is a comment, that is, the row after it is ignored.
     
  15. uppi

    uppi Deity

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    MikTex is a TeX distribution for Windows. For an IDE you want TeXnicCenter, TeXworks or any of the other available options on Windows.
     
  16. Atticus

    Atticus Deity Retired Moderator

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    Oh yeah, you're of course right, I got the names mixed up. :)
     
  17. nc-1701

    nc-1701 bombombedum

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    I like texworks, Tex is a pain to learn but really useful. I never got to be good with it, and I probably won't have the opportunity with my current path, but it's cool as hell and looks fantastic.
     
  18. Robert Can't

    Robert Can't Éponine

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    Well my computer decided it was tired of this futile life and so I'm back to scribblings on paper and blackboards.

    And now whiteboards as in an exciting turn of events the department has decided to cover the corridor walls with whiteboards. What a lovely idea.
     
  19. bhavv

    bhavv Glorious World Dictator

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    Round up the numbers in the following equation to their nearest whole:

    1.4 + 1.4 = 2.8.
     
  20. Atticus

    Atticus Deity Retired Moderator

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    :bump:

    To celebrate the Friday, here's a puzzle: You can travel from the left top corner of a chess board to the bottom right by going through all the squares exactly once: 7 down, 1 right, 7 up (this is NOT product placement), 1 right,...

    Can you do the same from the top left to the top right? How or why not?

    The allowed moves are left, right, up and down.

    This puzzle was brought to you by 7 up!
     

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