Let's discuss Mathematics

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

1. CKSDeity

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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:
(&#960; - 4)e2 + &#960; - 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. HarvEmperor

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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. sanabasPsycho BunnyHall 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)

4. Robert FINMonty 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 FINMonty 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. dutchfireDeityRetired 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 FINMonty n' Roll

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^ Yes, cool.

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

8. bhavvGlorious 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. HarvEmperor

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I looked at the last two pages and I think Americans are in the minority.

10. Robert Can'tÉponine

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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. dutchfireDeityRetired Moderator

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

12. Silv SomethingPi(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'tÉponine

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It is truly something of beauty

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14. AtticusDeityRetired 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. uppiDeity

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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. AtticusDeityRetired Moderator

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Oh yeah, you're of course right, I got the names mixed up.

17. nc-1701bombombedum

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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'tÉponine

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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. bhavvGlorious 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. AtticusDeityRetired Moderator

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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!