Let's discuss Mathematics

[CKS]

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).

 

[Harv]

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

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

(Notice that Harv dropped a minus sign - F and A are opposites of each other.)

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.

 

[sanabas]

Is this what you mean? It does not directly answer your question, but it might make the question more clear.

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*

 

[Robert FIN]

^^ 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.

 

[Robert FIN]

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?

 

[dutchfire]

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

 

[Robert FIN]

^ Yes, cool.

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

And the answer is right.

 

[bhavv]

Math sounds terrible you darn Americans.

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

Lern 2 English.

 

[Harv]

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

 

[Robert Can't]

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.

 

[dutchfire]

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

 

[Silv Something]

EDIT: I mean, just look at that font.

 

[Robert Can't]

It is truly something of beauty

 

[Atticus]

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 :

\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.

 

[uppi]

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

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

 

[Atticus]

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

 

[nc-1701]

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.

 

[Robert Can't]

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.

 

[bhavv]

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

1.4 + 1.4 = 2.8.

 

[Atticus]

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!