Math Questions

[moekamo]

yea thats correst how you've factorised it, you then need to get rid of the neg and swap the inequality sign, so you get (x-5)(x+3)>0.

now draw that parabola, x ints at -3 and +5 and its has a min. Now look when its greater than 0, from the graph this is when x>5 and x<-3, so your answer is x is an element of (-infinity,-3) U (5, infinity).

[#1procrastinator]

^ why is it not correct to multiply one of the binomials by the negative?

[kamil9876]

What do you mean exactly?

[#1procrastinator]

I mean when you separate


and then solve them where one is less than zero and the other greater, what is wrong with doing it the way I did it

and or and

Why can't you keep the negative?

---

Some other questions

2) Regarding vectors, when you let a represent a vector AB, and write it out, can you write a with an arrow over the top like AB, or does it have to be the squiggly line underneath?

3) Does the inequality sign with two lines underneath mean the same thing as one with one line?

4) When do you use the triple line equal sign (identical to?)?

[kamil9876]

Yeah that's fine it also works.

2),3),4) all have the same answer: it doesn't matter, it's just notation,depends on the context and what you are reading/doing.

Wilson conjectured a now famous result in number theory but was unable to prove his conjecture. He thereupon remarked that perhaps an entirely new notation for number theory would be needed to prove the conjecture. When Gauss heard about the affair, he proved the conjecture in a few minutes by a very simple argument, and acidly remarked 'what he [Wilson] needed was a notion, not a notation.'

From experience though, can be used in many ways, there are many important notions of equivalence out there. For example because they are both odd (see modular arithmetic) or, according to a topolgist because you can continously deform one into the other.

[dc302]

^ In spesh, the equivalence sign is used pretty commonly when you're doing partial fractions. This is to indicate that the statement is true for ALL x, not just some x.

For example, if you have x/(x+1)(x-2), and you want to express it in the form: A/(x+1) + B/(x-2), in your working you would have a line that says...

A(x-2) + B(x+1) is equivalent to x

This means that you can put ANY value for x in and the statement is still true, whereas if you had a normal equation, x+5=10, this means that there are only some values of x that will work. With this idea, it would be wrong to say x+5 is equivalent to 10.

[#1procrastinator]

Ok, I'll try the inequality again

Case 1:




and



Case 2:
Thanks





and



screwed up again somewhere, lol

Thanks kamil9876 and dc302. the example with x's makes sense to me but I guess I have to learn to identify when it's appropriate to use it, e.g. my physics text states the density formula as:



but my teacher used an equal sign. i suppose the difference is that the book is saying that density is basically the amount of stuff over a certain volume, giving the equivalency (is that what it's called when you use that symbol?) so you can think of it that way conceptually whereas my teacher was just showing the formula/equation for calculating it without going into why it's that way (though it's obvious)...does this make sense?   

edit 2: why is the square root of some number not a + or -?

e.g.

---

does the inequality symbol with two horizontal lines beneath mean the same thing as ?

[kamil9876]

Hrmm I've seen used when you want to emphasize that is the definition of as opposed to some theorem about , which was previously defined.

As to your inequality. Correct working but now the question is how do you interpret the result? The solution is "case 1 or case 2". You've shown Case 1 is "x>5 and x>-3" but this can be simplified to "x>5". You've shown Case 2 is "x<5 and x<-3" and this can be simplified to "x<-3". Hence the final solution is "x>5 or x<-3".

[#1procrastinator]

^ aaah, thanks a lot! for some reason i kept thinking it had to be either one or the other

[#1procrastinator]

I posted this in the GMA forum but it's gotten no responses so I'll try here...
---

Find all 2x2 matrices such that A=A^-1

Using







I got the following:






But the answers also have this:



If you can write c as (1-a^2)/b, couldn't you do the same with b (write it in terms of c and c)?

[b^3]

I posted this in the GMA forum but it's gotten no responses so I'll try here...
---

Find all 2x2 matrices such that A=A^-1

Using







I got the following:



But the answers also have this:



If you can write c as (1-a^2)/b, couldn't you do the same with b (write it in terms of c and c)?

Sorry, I'm not sure how to get rid of the <br/>, it turns out find in the latex sandbox

This is the code you have right now for the LaTeX

Code: [Select]

[tex]

\begin{bmatrix}
a & b \\
\frac{1-a^2}b&-a
\end{bmatrix}
[/tex]
Now where you see the "\\", means that it should go in the next line by the editor. But for some reason here it doesn't do that, so what you have to do is put the "\\" on the next line and then put a space after it, then delete the enter so that the line below becomes on the same line as the "\\".
i.e.

Code: [Select]

[tex]

\begin{bmatrix}
a & b
\\ \frac{1-a^2}b&-a
\end{bmatrix}
[/tex]
Result:


So that means


EDIT: 1700^th post

[#1procrastinator]

cleaned it up, thanks a lot b^3!

[#1procrastinator]

How do you tell when an expression is in its simplest form? Are there any rules of thumb? Been looking through some old posts and there are some nasty looking ones that when simplified, doesn't look 'simplified' to me at all (but I'm only used to seeing baby expressions)