Old 15th June 2005, 10:49   #1
mysterious_w
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Maths

Had my GCSE maths paper today. Went pretty well I thought, but they was a couple of simple algebra questions that stumped me, so I wrote them on my hand in the hope that one of you would know how to do it:

code:
1. Factorise:

a^2-9b^2

2. Simplify Fully:

x^2-3x
-------
x^2-8x+15






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Old 15th June 2005, 11:03   #2
shakey_snake
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(a+3b)(a-3b)
(factorise should be spelt with a 'z' )

2.

x(x-3)
------
(x-3)(x-5)

x
-----
x-5

where is Mathml hen we need it...


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Old 15th June 2005, 11:49   #3
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Actually, it's only with a z where you live. Sometimes you Americans seem to forget there are other countries.

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Old 15th June 2005, 11:55   #4
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There are?
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Old 15th June 2005, 14:14   #5
matt_69
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what grade of maths is that? i was strugling to remember the rules for that, and i do 2 maths at school . tho i do challenge you to find the derivative of 3x^4+3x using first principals haha (not really that difficult but hey, i did that on my exam today)

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Old 15th June 2005, 14:23   #6
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Quote:
Originally posted by ElChevelle
There are?
Yeah. Canada is actually a separate country, you know.
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Old 15th June 2005, 14:58   #7
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Quote:
Originally posted by matt_69
what grade of maths is that? i was strugling to remember the rules for that, and i do 2 maths at school . tho i do challenge you to find the derivative of 3x^4+3x using first principals haha (not really that difficult but hey, i did that on my exam today)
wtf is first principals? Is that the same thing as the power rule? Anyway, 12x^3 + 3

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Old 15th June 2005, 15:07   #8
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Heh, i did this paper too. Hadn't a clue about these ones but the rest of the paper was pretty okish.
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Old 15th June 2005, 15:58   #9
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Quote:
Originally posted by Wolfgang
Yeah. Canada is actually a separate country, you know.
Yeah, mostly. Same country code in the phone system. Same language (basically). Same accent as the people living on the border to Canada.

Anyway Wolfgang, shakey_snake didn't say that it is spelt with a "z", only that it should be. =P

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Old 15th June 2005, 16:55   #10
hgnis
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Quote:
Originally posted by matt_69
tho i do challenge you to find the derivative of 3x^4+3x using first principals haha (not really that difficult but hey, i did that on my exam today)
3x(x+1)(x^2-x+1)

=> 3x(x+1)[(x-1/2)^2+3/4]

QED.

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Old 15th June 2005, 18:16   #11
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2+2=4

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Old 15th June 2005, 20:30   #12
shakey_snake
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Quote:
Originally posted by Wolfgang
Actually, it's only with a z where you live. Sometimes you Americans seem to forget there are other countries.

I was joking (hence the winking), but thanks for trying to be informative...


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Old 15th June 2005, 23:32   #13
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Quote:
Originally posted by xzxzzx
Anyway Wolfgang, shakey_snake didn't say that it is spelt with a "z", only that it should be. =P
SHOULD BE? I may be a bit pissdd, but I feel I have to be as obnoxious (or informative??) as possible here. You lot have desecrated the English language. Particulalry with things like "thru", "aluminum" and the removal of the letter U from words like colour and neighbour. I also find the labelling of perfectl y arable earth as "dirt". Dirt is simply stuff you throw in the bin, not the stuff you farm with.
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Old 15th June 2005, 23:35   #14
shakey_snake
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Wolfgang...
You are American.


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Old 16th June 2005, 01:15   #15
matt_69
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Quote:
Originally posted by hgnis
3x(x+1)(x^2-x+1)

=> 3x(x+1)[(x-1/2)^2+3/4]

QED.
nah, k_rock923 got the answer, its 12x^3 + 3. and yeah, first principals is the very long and stupid way of doing the rule. uses limits and shit, too much work if you ask me.

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Old 16th June 2005, 02:17   #16
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Dirt is dirt is dirt to city folk. Go in the rural areas where we have soil. :P

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Old 16th June 2005, 12:13   #17
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Quote:
Originally posted by shakey_snake
Wolfgang...
You are American.
This is true, but does not mean I speak American English. Anyway, it would be a bit pedantic to start referring to you as a United Statesean or USAean.
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Old 16th June 2005, 15:38   #18
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Quote:
Originally posted by Wolfgang
"thru"
"Thru"?

I'd smack someone for writing "thru".

Your examples are pitiful, wolfgang. The vast majority of differences between (American) English and British (=P) are arbitrary, such as the spelling of "check" (cheque), or the different meanings of things like "chips".

Both of them have about the same degree of self-consistancy. So here's the thing: economic powers make the languages. It's always been that way. Therefore, British English is actually non-standard, because American English is spoken by the world's largest economic power. Which is fine, I'm not trying to say that you should speak American English. You can speak whatever you like. But don't try to pass off this "my language is better than yours" crap.

And Wolfgang is not "American", shakey_snake. "American" is someone from the United States (this is even more prevalent in British English, truth be told). You might call Wolfgang "panamarican".

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Old 16th June 2005, 16:01   #19
shakey_snake
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Quote:
Originally posted by xzxzzx
And Wolfgang is not "American", shakey_snake. "American" is someone from the United States (this is even more prevalent in British English, truth be told). You might call Wolfgang "panamarican"[sic].
Yes, we from the US typically think that we are the only ones considered American, but most of Central and South America would repectfully disagree with you. Just an example of things you pick up when you travel.

here is decent documentation on differences between the two Englishes.

Wolfgang, you haven't started using 'vosotros' have you?


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Old 16th June 2005, 17:53   #20
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Quote:
Originally posted by shakey_snake
here is decent documentation on differences between the two Englishes.
A good read.
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Old 16th June 2005, 17:55   #21
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Quote:
Originally posted by matt_69
what grade of maths is that? i was strugling to remember the rules for that, and i do 2 maths at school . tho i do challenge you to find the derivative of 3x^4+3x using first principals haha (not really that difficult but hey, i did that on my exam today)
wow had to see if I actually remmeber this stuff:

code:

df/dx = lim h->0 (f(x+h) - f(x)) / h
= lim h->0 (3(x+h)^4 + 3(x+h) - 3x^4 - 3x) / h
= lim h->0 (3x^4 + 12(x^3)h + 18(x^2)(h^2) + 12xh^3 + 3h^4 + 3x + 3h - 3x^4 - 3x) / h
= lim h->0 (12(x^3)h + 18(x^2)(h^2) + 12xh^3 + 3h^4 + 3h) / h
= lim h->0 12x^3 + 18hx^2 + 12xh^3 + 3h^4 + 3
= 12x^3 + 3


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Old 16th June 2005, 20:16   #22
hgnis
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oops, Matt I was thinking about the divisor-quotient factors not derivatives at the time.

I am so important I feel the need to let it be known like a liberal discovering the internets for the first time. Uh hur hur hur. I also wash myself with a rag on a stick.
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Old 17th June 2005, 13:50   #23
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Quote:
Originally posted by xzxzzx
"Thru"?

I'd smack someone for writing "thru".

Your examples are pitiful, wolfgang. The vast majority of differences between (American) English and British (=P) are arbitrary, such as the spelling of "check" (cheque), or the different meanings of things like "chips".
But don't try to pass off this "my language is better than yours" crap.

And Wolfgang is not "American", shakey_snake. "American" is someone from the United States (this is even more prevalent in British English, truth be told). You might call Wolfgang "panamarican".
Pitiful or not, I don't like them. Hearing or reading "aluminum" makes me cringe. It occurs to a lesser extent with "harbor" and "favorite", but I still don't like them. That's all. And if you read what I wrote, there was some sarcasm and light humour in it, so don't pounce on me and get all defensive about it. I never said my language is better, though it's quite obvious I do think it is better. We are all entitled to our own opinions, just like you probably believe your country is amazing and better than any other.*

I think you'll find most people who aren't American believe British English is "proper English". It's the original item. And I'm fine with the US being the biggest economy, despite how it abuses this position, and I do agree with you in that it's only natural for the language spoken in this country to proliferate around the world. I just don't like the language.

I am American. I live in America, hence I am American. It annoys me how Brits and other people refer to the USA as "America", as if it were the only important thing in America (the continent). I think it's very arrogant of you to say that only people from your country are Americans. I just have to adapt to everyone else and refer to you as an American, but I refuse to refer to your country as America.


* NOTE: I'm speculating. Don't chew my head off. It's sad I actually have to point this out.

Quote:
Wolfgang, you haven't started using 'vosotros' have you?
hah. no! never! I'm not a great fan of Spanish Spanish. Incidentally, the worst-sounding by far, in my opinion, are Venezuelan and Chilean Spanish.

Old Spanish, like what is spoken in Spain and to some extent Argentina, just sounds like using "ye", "thou", "thine" and such words to a South American. I don't dislike it, I just think it sounds odd.
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Old 17th June 2005, 14:42   #24
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Quote:
Originally posted by crackity
wow had to see if I actually remmeber this stuff:

code:

df/dx = lim h->0 (f(x+h) - f(x)) / h
= lim h->0 (3(x+h)^4 + 3(x+h) - 3x^4 - 3x) / h
= lim h->0 (3x^4 + 12(x^3)h + 18(x^2)(h^2) + 12xh^3 + 3h^4 + 3x + 3h - 3x^4 - 3x) / h
= lim h->0 (12(x^3)h + 18(x^2)(h^2) + 12xh^3 + 3h^4 + 3h) / h
= lim h->0 12x^3 + 18hx^2 + 12xh^3 + 3h^4 + 3
= 12x^3 + 3

spot on, tho i do mine a bit differently. i work out the f(x+h) bit on the side, then just sub it in. makes it look a lot neater .

you wouldn't happen to b australian would you?

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Old 17th June 2005, 15:35   #25
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Why use the method with limits? It only creates more work.

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Old 17th June 2005, 19:29   #26
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Quote:
Originally posted by shakey_snake
Yes, we from the US typically think that we are the only ones considered American, but most of Central and South America would repectfully disagree with you. Just an example of things you pick up when you travel.
Apparently (I read a linguistics article on this for some reason, was linked to it), nowadays, "American" does mean "from the US". people from North America, though, are "North American", and likewise "South American". But the generic term refers solely to people from the states.

Just common usage, I suppose!

Quote:
Originally posted by shakey_snake
where is Mathml hen we need it...
I'll mark it up in LaTeX and post it as an image, if you really want.

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Old 17th June 2005, 21:01   #27
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Quote:
Originally posted by k_rock923
Why use the method with limits? It only creates more work.
The limits way is the definition of a derivative, and the shortcuts that your are talking about are all derived from the limits way. So by learning the limits way you have the general solution and can solve problems that dont take a cookie cutter type form.

But yes, for cookie cutter type problems, using the known formulas is much faster.... as long as your remember the formulas.

Quote:
Originally posted by matt_69
spot on, tho i do mine a bit differently. i work out the f(x+h) bit on the side, then just sub it in. makes it look a lot neater .

you wouldn't happen to b australian would you?
nope, just a silly american who got drunk one day and decided to get a math major with my comp sci degree.

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Old 17th June 2005, 21:32   #28
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Quote:
Originally posted by zootm
Apparently (I read a linguistics article on this for some reason, was linked to it), nowadays, "American" does mean "from the US". people from North America, though, are "North American", and likewise "South American". But the generic term refers solely to people from the states.

Just common usage, I suppose!
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