pre cal for geniuses - lets play
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zarathustra
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pre cal for geniuses - lets play
Find the inverse of g: g(x)= x^2 + 2x + 3, when x is greater than or equal to -1. This is what I have:
y=x^2 + 2x + 3
x=y^2 + 2y + 3 (which can also be written as x-3=y(y+2)
This is what I've done so far...
x - 3 = y^2 + 2y
x - 3 + 1 = y^2 + 2y + 1
x - 2 = (y + 1)^2
so y + 1 = +/- sqrt(x - 2)
y = -1 +/- sqrt(x-2)
Can anyone advance this further?
z
y=x^2 + 2x + 3
x=y^2 + 2y + 3 (which can also be written as x-3=y(y+2)
This is what I've done so far...
x - 3 = y^2 + 2y
x - 3 + 1 = y^2 + 2y + 1
x - 2 = (y + 1)^2
so y + 1 = +/- sqrt(x - 2)
y = -1 +/- sqrt(x-2)
Can anyone advance this further?
z
- Kevin Solway
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Re: pre cal for geniuses - lets play
Unless this topic has something to do with enlightenment or wisdom, it will be removed.
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Ignis Fatuus
Re: pre cal for geniuses - lets play
If I hadn't dropped out of school a week ago, I probably would've been able to understand this. I was taking pre-cal and it was going well for a highschool dropout...
Fuck!-Why is Dan always right!
Fuck!-Why is Dan always right!
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zarathustra
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Re: pre cal for geniuses - lets play
truth, courage, honesty, LOGIC...
Precalculus attempts to show you that its ideas can serve as a mathematical model of a tremendous number of phenomena in our everyday experience.
Most of precalculus is just looking at examples, listening for these key words and phrases as they are used to describe different situations, and slowly coming to an understanding of how a few simple notions can help us to appreciate THE UNITY AMONG NATURE'S VARIETY...
Precalculus gives you lots of opportunities to explore these notions in interesting places, at your own pace. Enjoy the trip, enjoy the experiences, and trust your subconcious to begin forming the connections.
Its obvious that Precal is a 'language' which can be incorporated into philosophical thinking, in a less 'cluttered' way than words, as it deals directly with 'spatial' concepts and problems. Solway's assumption that it is 'a useless topic' does nothing but demonstrate his ignorance. Mathematics has always had a place in philosophical thinking. That some in this forum cannot think that way, OR JUST DON'T GET IT, is no case for ITS exclusion...
z
Precalculus attempts to show you that its ideas can serve as a mathematical model of a tremendous number of phenomena in our everyday experience.
Most of precalculus is just looking at examples, listening for these key words and phrases as they are used to describe different situations, and slowly coming to an understanding of how a few simple notions can help us to appreciate THE UNITY AMONG NATURE'S VARIETY...
Precalculus gives you lots of opportunities to explore these notions in interesting places, at your own pace. Enjoy the trip, enjoy the experiences, and trust your subconcious to begin forming the connections.
Its obvious that Precal is a 'language' which can be incorporated into philosophical thinking, in a less 'cluttered' way than words, as it deals directly with 'spatial' concepts and problems. Solway's assumption that it is 'a useless topic' does nothing but demonstrate his ignorance. Mathematics has always had a place in philosophical thinking. That some in this forum cannot think that way, OR JUST DON'T GET IT, is no case for ITS exclusion...
z
Re: pre cal for geniuses - lets play
Zararthusta: Well said. - btw: The "three wise monkeys" have hijacked the meaning of word "genius" here, don't even try. DHoges might solve the equation though = Mathematician :)zarathustra wrote:truth, courage, honesty, LOGIC...
Precalculus attempts to show you that its ideas can serve as a mathematical model of a tremendous number of phenomena in our everyday experience.
Most of precalculus is just looking at examples, listening for these key words and phrases as they are used to describe different situations, and slowly coming to an understanding of how a few simple notions can help us to appreciate THE UNITY AMONG NATURE'S VARIETY...
Precalculus gives you lots of opportunities to explore these notions in interesting places, at your own pace. Enjoy the trip, enjoy the experiences, and trust your subconcious to begin forming the connections.
Its obvious that Precal is a 'language' which can be incorporated into philosophical thinking, in a less 'cluttered' way than words, as it deals directly with 'spatial' concepts and problems. Solway's assumption that it is 'a useless topic' does nothing but demonstrate his ignorance. Mathematics has always had a place in philosophical thinking. That some in this forum cannot think that way, OR JUST DON'T GET IT, is no case for ITS exclusion...
z
It's just a ride.
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mensa-maniac
Re: pre cal for geniuses - lets play
Zarathustra
Excellent, continue on as you are. You're wiser than most.
Excellent, continue on as you are. You're wiser than most.
Re: pre cal for geniuses - lets play
No clue what you are trying to do though I got calc4. =\
- David Quinn
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Re: pre cal for geniuses - lets play
hsandman wrote:
It was worldly, shallow-minded, mainstream people who hijacked the word and turned it into "being clever with what is trivial".
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The word "genius" originally meant "guardian spirit", which connected it to wisdom and spirituality. A genius was someone who guarded the spiritual welfare of humanity.The "three wise monkeys" have hijacked the meaning of word "genius" here, don't even try.
It was worldly, shallow-minded, mainstream people who hijacked the word and turned it into "being clever with what is trivial".
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zarathustra
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Re: pre cal for geniuses - lets play
There are several definitions of the word 'genius'...it doesn't necessarily follow that those who don't give primacy to David Quinn's definition are 'shallow minded...'It also means someone who has a great natural ability for original ideas; a special character or spirit of a nation, period, language, bla, bla, also the spirit which attends and guards a place ( David Q as mediator of Genius Forum?). One of the earliest definitions of the word comes from the Latin which refers to 'two opposing guardian spirits, one good, the other evil...' In fact, throughout history the word has also been used to describe 'any spiritual being' and in its earliest incantation was used to describe 'a male generative or creative principle....'
Precal is not 'trival' in fact what it reveals can be quite 'sublime'. That DQ and others don't understand the language, is no one's fault. The emotive outbursts he uses to describe his prejedice in relation to this subject, demonstrates a flaw in his own careless, emotive thinking, rather than the real situation. On the path to wisdom, like all of us, he still has a long way to go...
The precal problem is an 'advanced' problem, level 4 may not be enough to take it further...
z
Precal is not 'trival' in fact what it reveals can be quite 'sublime'. That DQ and others don't understand the language, is no one's fault. The emotive outbursts he uses to describe his prejedice in relation to this subject, demonstrates a flaw in his own careless, emotive thinking, rather than the real situation. On the path to wisdom, like all of us, he still has a long way to go...
The precal problem is an 'advanced' problem, level 4 may not be enough to take it further...
z
Last edited by zarathustra on Wed Oct 10, 2007 10:15 am, edited 1 time in total.
- Trevor Salyzyn
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Re: pre cal for geniuses - lets play
That's a lot of words to justify your attempt to get other people to do your homework for you.
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zarathustra
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Re: pre cal for geniuses - lets play
TS is like an impetious imp - with the disposition of a spoilt child - whose cleverness, is unfortunately, often peppered and fused with resentiment for anyone, despite their good intentions, who may view the dance of life from a different angle...
z
z
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Ergasiophobic
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Re: pre cal for geniuses - lets play
I'm guilty of thinking of the same joke as Trevor. :)
But i'm aware of the value of maths even though i'm horrible at them. My brother is currently taking Trigonometry (having a tough time with it) for Architectural Engineering. I recently mentioned to him how much significance I see in maths and how I think it can have an important role in Philosophy even though I don't know how to do them myself. I'm good with language and he's better with math. We decided that we should help each other learn the opposite subjects. He was quite surprised to find out that I had heard of the Golden Mean/Golden Ratio/Phi and the Fibonacci Series, though i'm really ignorant of the details.
When I complained to him about how I didn't want to learn math because of the complexity and complications of it, he pointed out that we all subconsciously use them everyday. Then I pointed out that we don't need to study how it's done to use it. (As I saw someone else mention once that they don't need to know geometry to place their hand in the right location to catch a ball. They do it automatically.) I guess the same can be said for Philosophy. We all think automatically, but some of us take it further and analyze this process and others don't care.
But i'm aware of the value of maths even though i'm horrible at them. My brother is currently taking Trigonometry (having a tough time with it) for Architectural Engineering. I recently mentioned to him how much significance I see in maths and how I think it can have an important role in Philosophy even though I don't know how to do them myself. I'm good with language and he's better with math. We decided that we should help each other learn the opposite subjects. He was quite surprised to find out that I had heard of the Golden Mean/Golden Ratio/Phi and the Fibonacci Series, though i'm really ignorant of the details.
When I complained to him about how I didn't want to learn math because of the complexity and complications of it, he pointed out that we all subconsciously use them everyday. Then I pointed out that we don't need to study how it's done to use it. (As I saw someone else mention once that they don't need to know geometry to place their hand in the right location to catch a ball. They do it automatically.) I guess the same can be said for Philosophy. We all think automatically, but some of us take it further and analyze this process and others don't care.
Last edited by Ergasiophobic on Wed Oct 10, 2007 11:07 am, edited 1 time in total.
- Trevor Salyzyn
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Re: pre cal for geniuses - lets play
z... yeah, math is boring.
Anyway, here's a hint: the vertical distance to the curve at any point x along the graph is the value of y at x; therefore, the sum of all the values of x between -1 and infinity is the area underneath the curve along this range.
Anyway, here's a hint: the vertical distance to the curve at any point x along the graph is the value of y at x; therefore, the sum of all the values of x between -1 and infinity is the area underneath the curve along this range.
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zarathustra
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Re: pre cal for geniuses - lets play
Mmm??
Not even close.
z
Not even close.
z
- Trevor Salyzyn
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Re: pre cal for geniuses - lets play
Pardon? I thought you said you were doing calculus. You're looking for either a slope or an area. In this case, since you are looking for the value of the function from one point til infinity (or until the graph intersects itself), it's an area.
By saying "not even close", you seem to have lost touch with what problem you are trying to solve.
By saying "not even close", you seem to have lost touch with what problem you are trying to solve.
- Trevor Salyzyn
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Re: pre cal for geniuses - lets play
I guess, to be fair, I'll give you a second hint (the second one will be as free as the first):
The distance from the upper portion of the curve to the lower portion of the curve, although it can't be effectively graphed due to the imaginary number in the solution, still can be modelled abstractly. To find this distance, you don't need to use any technique more complicated than subtraction.
The distance from the upper portion of the curve to the lower portion of the curve, although it can't be effectively graphed due to the imaginary number in the solution, still can be modelled abstractly. To find this distance, you don't need to use any technique more complicated than subtraction.
Re: pre cal for geniuses - lets play
He's not doing integrals in pre cal. GG Trevor, caught BSing again. :)
- Trevor Salyzyn
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Re: pre cal for geniuses - lets play
You have to admit it would be pretty cool if he was able to figure out how to create anti-derivatives before even touching on derivatives.
Re: pre cal for geniuses - lets play
You have to admit this is off topic and you were wrong. ;)Trevor Salyzyn wrote:You have to admit it would be pretty cool if he was able to figure out how to create anti-derivatives before even touching on derivatives.
- Trevor Salyzyn
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Re: pre cal for geniuses - lets play
Neil, the problem can be solved with integration.
From g^-1(x) = -1 +/- sqrt(x-2),
f(x) = -1 + rt(x-2) - (-1 - rt(x-2))
= -1 + rt(x-2) +1 + rt(x-2)
= 2rt(x-2)
Integrate that from -1 to infinity and you have the answer (well, it won't be infinity; it will be the point when g^1(x) intersects with itself [or when f(x) intersects with 0] but you get the idea). Again: this stuff is boring. A=A is all you ever need to know.
From g^-1(x) = -1 +/- sqrt(x-2),
f(x) = -1 + rt(x-2) - (-1 - rt(x-2))
= -1 + rt(x-2) +1 + rt(x-2)
= 2rt(x-2)
Integrate that from -1 to infinity and you have the answer (well, it won't be infinity; it will be the point when g^1(x) intersects with itself [or when f(x) intersects with 0] but you get the idea). Again: this stuff is boring. A=A is all you ever need to know.
- Trevor Salyzyn
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Re: pre cal for geniuses - lets play
Blah, I might as well finish it.
f(x) = 2rt(x-2)
= 2(x-2)^1/2
F(x) = 4(x-2)^3/2 + C
Area = F(2) - F(-1) [the constant will subtract out; therefore I can ignore it]
F(-1) = 4(-3)^3/2
= 4i * rt(27)
= 12i * rt3
F(2) = 0
Therefore,
Area = 12i * rt3 - 0
= 12irt3
Therefore, g^-1(x) when x is greater than or equal to -1 is 12rt(-3).
Fucking reverse psychology. >:(
f(x) = 2rt(x-2)
= 2(x-2)^1/2
F(x) = 4(x-2)^3/2 + C
Area = F(2) - F(-1) [the constant will subtract out; therefore I can ignore it]
F(-1) = 4(-3)^3/2
= 4i * rt(27)
= 12i * rt3
F(2) = 0
Therefore,
Area = 12i * rt3 - 0
= 12irt3
Therefore, g^-1(x) when x is greater than or equal to -1 is 12rt(-3).
Fucking reverse psychology. >:(
Re: pre cal for geniuses - lets play
Trevor, you're embarrassing yourself.
Playing into the idea that "genius" consists of, or even involves, the ability and/or willingness to function as a glorified $1.99 calculator supports and affirms a very silly and ignorant definition of the term. Certainly there are those of considerable intellect who naturally gravitate toward such things, and the physical sciences welcome them. However, I think the popular idea that one is a "pseudo-intellectual" if he cannot or will not work complicated math problems is utter rubbish of the worst kind. It's a way of effectively neutering exceptional intellect by forcing it to conform to some harmless and self-abnegating stereotype. If a "genius" does cannot or will not do the utterly uncreative monkey work that is solving equations and other "brainteasers," he can be safely disregarded, and we can go back to getting all of our intellectual guidance from people such as those who inhabit MENSA meetings. Which is to say, completely harmless, ineffective, and asinine "guidance" which is no threat to anyone's core ideological pathology.
Playing into the idea that "genius" consists of, or even involves, the ability and/or willingness to function as a glorified $1.99 calculator supports and affirms a very silly and ignorant definition of the term. Certainly there are those of considerable intellect who naturally gravitate toward such things, and the physical sciences welcome them. However, I think the popular idea that one is a "pseudo-intellectual" if he cannot or will not work complicated math problems is utter rubbish of the worst kind. It's a way of effectively neutering exceptional intellect by forcing it to conform to some harmless and self-abnegating stereotype. If a "genius" does cannot or will not do the utterly uncreative monkey work that is solving equations and other "brainteasers," he can be safely disregarded, and we can go back to getting all of our intellectual guidance from people such as those who inhabit MENSA meetings. Which is to say, completely harmless, ineffective, and asinine "guidance" which is no threat to anyone's core ideological pathology.
I live in a tub.
Re: pre cal for geniuses - lets play
And I freely admit that I have no idea how to solve the problem or even what most of the symbols mean. Being a person whose intelligence is not numerically-oriented, I consider it to my credit that I haven't wasted any of my time becoming familiar with such things, which are of no relevance to either my philosophical work or my interests in general.
That said, even if I could do the problem in ten seconds, I certainly would not simply to prove something to a heckler.
That said, even if I could do the problem in ten seconds, I certainly would not simply to prove something to a heckler.
I live in a tub.
- Trevor Salyzyn
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Re: pre cal for geniuses - lets play
You're absolutely right, Unidian. There was no value whatsoever in me being able to solve the problem. This thread is in Worldly Matters for a reason.
It is my dismay that I carried this glorified algebra into a couple years of university, and my embarassment that here I did not heed Confucius' advice: "a gentleman is not a vessel".
It is my dismay that I carried this glorified algebra into a couple years of university, and my embarassment that here I did not heed Confucius' advice: "a gentleman is not a vessel".

