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[Zrk2]

Curse all you advanced mathers. I'm currently doing Data Management. Easy class. I look at these equations and go:

  ...  ...  Then I remember that I'll be taught how to solve them before they get thrown at me. And equations always look more scary before they are explained to you. Like:

Spoiler (click to show/hide)

In grade nine I shat myself looking at it. Now I laugh and call it an easy question.

[Tellemurius]

just remember the stupid mnemonic and you're good.

[Christes]

And equations always look more scary before they are explained to you.

More or less true at every level.  Though they eventually stop being equations as such.  And eventually you end up teaching them to yourself.

just remember the stupid mnemonic and you're good.

Do tell.  I only know of one.  I nearly break out laughing every time:

Spoiler (click to show/hide)

Once there was a negative boy. He couldn't decide whether or not to go to a radical party. He was a square boy, so he missed out on 4 awesome chics. The entire party was over at 2am

[Sowelu]

Spoiler (click to show/hide)

Once there was a negative boy. He couldn't decide whether or not to go to a radical party. He was a square boy, so he missed out on 4 awesome chics. The entire party was over at 2am

Oh my god, you are my hero.

[Tellemurius]

thats awesome where was that when i was in high school

[Miggy]

Posting this here from my linear algebra class. Every week we get a "nut" to crack. This week's nut is:

Personally I haven't got much of a clue. The definition of linear independence is that for the set of vectors there must be only one set of constants that fulfill the term: c₁*v₁ + c₂*v₂... c_n*v_n = 0, and that must be zero.

However, how I can get to there from: i₁*j₁ + i₂*j₂ .... i_n*j_n < 0 ?

And yes, I did write that into an actual text editor and screen-shot it so I could get the notation correct... Only to find out I could probably get the same with the forum code.

[Phmcw]

hmm one vector and his opposite isn't a counterexample because of the S+1
my take at the demonstration bellow

Spoiler (click to show/hide)

OK here  go: It's a recursive demonstration : Let's first take a set of three vectors : {a,b,c}. if v_i^Tv_j>0 then they are linearly independant : let's assume they are not. then one of them is a combili of the two other like that : D*a+E*b=c
Then c.a=D*|a|²+(E*b).a=D*|a|²+E*(b.a)
and c.b=D*(a.b)+E*|b|²

There six if D<0, D>0, |a|<|b|,|a|>|b|, E<0, E>0 in either cases b.a is negative. It boil down to : let's say |a|>|b|, then 
either D and E are positive and |E*(b.a)|>|D*|a|²| then c.b will be positive (b.a)<|b||a|, then...
Boring, I let you do the rest

And then you use the good old let's say it's true for s vector let's show it's true for s+1.

you'll use a proof by the absurd with v_s+1= V₁*v₁+V₂*v₂+...+V_sv_s

I didn't made it to the end so I can't guarantee it'll work. I'll do it tomorrow if you still want.

[Bouchart]

Has anyone here ever taken any of the actuarial exams?  I'm wondering if someone could recommend some study material.

[Tellemurius]

what the hell are those?

[ZetaX]

Posting this here from my linear algebra class.  [...]

This is a mess without LaTeX, but anyway:

Let's write [x,y] for x^T * y (just looks better), use w for v_s (yes, s, not s+1) and t for [w,w] (this is >0). Let U be the hyperplane orthogonal to w, so U = { x | <x,w>=0 }. Then let p be the projection onto U, so p(v) = v - ([v,w]/t)w [an easy check gives that this is in U and it is a linear map].
We are given that <v_i,v_j> is <0 for i,j from 1 to s+1 and not equal to s. Thus
<p(v_i) , p(v_j)> =
= [v_i-([v_i,w]/t)w , v_j-([v_j,w]/t)w] =
= [v_i,v_j] - [v_i,w]*[v_j,w]/t - [v_j,w]*[v_i,w]/t + [v_i,w]*[v_j,w]*[w,w]/t² =
= [v_i,v_j] - [v_i,w]*[v_j,w]/t.
But [v_i,w] and [v_j,w] are <0 and t >0, thus - [v_i,w]*[v_j,w]/t is <0, too. Together with [v_i,v_j] <0, this gives that <p(v_i) , p(v_j)> is <0.

We have shown that after applying p, we got the same setting (but with one vector less as w is sent to 0 by p). So let u_1=p(v_1), ..., u_(s-1)=p(v_(s-1) and u_s=p(v_(s+1)) and we still get [u_i,u_j] <0 for i not equal to j. By induction on s, we may assume that we have already proven the result for s' = s-1. In other words, u_1, ..., u_(s-1) are independent. This means nothing else than p(v_1), ..., p(v_(s-1)) being independent. As a result, v_1, ..., v_(s-1) are independent, too (any dependence of the v_i would by p get an dependence of the p(v_i)). But w is independent from p(v_1), ..., p(v_(s-1)) as it is orthogonal to the plane U where they live in. But v_i and p(v_i) only differ by a multiple of w, thus also v_1, ..., v_(s-1) are independet from w=v_s, which we wanted to prove.

[Vector]

There's this problem I've been working on for the past... while.  Don't laugh, I'm panicking a bit because it's due tomorrow and I didn't start it soon enough.  Also because it's a pain to use the ancient Greek methods.  Also because I'm nearly certain that this is more than trivial.


Anyway, we've got a cylinder with base C and an inscribed prism inside it, Q--i.e. the base P of Q is inscribed in C.  Both of these figures have height h.

I need to prove that the volume V of the cylinder is not greater than the height of h times the area of C:

V > h[a(C)] is false.  I already proved that V < h[a(C)] is false, through pretty trivial methods (though I can provide a proof if necessary).  Basically, the proof method we've been ordered to use is "proceed by abusing trichotomy and double reductio ad absurdum."  So no, I can't just calculus this to death.

What I know is that for every e > 0 there is a P so that

e > a(C) - a(P) > 0,

i.e. the limit of the area of the polygons approaches the area of the circle, and that the volume of the prism is given by h[a(P)].


My problem with this is that I can't figure out how to relate V to the rest of the information in any meaningful way.  It's just kind of floating there.

... In fact, I'm currently thinking that I set this up wrong.  If anyone has any ideas, please just give me a hint; I really don't want the complete proof, just to figure out where my thinking is screwy.  Thanks in advance.


EDIT: Yeah, I was about to post this question somewhere else and then I suddenly realized what I was doing wrong.  Sorry about that.

DOUBLE-EDIT: And then I was wrong again    Advice would be great.

[Nivim]

 You've earned a reputation as one ridiculously good at math, so no one wants to approach a problem you're tackling (not to mention one that eschews the "normal complicated" math they are used to). Although despite knowing almost nothing about the proofs behind your problem, I think it would help if you at least summarized what methods you found to be wrong.

[eerr]

V= h pie r^2

R being both the radius, and the longest line you can draw from the inside to the outside in the pyramidal solid.

hint(I think?): calculus is all about dividing things up into peices, anyway.

You've earned a reputation as one ridiculously good at math, so no one wants to approach a problem you're tackling (not to mention one that eschews the "normal complicated" math they are used to). Although despite knowing almost nothing about the proofs behind your problem, I think it would help if you at least summarized what methods you found to be wrong.

It's not what Vector is using wrong, it's what she is supposed to be using, that remains unclear.
It's literally stuff my calculus teacher told us flat out, and did not make us do problems about.

Would be ironic if the answer is in the book though.


Or if this actually has nothing at all to do with calculus class.

[Heron TSG]

Okay, you want V to be related to something? I can attempt to do that, though I don't fully understand what you're trying to say.

The volume of a cylinder is this, as you know.

V = (πR²) multiplied by the height, H.

Thus...

V = (πR²)H
H = (πR²)/V
R = ((V/H)/π)^1/2

I don't know what exactly you need help with, not having done that type of problem before. Maybe one of these is the formula you need, though. You never know.

[Vector]

Okay, let me make this clear:

we still don't know what pi is.  We don't have the formula.  I'm trying to prove this sucker with ancient methodology, and they didn't have pi yet--as I said in my post, those things are literally the only things I can use.

Attempted methods in the next post.