Random do my math homework for me thread

[Siralin]

Sorry that I can't proide any input to a previous question before asking my own, but here goes...

Spoiler: show

http://is200.imagesocket.com/images/...32357-4jns.jpg

It's our EC question due Thursday...I have the solution printed out from wolfram alpha, but can't really make heads or tails of it. What I've done so far is factor the bottom to split it and use partial fractions...so you end up with

x(x+sqrt(-1+i))(x-sqrt(-1+i))(x+sqrt(-1-i))(x-sqrt(-1-i)) or x((x^2)+(1+i))((x^2)+(1-i))

Partial fraction split would be... left side = A,B,C,D,E over each of those factors or a/x then Bx+C & Dx+E if you used the x^2 factors

Multiply by lcd...then...yeah. I'm not sure if this is something simple and I'm just getting bogged down by so many factors, variables, and the ever so wonderful i. But If you could point me in a direction to try that would be great.

[SDSD]

So I need help with my last homework question I passed over and just can't wrap my head around. Might be because of lack of sleep.

The question is, "What is the value of (AXB)^2 + (A*B)^2?" where the first is the cross product and the second is the dot product and A and B are obviously vectors. I know it has something to do with Lagrange's identity I just can't fucking figure it out. Any help is appreciated.

(|a|^2)(|b|^2) = |a X b|^2 + (a*b)^2 from Lagrange's identity when you're working in ℝ3

[Byrthnoth]

Siralin, try simplifying it using trig identities and substitition? Maybe x = tan(u) would be a start?

[Siralin]

I was able to crank out an answer through partial fractions...but who knows if it's right. If anyone is bored enough to go through the algebra to confirm it's right/wrong I'd appreciate it.
https://dl.dropbox.com/s/nz62u45uugm...thEC.docx?dl=1

[oldoldman]

(|a|^2)(|b|^2) = |a X b|^2 + (a*b)^2 from Lagrange's identity when you're working in ℝ3

Yea I figured it out the next morning, they were trying to get us to identify that it ends up being |A|^2|B|^2 (Cos^2(theta)+Sin^2(theta).

[Blubbartron]

Yea I figured it out the next morning, they were trying to get us to identify that it ends up being |A|^2|B|^2 (Cos^2(theta)+Sin^2(theta).

They were trying to get you to identify that it's (|A|^2)(|B|^2)(1)? What the hell?

[oldoldman]

Yea... It's the rough proof for that rule.

[Ddz]

Having issues with a logarithm problem. Order of operations is throwing me off. I have the answer but I don't know how to get it. Help please:

2^4t x 2^3t-5 = 94

I keep getting t=1.1825 when it should be 1.6507? What am I doing wrong?

Nevermind I got it. I accidentally multiplied the bases to 4 when they should have remained 2. Sorry!

[BerenTebogo]

Reviewing some Linear Algebra and I've come across what seems to be an interesting property of determinants that I didn't know before and don't quite understand, was hoping someone might have some insight into it for me.

For square matrices of the form:





I.E. a square matrix with squares of zeros of size (n-(1/2)n) x (n -(1/2)n), where n is an even number, appear to follow an almost triangular matrix rule when taking the determinants.

It seems, so far, that instead of using either the general cofactor rule or the identity matrix method you can take the determinants of the two smaller non-zero square matrices and multiply the answers together to get the determinant.

Has anyone seen this before or have a reason why it would work? It's pretty cool, if overly specific, but hey.

[Blubbartron]

Reviewing some Linear Algebra and I've come across what seems to be an interesting property of determinants that I didn't know before and don't quite understand, was hoping someone might have some insight into it for me.

For square matrices of the form:





I.E. a square matrix with squares of zeros of size (n-(1/2)n) x (n -(1/2)n), where n is an even number, appear to follow an almost triangular matrix rule when taking the determinants.

It seems, so far, that instead of using either the general cofactor rule or the identity matrix method you can take the determinants of the two smaller non-zero square matrices and multiply the answers together to get the determinant.

Has anyone seen this before or have a reason why it would work? It's pretty cool, if overly specific, but hey.

Might want to simplify your description, since (n-0.5n) = 0.5n.

It's pretty obvious why it works. It's because multiplication is commutative. (abcd) = (ab)(cd). That's all that's happening. If you determined the determinants of the smaller square matrices by making them triangular, it should've popped right out at you. In the long run, you're just making the big matrix triangular, then multiplying the diagonals, and of course the smaller diagonals' products are the determinants of the smaller matrices. Then the product of the two smaller determinants is naturally equal to the large determinant.

edit: I should add that the zero squares are necessary to make it possible to triangularize the overall matrix without cross-referencing the two inner matrices. As soon as any number pops in where you have zeroes, it goes kerplooey because the inner square matrices are no longer independent of one-another.

edit2: I might be a little high on adderall, so if that doesn't make sense because I skipped some explanation, let me know and I'll try to elaborate later.

[BerenTebogo]

It's finals week, anyone reading this thread is on adderall, lol.

But yeah, that makes sense now. I was having a tard moment in doing my row reductions so I wasn't seeing the correlation when I went to make the large matrix triangular. Thanks.

[Woozie]

http://en.wikipedia.org/wiki/Block_matrix

Or

http://www.hostemostel.com/pdf/MTH/0.pdf

What you're finding is a consequence of theorem 1.

[Fondue]

Can anyone find what I did wrong here, partial fraction decomposition for integration with an irreducible quadratic and trig substitution... Original problem is top left. The ln|cos(arctanx)| looks wrong and bad but I dont know trig identities very well to know if that can be simplified

[Anoat]

Reporting this thread to Aks, this is all going on your permanent records.

[Fondue]

DONT FUCK ME BRO

[Teorem]

Using x=0 and i, I got the same partial fraction decomposition.

Hints:

- Use u substitution to integrate (x)/(x^2+1) dx
- There's a trigonometric identity for indefinite integrals of form 1/(x^2+a^2) dx

Spoiler: show

My napkin math says: (2/4) ln|4x+1| + (1/2) ln|x^2+1| - arctan(x) + C

[Fondue]

oops forgot to reply, that should have been obvious yeah- I was just trying to shoehorn the trig sub for some reason

if I can remember all of these trig sub things for the test on tuesday I might make it q.q everything else is reasonable

Thanks!

[steph33]

hey..in similar trouble - stuck with geometry - need to solve this:

so far I've got this

but my answer isn't among the given ones..I'm kind of lost..spent hours on this and I've got no where..even though of going to https://www.enotes.com/homework-help or http://yourhomeworkhelp.org or https://socratic.org/ though do not want to do it..I'll appreciate any hint..thanks