The D.R.K Club (Dune!)Follow

Haha, I remember when that was one of my money makers.

I'd call you Mitchell, and imagine you to be Joe Don Baker.

Anyone in the mood for a math problem?

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.

I looked at the question for 5 seconds, hence I have no idea how to solve it or what the solution is at this time, but two things I'd try (and in this order):

Integration by Parts
Substitution

My goal would be to keep things clean. I have no clue how this problem comes into what your class if covering, so I might be off.

Then in that case...

Wolfram|Alpha?

Also, I already punched it in SpoilerSolution (honestly, this really isn't even spoiler material, the problem is so @#%^ed up, but it uses partial fractions!). Your professor is such a dick, that's all I can say.

Edited, Oct 9th 2012 4:06pm by xypin

Ahh, I was thinking this was a homework problem.

Then in this case, it's probably easier to solve partial fractions twice because of the imaginary parts.

N = numerator of original problem
D = denominator of original problem

So you'd first find partial fractions for x*(x^4 + 2x^2 + 2 )
You'll need to solve the following equation

N/D = A / x + (Bx^3 + Cx^2 + Dx + E) / (x^4 + 2x^2 + 2)

The numerator of partial fractions is one degree less than its denominator.

From here, multiply out, solve the equation.

The second is a bit tricky. You've already got the denominator parts:

x^2 + 1 - i
x^2 + 1 + i

but since there is an imaginary part, for the partial fractions you want to use the form
Ax + Bx*i + C + D*i

Even though the imaginary part is only a constant in the denominator, you still need it as function of x for the numerator. If it is indeed the case that there is no imaginary part (in this case B), then that variable will be equal to 0.

This is how I was taught partial fractions anyway. Is this any help?

Edited, Oct 9th 2012 4:39pm by xypin

Get any further?

Image of my partial fraction solutions: http://i180.photobucket.com/albums/x308/xypin/math.jpg
(Warning, might be more confusing)


PDF document outlining my partial fraction work: https://dl.dropbox.com/u/80054039/math_solution.pdf
(Slightly more detailed)

If you're still stuck on that part, this might be helpful.
Oh, I pulled out a 1/2 in the second part, it's there... just not there. So keep that in mind if you try this method.

Also, in the link you posted, while your setup isn't unsolvable, it's just really, really hard (something may or may not be wrong with the algebra, didn't check toooo closely). The difficulty comes from the fact that B, C, D, and E are all complex. The real(B-D) + imag(C +E) has to equal 2 while the other parts have to sum to 3/2. Setting B = a + bi and similar for other variables if you wanted to continue from that point would probably fix this.

Edited, Oct 9th 2012 6:51pm by xypin

The first part is finding partial fractions for...

N / (x)(x^4 + 2x^2+ 2)

You actually answer your question hereThe denominator will be quartic (x^4), so the numerator is cubic (x^3).

Edited, Oct 9th 2012 6:58pm by xypin

You're trying to find

P = (Bx3 + Cx2 + Dx + E)/(x4+2x2+2)

Since D = x*(x4+2x2+2)
then
D*P = x*(x4+2x2+2)*(Bx3+Cx2+Dx+E)/(x4+2x2+2) = x*(Bx3+Cx2+Dx+E)

I'll update pdf file in a minute as well.
Oh, I see, I missed an x... sorry for the typo, the pdf is updated, should clear up the confusion.

Edited, Oct 9th 2012 7:15pm by xypin

I'm nearing the point of saying @#%^ this problem. You have to do partial fractions like 2 more times to come to a really @#%^ing convoluted answer. Ugh.

The moment I popped it into Wolfram, I gave up on solving the problem beyond computing the first three partial fractions. Since there is a fourth part to the solution, I'm guessing the (x^2 +1-j) integral can be separated, but my interest stopped at the end of that pdf.

I just wanted to prove to myself that I could at least do that much.

Here we go....https://dl.dropbox.com/s/nz62u45uugmun0r/MathEC.docx?dl=1

(Obviously it could be simplified more...[factor then combine lns], but @#%^ that because @#%^ this problem.)

Edited, Oct 10th 2012 2:46pm by Siralin

I think I originally had (4/2i)+1 = B which apparently equals (1-2i) >.>

I wondering how long it takes until someone says STFU WITH THE MATH YOU GUYS TAKE IT TO PM.

He didn't even care when I mentioned it on facebook!

Gaxe, troll harder, you bore me.

He wasn't even trolling though... Sounded pretty reasonable to me. Few people enjoy this kind of stuff like xyp.

I think the last link Sira posted is the answer, mostly. I pointed out a few minor errors, but quickly became bored with that.

INB4 Rae get's here. {Blood Cuisses}

SPACE JUMPING

Pst, they had Joe Kittinger leading the team. Everyone knows it was previously done. (At a lower altitude, slower speed, and with a droge chute.) The only record thy didnt break was the longest freefall time, which can be attributed to the lack of a droge chute.

If you're trying to say it's not special because they were able to do it 50 years ago, gfy.

Everything that I'm finding (looked past wiki) is showing that he only hit 614 mph which is below the speed of sound at those altitudes. Even the Air Force's website states this. I was only able to find the 714 number at one link and it stated that Kittinger had stated this speed in later interviews.



No it's your own "I hate society and anything they think is cool" vision. You're taking the fact that this is a hyped marketing campaign and running with it to the point of discrediting the guy and the "mission." Sure there are some frat boys and video game majors out there going " BRO THIS IS THE COOLEST THING EVER THIS GUY HAS THE BIGGEST BALLS MAYBE HE SHOULD TAKE A PISS OFF THE BALLOON LOL THINK OF ALL THE SCIENCE THEY'RE GONNA GET FROM THIS BRO...@#%^ING SCIENCE," but that doesn't change the fact that it's pretty neat and a cool accomplishment. You would probably have some of the same (justifiable) criticisms as you do now if they had done this without big sponsors and it wasn't in the media, but you'd also be eating this sh*t up and bring it to us on your "I'm cooler than you because I know about things like this" platter.

I wouldn't compare you to Turin, but you are being a bit of a twat.

I hate the media as much as anyone else (ask my GF, she has to listen to me rant about sensationalist article titles about science and technology all the time), but you have to understand that they need to make it out to be awesome (and more than it actually is) because they're sinking a sh*t load of money into it hoping they'll see a return. You can't blame them for this, but you also don't have to buy into it. (Which you're clearly not.)

Edited, Oct 15th 2012 10:18am by Siralin

I'm good with that.

space jump is obviously cool regardless of whether it's in the 50s or now. imagine doing it. sh*t is crazy.

I really don't see why it's cool. From what I understand, he failed at everything he set out to do so it was just some dude parachuting.