@megakazul:
Er, if you time, can you explain surface tension? I don't really understand that concept either.
I don't really have time either, lol, but basically surface tension has to do with the strength of intermolecular forces tying the molecules together. I assume that since you're tackling the concept itself that you know what I mean when I say that molecules 'want' a net force of zero to balance everything out. Now under the water everything's fine, since there are enough molecules to balance it out, but on the surface, of course there's nothing in the air to balance out the net force, so the molecules on the surface will tend to cling downwards - but, obviously, part of the definition of a liquid is that it cannot be compressed, and so the molecules on the bottom will provide enough resistance to stop the surface molecules from just simply attaching to the bottom. Thus providing more support for the surface layer and that's why you can have very light things float on water.
e1n - you don't know how to do synthetic division ?! O_________O OMG that totally saved my butt in precalc a few too many times ! I'll see if I really remember what I am doing and try to teach you xD
you have 0=(2x^3) -x + 1. First you need to sort out ALL potential rational roots (which, if you recall, the rational root theorem is +/- (factors of constant)/(factors of first coefficient) ), and here the only possible ones are +/-1 and +/-(1/2).
Now we go to the CarlyCheeese Method Of Being Really Stinking Lazy Which Typically Is A Frequent Occurrence In Her Math Studies, she graphs it on her kickarse TI-89, she finds the only real rational zero is at -1, but how does she check that !
Answer: synthetic division plz.
Now, I hate writing it out longhand but I'll do it so you see first what it 'looks' like:
Then I rewrote it MY way:
And then from there I just yank the coefficients, nothing else, and leave the rational root itself on the left there:
And this is where it gets slightly tricky. Drop the first coefficient down and just leave it; then from there multiply that coefficient by the root and stick the number you get under the next coefficient. Add THAT coefficient to the number you just multiplied, drop the entire thing down, ad nauseum.
Anyway, once you get to the constant, if you add the multiplied number and the constant together and you get zero, then you know that the root you've been working with is actually a factor of your polynomial ! However, if it isn't, you either screwed it up or did something wrong. ;p
Here's my work on the polynomial:
And don't mind the -2 as the first coefficient, that's a mistake (I accidentally wrote -1 instead and I 'fixed' it) but you can see more clearly what work I did there.
Anyway if you have time yourself, I could really, REALLY use your help in trying to do trig identities. I literally have no idea where to start in them or how the hell I can proceed.
The one I'm working on atm is 2cos^2 -cosx = 0 and I'm just looking at that like "… dear god help me." I seriously cannot figure these out at all, even though something like that by all means SHOULD be easy. :\ Help ;_;