rocketman421

tree go take another look at the problem: "for every natural number n" "where x and y are two nonidentical real numbers"

ok ok i'm sorry i realized this is stupid as soon as i posted it... compared to science madness: its a lot better than science madness: Rank:  SF: 96,329  SM: 315,078 Visits:  SF: 0.0011%  SM: 0.00025% although i don't know how accurate it is, depending on the way they're calculated it must have some bias Merged post follows: Consecutive posts merged   

lets say x = amount of pasture a cow can eat in 15 days y = amount of pasture a duck can eat in 15 days z = amount of pasture a goat can eat in 15 days 3x + 3z = 1 4x + 4y = 1 6y + 6z = 1 x = (1-3z)/3 ... (4-12z)/3 + 4y = 1 4/3 - 4z + 4y = 1 4y = 4z -1/3 ... 6(4z-1/3) + 6z = 1 30z - 2 = 1 30z = 3 z = 10 i'm sorry i messed up somewhere

yeah lol thanks, care to delete that?

No! It was not spaceship1 or spaceship2. those ones are expensive and all you get is a tiny window on a space bus and i believe it costs like ~20 million. I think what i meant was "SpaceX" one of their newer prototypes is supposed to cost like 200k to get you up into space and its not like a spacebus or shuttle its two people, its just you and the pilot and you get to ride shotgun.

ah wrong thread

btw i was just on google.com and their "google" logo is embedded in some lunar terrain. apparently today is 40th anniversary of lunar landing... btw this is highly off topic but i never did get it: how come like jupiter and saturn and stuff (which has very large gravity and is very cold) a "gas giant" with ammonia and hydrocarbons or whatever... shouldn't the gases condense, be liquid or solid under all that gravity?

doesn't u.s. already have a man on permanent reserve at the moon? but yeah its pretty interesting i mean say like for 200,000$ i believe i read in popsci you can get a personal trip to space (i forgot its called xflyer or something) and the moon is like 5-6 days of travel so we could totally build like hotels & amusement parks over there as a luxury destination. also maybe we can drill it for oil & resources. hell, lets drill all the planets. i think the main problem with mars is it takes like 2 years for a person to get there which is incredibly boring. only thing that sucks is you'll have to stay indoors on the moon or otherwise wear a spacesuit if outside...

well i solved it before but i lost my solution so here i coiped it from some site: Prove that for every natural number n, (x - y) divides (x^n - y^n). Our first step in mathematical induction is the base case; that is, for n = 1. 1) Base Case: Let n = 1. Then (x^n - y^2) = (x - y), and (x - y) is obviously divisible by (x - y). Therefore, the formula holds true for n = 1. 2) Induction Hypothesis: Assume the formula holds true for n = k. That is, assume that (x - y) divides (x^k - y^k). ( We want to prove that (x - y) divides x^(k + 1) - y^(k + 1) ) But what does x^(k + 1) - y^(k + 1) equal? x^(k + 1) - y^(k + 1) I'm going to re-express these two terms. (x^1)(x^k) - (y^1)(y^k) x*(x^k) - y*(y^k) I'm going to use a little trick, by "adding zero" in the middle. x*(x^k) + 0 - y*(y^k) I'm going to subtract x*(y^k) and add x*(y^k). After all, subtracting and then adding the same term is the same as adding zero. x*(x^k) - x*(y^k) + x*(y^k) - y*(y^k) Now I'm going to factor the first two terms and the last two terms. x(x^k - y^k) + (y^k)(x - y) Look closely at this; (y^k)(x - y) is obviously divisible by (x - y). By our induction hypothesis, we assumed that (x^k - y^k) is divisible by (x - y). Therefore, x(x^k - y^k) is divisible by (x - y). The sum of two terms both divisible by (x - y) is also divisible by (x - y). Therefore, what we started with, x^(k + 1) - y^(k + 1) is divisible by (x - y) Therefore, by the principle of mathematical induction, x^n - y^n is divisible by (x - y) for all natural numbers n. Merged post follows: Consecutive posts mergedThread Closed.

interesting site: alexa.com like say here you can see scienceforums.net is ranked 96,329 and ~.0011% people who went on the internet yesterday visited this site, compared to 33.72% for google.com, yahoo.com was 1st and google was 2nd until ~2009 when it switched. google.com yahoo.com youtube.com facebook.com live.com msn.com blogger.com wikipedia.org baidu.com yahoo.co.jp myspace.com google.co.in google.de qq.com twitter.com microsoft.com rapidshare.com sina.com.cn bing.com google.fr Merged post follows: Consecutive posts mergedThread closed.

Are you smart enough to prove that for every natural number n, (x[math]^{n}[/math] - y[math]^{n}[/math]) is divisible by (x - y), where x and y are two nonidentical real numbers? I already solved its just it took me forever to get lol. If nobody solves it by the next time I visit, I'll post the solution.

my brain is at a loss when trying to make sense of this.

well yeah you might be right, i mean in the old days you could buy heroin and cocaine as easily as aspirin, it wasn't until that "harrisen act" or whatever that pretty much all drugs were criminalized... i bet being like a drug addict was similar to like being a smoker is like people would know "oh he's a smoker"... i think crime rate would go down since like right now doing/making drugs itself is a crime and trying to catch those people creates a lot of deaths in itself... also like right now i.e. narcotics are illegal so some opiate addicts try to rob pharmacies or stuff like that...

Martin... you're really quite smart yes that is what i had imagined and thanks for correcting my wording... i should have said "a dozen systems away". So like say the star sirius is 8 light years away, and dh said for the fastest ship it will be 20,000*8 years to get there, so it will only take like 160 thousand years to get there... yeah that is a long time nevermind this question... after all civilization has only been around for like 2,000 years so by that time we'll have flying cars and teleportation machines and ships that will overlap voyager 30 times traveling to sirius for now its best just to use telescopes as martin said i guess... if ships are too slow at least light isn't.