Let's make a homework help thread!

I think I may have found the most poorly-written math problem in the history of math.

How many four letter "words" can you make if no letter is used twice and each word must contain at least one vowel (A, E, I, O, U)?

Okay I know what they mean here is that the letter combination are not real words. However, if each word must contain one vowel, and you can't use letters twice, and there are five vowels, then the highest number of words you can make is 5, and the lowest is 2. If that's not the answer, I have no idea what they're talking about.

Maybe they mean that no letter is used twice in the same word?

And yeah. Very poorly worded.

^^My interpretation of it is that it's a permutations question. You have 26 letters, but each of the four letter words must contain a vowel. I haven't done permutations for a long time now, but I think the easiest method would be to find the total number of permutations (²⁶P₄) minus those with no vowels (²¹P₄). Check the maths, since my skills are very rusty.

Edit: I don't understand how you got the number five, so perhaps I'm misunderstanding the question? ABCD, ABCE, ABCF, ABCG, ABCH, ABCI... etc are all acceptable "words", and that's more than five already.

edited 19th Sep '12 10:57:54 PM by Yuanchosaan

That's the way I read it too. ABCD is a word. So are ACDB and ADBC and ADCB and so on, but BCDF isn't. Each word must contain "at least one vowel" so AEIO is also a "word". But AABB isn't.

So they mean once per word?

That's the way I read it, yes. Otherwise the answer is trivial: five. You can't use any vowel more than once, and there are five vowels. Therefore, you can only make five "words" before you run out of vowels that haven't already been used.

Stupid question: what does it mean to "prove" things?

In what context?

English? Logic? Geometry? Science? something else?

edited 27th Sep '12 8:17:09 PM by Madrugada

Math.

Like I know a thing and I know why it's a thing but I don't know how to prove it other than just explaining it.

Like this: In what cases is the Euler phi function odd? It is only odd in one case, and that's n=2. This is because all primes above 2 are odd, and phi(any prime) = prime -1, which is always going to be even. Also whenever you have an odd prime, you're going to divide your number by an odd number into an integer, which is then going to be multiplied by an even number, which is always going to be even. The only thing this isn't going to be true for is like other powers of 2, which is also always going to be even.

Like.

But.

How do I "prove"?

edited 27th Sep '12 11:11:53 PM by ohsointocats

It's basically what those big boards of symbols are all about in Science shows. See here. You can think of it as a logic/language derived train of thought. If that doesn't help, no idea.

edited 5th Oct '12 11:27:44 PM by Deboss

Can anyone tell me how the impulse isn't equal to 12 N*s over the 5 second interval?◊

EDIT: Problem solved, WebAssign was just being anal about vector notation.

edited 19th Oct '12 8:01:10 AM by hnd03

Me again.

An 2.4 kg object has a velocity of 7 m/s in the y direction. Then, a constant net force 11.0 N in the x direction acts on the object for 5.50 s.

Calculate the final velocity using the impulse momentum theorem (needs a direction)

I know that the theorem is mass*delta v=force*delta t

But since they're in two different directions, I don't know what to do.

edited 22nd Oct '12 7:44:04 AM by hnd03

The velocity in the y direction won't be changed.

So you must calculate the x component of the new velocity, using the information you're given, and then use Pythagoras to find the resultant new velocity.

For a political science class, I need to find an example of a country that transitioned to democracy after the year 1980. seems simple, enough, but I'm having trouble finding any information on this front. Can anyone offer any leads at all?

Russia?

That's one. I'd like to get a bigger list of countries to choose from, though.

Any former Warsaw Pact nation, I suppose.

Iraq? (laughs cynically)

So, a good chunk of Eastern Europe then...

What about in the Middle East and Africa?

edited 22nd Oct '12 10:07:32 AM by Wicked223

Dude, arab spring. Egypt, Tunisia, Libya...

edited 18th Nov '12 6:35:42 PM by Joesolo

EDIT- nevermind, I figured it out. I think.

edited 18th Nov '12 7:01:51 PM by Joesolo

Nevermind.

edited 20th Nov '12 10:01:22 PM by Marioguy128

Well TV Tropes I have an easy math problem.

Well, it should me easy buy being sick for the past few days.

EDIT: Never mind I figured it out. (thank you Khan Academy)I still need help with this other one though.

How do I factor binomials such as 4x^2-9y^2?

edited 26th Nov '12 12:39:18 PM by Somedude1337

For the first one, when you have a y^2 term like that on the end, that usually means the factors take a form of (ax+by) instead of (ax+b) You already know what the coefficients a and b are, you just need to put the y in.

For the second one, remember the difference of squares and think a little outside the box. What's the square root of y^2?

Oh right, 4 and 9 are both perfect squares. So this means the answer would (2x+3y)*(2x-3y) right?

EDIT: But what if one of the coefficients isn't a perfect square, say 2m^2-32n^2? Never mind I forgot they both share a common factor. (2)

EDIT 2:electric boogaloo: Okay, now I've found a binomial that isn't the difference of 2 squares.(namely 64am^3-27a) The only factor they share is a, which makes it a(64m^3-27). What do I do from here?

edited 26th Nov '12 2:11:27 PM by Somedude1337

We're looking at a difference of cubes—there's a formula for that too. Alternatively, there's always the rational root theorem.