Screw school im on holidays .. in 2 weeks ill post again :P

So I have only seen Calculation done in this thread, not actual math. Here's a nice eas warm up question:

Let U be a subspace of a finite-dimensional vector space V. Show that if dim(U) = dim(V) then U = V.

 I'm sorry, but I don't understand what you're asking. I haven't seen vector space stuff yet. I'll let another person answer this.

For my prior problem, the guy who said the answer was 10⁹ is almost right, but since the problem is M/N and not N/M the actual answer is 1/10⁹. However, it's awesome that you were able to do it congratulations!

Here's a math problem like vlad requested. Even I do not yet know the complete answer to it but I should know in a few days. It should also be noted that I could very easily get the answer with a calculator but that's not the point. Try being true and do it without a calculator. Here's the problem.

Find 4 prime numbers below 100 which are factors of  3³²-2³².

Good luck!

9001!!! =D

Fine, how about some simple statistic problems?

A trainload of unnamed consoles are set to arrive at a distribution center between 8 and 8:10PM. It is now 8:03PM and the train still has not arrived. Assuming the train will arrive in the designated window, what is the probability it will arrive within the next minute? What if it's 8:07PM and the train has still not arrived, what is the probability it will arrive within the next minute?

Say the same unnamed console has a failure rate of 1/10 within the first 15 minutes of being powered on. If there is a stack of 20 of these consoles and 8 have already been picked, tested for 15 minutes, and passes, what is the chance the one you pick will fail within the 15 minutes of being powered on?

Damn it I haven't had statistic classes yet, that's for next year's class. I'll try to figure out the answer though with reasoning rather than formulas because I do not know any of them.

Well, since the possibilities for the first question are 8:04, 8:05...8:10, there are 7 possibilities. then 7->100%. Since 8:04 represents one single possibility, then there is a probability of 14,29% for the train to arrive at 8:04.

For the second question, there are 3 possibilities, that it'll arrive at 8:08, 8:09 or 8:10. Then 3->100%. Since 8:08 represents one single possibility, then there is a probability of 33,33% for the train to arrive at 8:08.

For the last problem, since there's a failure rate of 10% for 20 consoles, then 2 of these consoles will fail. Since 8 have been already picked, that leaves us with 12 consoles, out of which 10 work and 2 fail. Now, 20->100% 2->10% of 20. And 12->60% of 20. 8->40% of 20.
Then we have 2->16,67% of 12. That's the chance we're looking for.

 That's it I hope I'm right. Why don't you try solving my problem twesterm? from the looks of your problems you're really smart.

I encourage everyone to continue answering problems and posting further problems!

1, 5, 13, 97

Please, support your answers with correct mathematical procedure.

Besides that, 1 is not a prime number. It's a special number that's neither prime nor composed.

I'll be waiting for your interesting solution!

First one, it's right but much easier to say 1/7 and 1/3. 

Second one is wrong.

Answer if you want to know but I'll keep it blacked out in case people want to think about it:

The answer is 1/10.  Every console has a 1/10 failure rate.  Just because 8 of those consoles haven't failed doesn't mean one of the next two will fail, they still have the same 1/10 chance of failing.  It's like if you flip a coin and it lands heads, it still has the same 1/2 chance to land on heads again if you flip it again.

Your answer would be correct if I said I had 20 marbles with 2 red ones and 18 black ones.  If 8 black ones had been picked, what is the chance I pick a red one?  1/6.

Ok, i don't know if this procedure is the most viable, but knowing that 3³² - 2³² is an operation with mathematical powers that have different bases, it cannot be done directly, so in the first step, you simply each power and then calculate the resulting subtraction, in which case we get

3³² - 2³² = 1853015893884545

In this scenario, we clearly see 5 as a factor to this operation, given that any number that ends in 5 and 0 is divisable by 5

Then you begin the factorization process by using 5, which will get you

1853015893884545/5 = 376603178776909

If you keep on factoring this number using only prime number, you'll find that the next one is going to be 13, thus

376603178776909/13 = 28507936828993

Repeating the step above, the next prime factor will be 17 (the one that i missed before), so

28507936828993/17 = 1676937460529

Thus for the last number, the same step once again, finding that 97 is the last prime number factor below 100 in 3³² - 2³²

1676937460529/97 = 17288015057

I know it's a crude way to solve this problem, but it was the only one i could think of ;)

Now i have a question for you.

Can you find me the first derivative of the Arctan(x² + x) equation?