It's good for not even thinking about Math for the last 3-4 years :-p

Now I gotta go look up and see what I did wrong...

Oh, lol, I did have the arctan derivative right, I just forgot to take the derivative x² + x

No need to be harsh, everyone makes mistakes and again, that was good enough for not thinking about arctan derivatives for 3 years and doing it from memory (though have to admit, didn't do the DiffEQ problem from memory) :-p

Oh you're right, totally forgot to derivate the X² + X factor in the arctan, given that you have to treat the equation as being arctan (u) with a derivative as follows

(arctan (u) ) ' = u' / (1 + u²)

thanks for pointing that to us ;)

Well i don't have a minor nor a degree in maths, i'm a biochemistry student, and it was only in my first year that we had calculus (or applied maths I, II and Linear Algebra and Geometrical Analysis in my university), so my math skills are a bit rusty, as it was shown solving that other problem :P.

Hope the problems keep on coming ;) need to brush up these math skills

yeah, it's easy to forget it :) but when somebody is posing it as a derivative question you should see it coming :)

Yeah you're right Lingyis ;) Oh i see that you've got a nice Protein Avatar, did you get that pic from the Protein Databank? if so, are you into anything Biologically related?

Hey twestern, analizing your answer for your own problem, I now understand, you're right. Damn it it was so easy! :p

Well, I can't help with derivatives...that's for university right?

And lestatdark, that's not the point of the exercise. You did that using a calculator, and the problem is to be solved with mathematical skills. However, I believe you got the answers right, at least I know 2 of them are right.

I'll try solving the problem again and I'll post the answer soon. For the meantime, here's another problem to keep you guys entertained.

A cage contained 100 fruits between apples and oranges. After a few days, some fruits got ripped. When the cage was opened, it was observed that of the fruits that were good, the eleventh part was oranges; and the fifth part of the ripped fruits were apples. Then the ammount of the ripped fruits is: ?

And that's the problem. Please, spare me the grammatical mistakes since english is not my first language and the problem was originally in spanish. ;)

I know it was not the correct way to do it TheLivingShadow ;) i said it myself.

However, as my Applied Math teacher taught us, all mathematical procedures are correct if the theory behind it is correct. I used the factorization theory because it was the only one i could remember, it's crude but i think it gives a correct answer ;)

As for your problem, I cannot help you there, Probabilities were never my forte, i cannot output the correct theory to fundament my calculations, but i can tell you that there are 55 good fruit and 45 ripped fruit, 5 good oranges, 50 good apples, 36 ripped oranges and 9 ripped apples, all done through calculations on paper, not calculator ;)

Hopefully someone can input the correct mathematical procedure

Hey guys here I am again. Sorry for the double post, but I consider this post had to be separate from the last one. I've already found the answers to the 3³²-2³² problem, suffice to say that lestatdark is right with 5, 13, 17 and 97. However, I won't post the solution yet, maybe some of you (twesterm, lingyis) can find the answers with the correct mathematical procedure, without the use of a calculator.

Also, keep in mind that that problem is one of the 10 problems that were tested in the finals of the Ecuadorian Math Olympiads, along with the M/N one. Good luck trying to answer!

If the procedure hasn't been posted until tomorrow night, I'll post my answer, deal?

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On another note, remember mathematics also includes geometry problems, and I have a few of them I'd like to share with you, but first I need to know how do I copy an image on a Word document, so I can post it here? If you tell me, you'll be getting a few geometry problems from me ;)

Edit:

lestatdark you're right! Congratulations! For that problem, mathematical procedure isn't needed, as long as you got the answer right, simply because it's too hard to write it all. But for the powers one, a mathematical procedure is required because otherwise I can tell you're cheating. Also factorization is the right way to do it. The only fault I find in your procedure is the use of a calculator to determine 3³²-2³², after that what you're doing is obviously right.

Your answer is completely right, and here I'll post the procedure you mentally must have done.

Let b be the number of fruits in a good state and d the number of fruits in a bad state. Since we're talking about fruits, the fractions must be fractions of natural numbers, and the fractions themselves must be natural numbers too. We also have the following equations given to us by the problem:

b=ab+ob , where ab represents the apples in good state and ob represents the oranges in a good state. We also know 1/11b=ob.

d=ad+od , where ad represents the apples in a bad state and od represents the oranges in a bad state. We also know 1/5d=ad.

b+d=100

Now, since all numbers must be natural, then b is a multiple of 11 and d is a multiple of 5. Then we have

b=100-d , and since both 100 and d are multiples of 5, then b must be a multiple of 5 too. Then, b is both a multiple of 11 and 5, and it must also be lower than 100. The only number satisfying the condition is 55. So b=55, and then we know d=45, which is the value we were looking for.

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Come on guys you should try posting problems too!

TheLivingShadow to copy an image from a word document, just make a print screen of the word document, and then in Paint or some other image editor tool that you have, Paste the print screen and Cut the image that you want, Ctrl C it, and then open a new Paint file, and paste it there, then save the file in JPEG or BMP, whichever you want.

Oh TheLivingShadow, i didn't use a calculator in any of the problems, here in portugal we are taught never to use a calculator, so im pretty confortable doing all these calculations on paper, especially that these were simple math operations and logical thinking ;) just thought you should know

Thanks for telling me, I'll try that later after some other people answer my already posted problems!

So you didn't use a calculator for the 3³²-2³² one? Hmm I find that strange, I mean it's possible to do it multiplying the 3 32 times and then the 2 32 times and then sustracting them, but that takes an awful lot of time?

Besides, the problem was just one problem of 10 other similarly hard problems that had to be done in the space of 3 hours. So there was a time limit.

I'm not saying that you're wrong, if you're telling the truth and you didn't use a calculator, then what you're doing is by all means right, but that's not the procedure I'm looking for.

Try posting some problems from Portugal! Maybe they're harder than mine

It's just a matter of simplyfing the powers, so 3³² becomes 9¹⁶ then becomes 81⁸ then 6491⁴ and so on, it's quite simple actually =)

I'll try to find some problems in my old math books, haven't touched those in a while x)