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Hi willis. I just used the calculator and found the results:
cos x = 0,3456 : x = 69,78 (approximately)
sin x = 0,3456 : x = 20,22 (approximately)
tan x = 0,3456 : x = 19,06 (approximately)
You're right. This answer doesn't make much sense, but it is writen like that in the answers section. Probably it is a typo. The book is Augusto Morgado's "Análise Combinatória e Probabilidade", it's a brazilian one. I'm starting to get tired of this book actually, it doesn't help me too much.
Thanks bobbym. I already have this book (didn't read it yet though). I'm also using Andreescu's book of combinatorics. I'll try to find a method for solving such summations in those books. This question looks harder than it should be...it is in a high school level book. I forgot to post the answer:
(maybe looking at the answer will refresh your memory =P)
I don't know how to deal with these products in the summation. Any assistance is welcome!
Thanks mathsyperson! I could solve the problem. I counted all the possible f: A -> B (that would be p^n), then I subtracted from it all the non-surjective functions (that would be (p-1)^n, (p-2)^n, etc.). Finally the awser became:
Took me some time but I finally got it!
I'm having some difficulty to understand this question:
Let A and B be two finite sets, with |A| = n and |B| = p (n is greater or equal to p). Determine the number of surjective functions f: A -> B.
Can anyone explain me how does it works?
The chords AB and CD don't cut each other inside a circle of radius R.
The lines AC and CD make an angle of:
a) 36º
b) 21º or 51º
c) 57º or 87º
d) The problem is indefinite
e) None of the previous answers
C is the correct answer.
PS: I can see that AB equals the side of a star pentagon and CD equals the side of a convex decagon. Anyhow, I couldn't get the problem solved. I appreciate any assistance.
Great! I'll not be able to use those methods in a test, but they are really nice though. Thanks a lot.
Actually, I would like to know a faster way to solve it. I'm studing for an entrance examination and I need to be able to solve these simple (but tiring) problems without wasting much time.
I got it right now! Thanks for your assitance.
PS: You're right Bobby, the anwser is 825, it was a typo.
Hi everyone! I've tried a lot but I can't solve this question...can anyone help me?
How many are the integer, non-negative solutions of x + y + z +w = 20 if x > y?
The answer is 815.
I was doing the reduction wrong! I found the right answer now. I just used the gaussian elimination, and it was easy to solve. Thank you for your assistance.
That's it, I got confused with the names in English (I'm brazilian). I will try to solve it again, maybe I'm doing something wrong in the reduction...
Actually I've reduced it using the Chió Rule. I was trying to find the
using the Cramer's method (the most logical way of solving it). But I coudn't find the right answer. This question is from the admission test of IME, so I have to solve it by hand. I'm having a hard time here...I having some trouble with this question. It's a question from IME (Instituto Militar de Engenharia - Engeneering Military Institute):
Determine the value of
that satisfies the system of linear equations:(I coundn't figure out how to use the array comand here...)
I hope someone can help me...=)
The answer:
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