Math Forum / Mathematics / Undergraduate Math / March 2007

find the coefficient of x^5 in (x-1)*(x^2-2)*(x^3-3)..............
(x^100-100)

Create a geometrical sequence in which: All terms are Proper complex numbers, with but one exception.
a + bi......where neither a or b = 0
Create a geometrical sequence in which: The main exponent and independent variable is always a proper complex number, with but one exception. ...

I am having difficulties with these theorems. are there anyone here
who (completly) understand this, and can manage to explan the proof of
the lagrange multiplier method? I do not understand the proof in the
book, so I probably need careful explaination of this...

I hope that someone could help me.
I am looking for some help I guess in the way of a software tutorial
type program.
My math skills are not that great and I need to learn (s) and (z)

Theorem: If p is prime, and a + b = p - 1 for a, b positive integers, then a!*b! "is congruent to" (-1)^(b + 1) (mod p)
a.) Illustrate two examples (w/ primes that are greater than 5) showing the theorem above.
b.) Prove the above theorem.
WORK:

Could someone please help me with this ..thanks very much in advance
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Let G be the symmetric group S3 (S subscript 3)
Show that G contains just 1 subgroup of order 3, and 3 subgroups of order 2.

if i have two of the three cartesian coordinates of a right angle triangle, and the length of two of the sides (and of-course the hypotenuse as well, though i would prefer, for reasons of programming efficiency, not to have to calculate this if it can be avoided)what formula ...

does anyone know of a good website that contain the theorems (with
proofs) involving matrix operations, determinants and linear systems?

What is the probability of this beeing an winning bet.
   I'm gonna trow my cigarrette onto the air and it will fall on its feet,for at least three seconds.Knowing that in 10 millions tries one cig can't do that even for 1 second.Do you think this is a winning bet?Calculate its ...

Hello everyone..
I am new to the forum and was wondering if someone could help me. This question is driving me crazy. Any help would be appreciated. Thanks.
For the given cost function - C(x)= 8450+230x+0.4x^2
and the demand fuction p(x) = 690

Here are three goodies I need help solving:
1. Let F5 = 2^(2^5). Compute 3^(F5 - 1) mod F5.
2. (RSA) Decode this message: 5192, 2604, 4222. The message was sent
using modulus m = 7081 and exponent k = 1789

I was wondering if you guys & gals might be able to help me out with a data
fitting task I've got:
I have 8 workers who have worked on 5 different projects for me. Each person
works on the same project until the entire project is completed. The data that

Could anyone help me with this problem? I need some hints.
Prove that if H is abeliansubgroup of a group G then <H, Z(G)> is abelian.
Give an explicit example of an abelian subgroup H of a group G such that <H,
Cg(H)> is not abelian.

I need some Help with this integral.
int int _T 1/(1+x^2+y^2)^2 dx dy, with T the triangle with vertices in
(0,0), (1,3^(1/2)) and (2,0).
thanks

1- Consider th matrix 3*3
[3 -1 2]
[2  1 1]
[2 -1 2]