Math Forum / Mathematics / Undergraduate Math / April 2007

I got a question that bothers me a lot...
Given N>=2 squares of different sizes, they can be cut and reassemble (without overlap) to make a single square. The cuts should be 'straight' cuts. Proof by induction.
I know that I can cut from a to b, then b to c in order to make a big ...

Let S(n) be the set {1,2,3,4,,2n-1,2n}. Let A be any subset of S(n) containing (n+1) elements. Show that there exist elements a and b in A such that a|b. and S(n) for all values of n.
Can anyone help me out with this?

I am trying to assist my son on his homework and can't figure out the correct answer to this algebraic expression question:  Evaluate the expression:
(s^3t^2 - v)^2, where s=4, t=3 and v=7.
I have worked this problem upside down, side to side and have come up with several different ...

Hello. I was solving a problem but I got a different answer than my friend.
Could anyone tell me which answer is wrong and where is a mistake?
The problem is:
Three balls are to be randomly selected with replacement from an urn

You are stranded on a deserted island, and along the way you stumble across a genie. He says he will get you off the island provided that you can meet his conditions. He hands you a 20-sided die, and says that you need to roll it 1000000 (one million) times. If you can roll ...

In GAP, if I construct an external direct product,
for instance:

(The example comes from Gallian ,Rainbolt, Chapter 8) then,

I am really asking to have my work checked here.
The question is as follows:
Find the minimum distance between the point w = (3, 4, 5) and any point on
the line (x, y, z) = ( 1, 3, -2) + t(0, -2, 1)

I'm studying for my final exam in number theory, and the professor
has provided us with exams from when he taught the course two years
ago.
Here is the link for the old exam, which is dated May 4, 2005:

This is a question I spent days on thinking I could solve it , but so far failed!!
The question is divided into 2 parts, I did the first as it is quite easy and would really like help for the second..
PART 1 )
α β are constants

Assume that S=(a.b) What is the (a+b) raised to the power of 3 equal
to?
(a+b)(a+b)(a+b)(a+b)  or  (a+b) (a+b) (a+b) or (a+b) (a+b)
or all of the above.

hi, i was wondering if someone could explain the procedure for evaluating a laplace transform such as L{(t^n)(e^(kt))} for n>=0.
Im not looking for you to give me a solution, just get me started.  Im just not sure what to do with this type of Laplace transform.  Do i use ...

S-->aS
S-->empty string
Possible answers:
a*

Please help me solve these theorems...
Theorem 1: Let a and b be elements of a group G. If (ab)2= a2b2, then G is Abelian.
Theorem 2: ø(a,b) = (b,a) is an automorphism of R2 under compontentwise addition.
Let Zn =  {0, 1, ....n-1}under addition and multiplication modulo n.

I have no trouble finding the equations of the tangent plane and
normal line to a surface at a given point.  However, how do I find
another point on the surface where its tangent plane is perpendicular
to the first plane I found?

Contact me if you are interested in any of the following
bwennny@hotmail.com
A Course in Game Theory by Martin J. Osborne and Ariel Rubinstein
A First Course In Probability 7th Ed by Sheldon Ross