Math Forum / Mathematics / Undergraduate Math / April 2005

I was checking out my homework solutions from a class I took 4 years ago.  I came across a couple of problems that I'm not sure how to approach.  Any hints would be welcome.
Using Euclidean Algorithm, find x,y E Z such that gcd(42,81) = 42 x + 81 y
I know how to use the Euclidean ...

Find all real solutions of this equatation: x on 2,2 minus 2x plus 1 equals zero. Solutions must be on five decimal places.

I'm having a hard time proving a variety of set identities, De morgans
Laws, absorption laws, etc.  Is there a website that would have a step
by step approach for proving set identities?

Draw diagonals on a squre to form 4 equilateral triangles which should be coloured using not more than 3 colours. form all possible squares, how many are there? Can you form them into a rectangle so that where squares touch they have the same coloured edge? Can you do this with ...

I have a compound interest question which i need to use Differential equation to solve.
This is the qustion:
If an investor invests $250 per month in an account paying an annual interest rate of 10%, compounded monthly, how much will the investor have accumulated at the end of 10, ...

I have a function f(x), I need to transform x to y using:
y=exp(a*x+b) with a and b two known parameters.
Now I'm searching for a function g(y) which gives the same values as the corresponding f(x), i.e.
g(y)=f(x)

When a_n >=0 for all natural number n,
If Sum_(n=1 to oo) a_n converges then
1) Show that Sum_(n=1 to oo) a_n /(1+a_n) also converge.
2) For p>=1, Show that Sum_(n=1 to oo) (a_n)^p converge.

If 2 dice are rolled, what is the probability of coming up with a 3 on exactly one of the die?

I have two integrals:
I=\int_{-\infty}^y f(y,x)*g(x)dx
II=\int_{y}^\infty f(y,x)*g(x)dx
where y>0, \int_R g(x)dx=1 and f(y,x)-> 0 as y->\infty. Also, g and f are bounded, smooth and continuous functions.

I need help. I homeschool & I am pretty good at school normaly, but since I started algebra I've been soo confused. I'm having a problem with mainly just understanding algebra, I don't know if it's my concentration or what. I've been really struggling with literal equations. I ...

I've talked about it before, but I thought it might help to remind that
I practice what I call extreme mathematics.
The idea is to hurl yourself at various problems, especially older
"hard" math problems, and brainstorm out a solution, talking it out in

I just wanted to make sure I'm doing the right thing!
f(x)=3x^2+2x+3
I used Quadratic formula and I got this values: -1.27,1.27
is this correct?

Hi, I have a proof that I don't know what to so with.  Any help would be appreciated.
"Let Q=[0,1]X[0,1] be the unit square in the plane.  There exists a constant C, tell what it is (1000 should be large enough), so that for any number λ>10 and any function f on Q, twice ...

Let we call a natural number "good number" which can be divided by every positive number that is equal or less than its square root.Find the greatest good number.

I'd like to find F'(x):
F(x)=(4x-3)/sqrt(x^2+1)
how to get from below to this:
F'(x)=(3x+4)/sqrt(x^2+1)^3