Math Forum / Mathematics / Algebra Help / November 2003

Train A  pulling 70 cars is travelling at a constant speed of 50mph on Track
A The engine is 80' long and each freight car is 60' in length.There ai 2'between
each carswhere the couplers connect the cars.
Train B which is moving faster than TrainA on Track B-parallel tracks to

I have a problem I'm working on: (1-i)^20
the steps I took is, I went out 1 place on the X axis, -1 on the Y
(imaginary) axis and found the magnitude to be sqrt2
so my equation will be:

Given any ellipsis of the equation
[(x^2)/(a^2)] + [(y^2)/(b^2)] = 1,
(meaning that the major axis is on the x-axis and the center is the origin),
and a point P(x,y) on the ellipsis,

So, I know that a group of order 108 must have a normal subgroup of
order 3, 9, or 27. But I'm not really sure how to eliminate the '3' in
that list of options. (I know it can be done) Any help?
Defining a homomorphism from G->(G/N) (by multiplication) gives me

How can I find a vector that's tangent to a point in 3d space? I'm
trying to find tangents to points of a hermite curve. I guess what I'm
looking for is the velocity at each point because there are many
tangents to a point of a curve in space, but I want the one that

Hooke's Law states that the force F required to stretch or compress a spring
x units is k*x, where k is a characteristic constant for the spring, or
"spring constant."  In other words, F(x)=kx.  The _work_ exerted in
deforming a spring by distance x is then given by the integral

Can someone give an axiomatic definition of complex numbers? Or point
to someplace where one is given.
I'm looking for something like like "Complex numbers are a set with
the following properties..."

This involves an application where all the members of a group get a profit
from a sale of a product.  The higher their ranking in the group the more
they make.
Lets say their are 10 people in this group.

Don't necessarily need the solutions, but can someone at least tell me if
the folowing 3 expressions can be completely factored, so at least I stop
pulling my hair?
75 + 3*x^2 - 3*y^2 - 30*x

I need some help with these equations....i just don't get it at all.
5 n5/2 + n2/5
6 log2 (n) + 9 n
3 n4 + n log2 (n)

Hello, I need help finding an algorithm that will give me the point of
intersection between a plane and a line traveling perpendicular to the plane
when the line passes through an arbitrary point in space. Basically, all I
have to work with are the coordinates of three points which ...

please *show* me how these probs are done...i'm stumped:
Find EXACT values of x:
1.)  cot x = 3, pi< x < 3pi/2
and

Very Very Sorry!!!!
it's ...
sec 2x = 5/4
thank you once again!

Hi!  In my calculus homework, I've run into a problem that asked for the
value of an integral that looks like this:
int[1,1](3f(x)+2g(x))dx
That is, the upper and lower limits of the integral are both 1.  Now, the

I'm looking for simple quizz after the Vectorial Space's first chapter  (or
simple exercices).
Thanks for your help.
Louis