Math Forum / Mathematics / Undergraduate Math / June 2005

I'm lost on how to solve the system of equations by the Gaussian elimination method
2x + y - 3z = 1
3x - y + 4z = 6
x + 2y - z = 9

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Let f be monotonic on [a,b],
and g be continuous on [a,b].
In addition, g(a)<f(a)<=f(b)<g(b).
Prove that, there exists some c in (a,b) such that,

I have a practical trig problem that I've been trying
to solve for many hours already without success.. and
I have to admit that feel pretty stupid for it. :-|
I have uploaded a drawing of the problem here:

We need to calculate sag where a point on the curve is known.
For example, we know the distance between supports and attachment
heights on the supports of a cable that crosses a river; we also know
the height at the river's edge and the distance from each support to

show that if n and m are odd and not divisible by 3, then 24 | n^2 - m^2
thanks

Let f be monotonic on [a,b], and g be continuous on [a,b]. Moreover, g(a)<f(a)<f(b)<g(b). Prove that, there exists some c in (a,b) such that f(c)=g(c).

first of all, this IS homework, but I don't want an answer- I want a
hint as to how to do it.
" Suppose the average American has a 0.004% chance of contracting cancer
  during her lifetime as the result of eating peanut butter that

I hope you can help me settle a ongoing difference of interpretation of what would be the cumulative increase of the following five numbers.
469.6
477.6
492.8

Need some help with a few problems.
1). An objective function is to be maximized given the following constraints: x + 2y<=4, x - y<=1, x>=0, y>=0. Find the vertices of the set of feasible solutions.
I'm having trouble finding the vertices. I found the points of intersection are: ...

If I have 2 vectors from 3 points <a,b> and <a,c>, how can I calculate the bisector of these, so that the resultant vector is always positive between <a,b> and <a,c> in a clockwise direction?
i.e. I am looking for a way to get the angle between two vectors in a clockwise direction ...

I was just wondering
I have figured half of it out, but my proffessor at harvard told me i should carry the 3 instead of the two, i thought this was ludacris...MAHOOIIIIII!!!!!!

 I trying to  solve a certain problem from Herstein. The problem is the following :
 group,G = union of subgroups A, B and C.
 We have to show that G is homomorphic to 'the'non-cyclic group of order 4, V4.
 I have been able to show G to be homomorphic to a group, say K, with ...

hi.
I need some help, here the question:
3. How many yards of material from a 24-yard length of cloth remain after 3 pieces, each 3 1/2 yards long, and 5 pieces, each 2 1/4 yards long, are removed?
a. 2 1/4

I have n spheres and i know their radius and their centers. How do i determine whether they intersect at a point in space or not ?
i have (x- ai)^2 + (y - bi)^2 + (z-ci)^2 = ri^2 where i = 1 to n. Now i have to determine whether all these spheres intersect at a point or not. What ...