Math Forum / Mathematics / Undergraduate Math / March 2005

1 What does it mean to you when a system of two linear equations is Independent? Inconsistent? Dependent?
2 If a system of linear equations is Independent, how many solutions are there?
3 How many points lie in a region?

Hi, I'm an A-level student doing Further Maths and this question is really bothering me; I was wondering if anyone here can help. The question reads:
            __________________________
A small smooth ball bearing falls from rest at a height H above a smooth horizontal plane. ...

Dear Group.
Can these three points form 'equilateral triangle'?
P0 (B+R, -a)
P1 (B-0.866R, -a+0.866R)

If u, v, and w are mutually perpendicular, linearly independent vectors, are the vectors u+v, v+w, and w+u linearly dependent or linearly independent??
I know that the answer to this is linearly independent, but Im not sure how to show that on paper for full marks, can somebody ...

1)When we throw a perfect dice consider the result "number inferior to 5"
a)Calculate the the probability that in 10 consecutive throws the results are only once a number inferior to 5.
b)Determinate the probability that the result happens at least three times in the 10 throws.
2- ...

Ive got quite a difficult problem here, any one know how to find the answer to this?
I need to evaluate this integral
http://img112.exs.cx/img112/350/picture11my.gif
(the equation is in the picture)

I need to get the equation 4x^2-8x-y^2+6y-41=0 in terms of Y by using the quadratic formula.  Below is the steps I took and think they are right but get stuck after this point.
1. y^2-(6)y+(4x^2-8x-41)=0
2. y^2-(6)y=(-4x^2+8x+41)
3. y^2-(6)y= (x+(2+(3)square root 5)/2)) ...

If you know the distance formula then the equation:
Sqrt[(x--3)^2+(y-0)^2]=2*Sqrt[(x-3)^2+(Y-0)]
is obtainable DIRECTLY from the given info.
simplifies to

I don't understand how to calculate the limit of a geometrical series, ar^n (assuming it converges).  Take for Example:
(infinity)E(n = 1)  (7/(4^n))
I'm quite sure that the limit of a geometrial series ar^n is:
a / (1-r)

My question concerns excercise 3.18 in Rudin's Principle of mathematical analysis:
In it one is asked to define a recursive series by setting
x[n+1]= ((p-1)/p)*x[n]+ (a/p)*x[n]^(-p+1)  ,
where p>2 and a>0,

Then, solve this:
"A company producing stone has two quarry sites A and B. Each site produces three
grades of stone- high, medium and low grade. Site A produces 1 tone of high grade stone,
3 tones of medium grade and 1 tone of low grade stone for each hour that it is mined. Site

What is the easiest way to attack word problems?  Often times I get quite
confused even while trying to follow examples in the book.  Any tips or
pointers that any of you could possibly give to me?

I have this HUGE reputation as a crank or crackpot on math newsgroups
when I state very clearly what I do, and why I do it.
I brainstorm.
Some of you may know about brainstorming and you may also know that

I'm writing this post immediately, so if the topic is wrong sorry for this...
I've written a matlab program for amplitude modulation.. Here is my codes...

Hi i cant get the answer of the following:
Let X_1,X_2,....X_625 be independent identically distributed random variables, with density function f given by:
   f(x) = 3(1-x)^2  for  0 <= x <= 1
          0              otherwise