Math Forum / Mathematics / Undergraduate Math / July 2006

I was doing my weekly assignment for calc class, and I got stuck on these two problems. My friend and I were trying to figure them out but we have no idea. Can anyone help with these? Thanks!
1. Find the center and radius of the sphere given by x^2+y^2+z^2-2y+2z-2=0.
2. Let P=(3,2 ...

Reposting from Gnu Math Archives (4dstudios.2006).
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Preview of what this is about:
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What theorem in geomtry guarentees that the length of a chord of a 40 degree
angle is not going to be double the length of a chord from a 20 degree angle

my friend asked me if I could do this problem. after looking at it I
said no.
here's the problem integrate from zero to infinity    
dx / [(x^2+a^2)^2(x^2+b^2)] ,a>0,b>0

y=x^2+z^2
is this a function?
i don't think it is, but i want to make sure.
and does this graph look like a paraboloid facing toward positive y-axis?

okay here it is
hm how shall i put it
integration from zero to infinity of  dx / [ (x^2+a^2)^2(x^2+b^2) ]
,a>0,b>0

Here's a question for some of the smart guys -
Given the choice of three doors, one of which conceals a prize, the other
two hold nothing.  The contestant then chooses a door.  They have a 1/3
chance of having selected the right door.

when you do a line graph in excel, do you adjust the scale so that the data covers 50-75% of the graph even though it might make the increase/decrease look much more significant?
what's the general rule?

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If there is a function f(u,v) such that df/dv = u (df^2 / dvdu), what is f?
Is there any kind soul out there that could enlighten me? :-)

pls, can somebody help me solve this problem
differentiate the following function
y=ln 5/x

1.  What in the world is a Chi-squared Distribution?  I looked it up on
the internet and still do not have a clue.

If one would like to calculate the curve integral of the function f(x,y,z) =
x^2 + y^2 over the curve C: r(t) = (e^t cos(t), e^t sin(t), t) where t goes
from 0 to 1, what would the result be?
The curve is clearly somewhat spiral-shaped with a radius increasing with t,

Hi every body,
There is a problem I have exposed to but, though being badly in need of
an answer, I have not yet been able to solve it. I am not quite sure if
it is better classified as a graph theory problem or a combinatorial