Science & Mathematics - 25 November 2007

Hi I'm having a lot of trouble with this question, any help or hints on either or both would be greatly appreciated! These two parts are part of one question so they should go together.
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1) Suppose that {x_n} is a sequence in a metric space X with some distance function d(x,y), and that z is a point in X s.t. for each subsequence {x_n_k} of {x_n} there exists at least one sub-subsequence {x_n_k_l} which is convergent to z. Prove that {x_n} is convergent to z.

2) Then consider the function f:X*X->R (f is a mapping of the cartesian product of X with X into the real numbers)
and let f(x,y)=d(x,y)/(1+d(x,y)) for all x,y in X.

Show that f defines a distance function on X and that the identity mapping from X to X is uniformly continuous when viewed as a mapping between metric spaces in either way: (X,d)->(X,f) or (X,f)->(X,d)
(X,d) means metric space X with distance function d(x,y), likewise (X,f) means metric space X with distance function f(x,y).


Thank you so much!

2007-11-25 16:19:07 · 1 answers · asked by greeneggs4spam 3 in Mathematics

Which of the following is equivalent to sin (90* + x)

sin(x)
cos(x)
sin(-x)
cos(-x)
-cos(x)

2007-11-25 16:17:06 · 4 answers · asked by dustin_r_85 1 in Mathematics

Find the equation of the circle centered at (h,k) = (-4,-2) and passing through the point (-1,2)

2007-11-25 16:14:46 · 3 answers · asked by dustin_r_85 1 in Mathematics

In the battle of the Falkland Islands in 1914, the shots of British gunners intially fell wide of their marks because their calculations were based on naval battles fought in the Northern Hemisphere. The Falklands are in the Southern Hemisphere. Explain the origin of their problem.

Please help, this question is from a physics textbook chapter 11 covering angular momentum and I've no idea how to answer it. Thanks!

2007-11-25 16:12:21 · 4 answers · asked by Kiwikahuna 2 in Physics

25 g Reptile and 25 g Mammal are both in a environment with 10 deg C. Which would have a higher rate of Cellular Respiration? Reptiles are cold blooded, and mammals are warm blooded... Please help? This is for AP Biology Lab. :P

2007-11-25 16:11:47 · 6 answers · asked by scatteredth0ughts_ x 3 in Biology

x+2y=8
x=-2y+8

2007-11-25 16:10:39 · 3 answers · asked by joe78521 2 in Mathematics

By what different methods (there are at least 2) do we infer that globular clusters are the oldest things in our galaxy? How do we infer that objects in the spiral arms are the youngest members of the galaxy?

2007-11-25 16:10:19 · 3 answers · asked by Anonymous in Astronomy & Space

2007-11-25 16:04:07 · 10 answers · asked by Love Exists? 6 in Biology

(a) A hanging spring stretches by 35.0 cm when an object of mass 450 g is hung on it at rest. In this situation, we define its position as x = 0. The object is pulled down an additional 18 cm and released from rest to oscillate without friction. What is its position x at a time 84.4 s later?
______ cm
(b) A hanging spring stretches by 35.5 cm when an object of mass 440 g is hung on it at rest. We define this new position as x = 0. This object is also pulled down an additional 18 cm and released from rest to oscillate without friction. Find its position 84.4 s later.
______m
(c) Why are the answers to the parts (a) and (b) different by such a large percentage when the data are so simliar? Does this circumstance reveal a fundamental difficulty in calculating the future?

(d) Find the distance traveled by the vibrating object in part (a).
______m
(e) Find the distance traveled by the object in part (b).
_______ m

2007-11-25 15:58:02 · 1 answers · asked by thegenuwineone 2 in Physics

A company is engaged in direct marketing of exercise CDs that sell for $ 18, including shipping and handling. The monthly fixed costs (advertising, rent, etc.) are $ 24000 and the variable costs (materials, shipping, etc) are $ 6 per CD.

Ok so far I'm here: 24000+6x as my cost function...

How do I find my revenue function and the break even points???

2007-11-25 15:57:47 · 3 answers · asked by RedSparkle 1 in Mathematics

and the slope of the line y=2/3x+6??

thanks!

2007-11-25 15:53:41 · 14 answers · asked by Anonymous in Mathematics

2007-11-25 15:53:23 · 8 answers · asked by Michael P Marshall 1 in Astronomy & Space

2007-11-25 15:47:52 · 6 answers · asked by Mandy P 1 in Mathematics

Mine is a panda and monkeys!.
Whats yours??
[[♥]]

2007-11-25 15:46:17 · 5 answers · asked by ♥Shorty♥ 2 in Zoology

timothy was 7 years old when ada was born. hal, who is 5 years older than timothy, is now 3 times as old as ada. how old is each person now?

2007-11-25 15:45:29 · 3 answers · asked by wowz 2 in Mathematics

A 0.329-kg puck, initially at rest on a frictionless horizontal surface, is struck by a 0.222-kg puck that is intitially moving along the x-axis with a velocity of 2.24 m/s. After the collision, the 0.222-kg puck has a speed of 1.24 m/s at an angle of 24 degrees to the positive x-axis. (a) Determine the velocity of the 0.329-kg puck after the collision. (b) Find the fraction of the kinetic energy lost in the collision.

2007-11-25 15:43:52 · 2 answers · asked by grouchy187 2 in Physics

Does anyone know where I could find flash cards for the 88 constellations?

2007-11-25 15:40:53 · 6 answers · asked by Richard M 2 in Astronomy & Space

how are endothermic and exothermic reactions related to loss or gain of heat

2007-11-25 15:36:26 · 2 answers · asked by Corey R 2 in Chemistry

Tony (of mass 55kg) coasts on his bicycle (of mass 5kg) at a constant speed of 5 m/s, carrying a 6kg pack. Tony throws his pack forward, in the direction of this motion, at 1 m/s relative to the speed of bicycle just before the throw. The initial momentum of the system (tony, bicycle, pack ) is 330 kg* m/s. The momentum of the system after the pack is thrown is 330 kg*m/s.

What is the bicycle speed after the throw? answer in kg*m/s

2007-11-25 15:36:09 · 1 answers · asked by Light Up the Sky 1 in Physics

I am doing a project for science fair, and we have set out the bread, but nothing has really happened. The bread has started to harden but thats it.

2007-11-25 15:33:27 · 3 answers · asked by =] 1 in Biology

2007-11-25 15:32:41 · 8 answers · asked by wallace 2 in Biology

management thinks that 45 % of current stockholders will want to make a purchase. A random sample of 130 stockholders is selected, 63 of whom express a desire to buy.
(a) what is the standard error of the sample proportion?
(b)what is the mean of the sampling distribution of sample proportion?
(c) what is the probability of obtaining the results described in the problem if p = .45?

seem to have gotten rusty over the holiday, don't remember how to do this question. help is appreciated.

2007-11-25 15:31:34 · 1 answers · asked by Andrew B 2 in Mathematics

2007-11-25 15:30:08 · 2 answers · asked by jonas m 1 in Biology

2007-11-25 15:28:23 · 3 answers · asked by jonas m 1 in Biology

My cat was just killed by this huge animal and we are trying to find out what kind it was.... HELP!! (10 pts!)
well my cat went missing a few months ago and we think she must have gotten attacked by another animal because she was very territorial. we never exactly found out what happened though. but today, i went outside cuz i thought i heard my new cat meowing and sure enough he and this HUGE animal were right next to each other and it almost killed my cat. I had to run over to my cat and pick it up and run into my house. I need help identifying what kind of animal this was. Heres a description of it:
Color: White and Black (More white than black)
Size: Spaniel
Very slow runner
Much bigger than a skunk
deff not a dog because it had these weird undescribably facial features
HUGE legs
If it makes a difference I live in a cold climate in Connecticut.
Please help me here!

2007-11-25 15:22:46 · 9 answers · asked by Anonymous in Zoology

I already asked this question, but I did not recieve a clear enough answer, and they changed base 2 to 4.

log base 2 (3x+2) - log base 4 (X) = 3

The book says to change log base 4 to 2. Its not so much the answer I am looking for, just how this works.

2007-11-25 15:14:47 · 5 answers · asked by John 1 in Mathematics

Or do you live near a famous one? Tell us about & if you have photos please share.

2007-11-25 15:12:49 · 9 answers · asked by Anonymous in Paranormal Phenomena

** = square root

SIMPLIFY
4*12* - *18* + *108* + 7*72*

SIMPLIFY
(7 - *5*)(3 + 2*5*)

2007-11-25 15:07:42 · 1 answers · asked by darkmage1235 2 in Mathematics

2007-11-25 15:04:45 · 4 answers · asked by Anonymous in Biology

the product of any two self adjoint operators on a finite dimensional inner p=roduct space is self adjoint...... No non-sense replies please, just if you know the answer or can help. thank you..

2007-11-25 14:56:35 · 1 answers · asked by handsome_joy 3 in Mathematics