Maths/Physics help

[astarmathsandphysics]

The diazstance is also doubled

[astarmathsandphysics]

The disatnce is aLSO DOUBLED

[omarsubei]

OK ok ok. Thanks a lot

[omarsubei]

I just can't get this question:

A container is filled with a mixture of nitrogen and oxygen. What is the ratio of the rms (root mean squared) speed of oxygen molecules to that of nitrogen molecules? (Molar mass of oxygen=32 g mol^-1 ; molar mass of nitrogen=28 g mol^-1

I'll tell you the answer this time : 0.935

[astarmathsandphysics]

I just can't get this question:

A container is filled with a mixture of nitrogen and oxygen. What is the ratio of the rms (root mean squared) speed of oxygen molecules to that of nitrogen molecules? (Molar mass of oxygen=32 g mol^-1 ; molar mass of nitrogen=28 g mol^-1

I'll tell you the answer this time : 0.935

All the molecules have the same kinetic energy
therefore0.5m(ox)v(ox)^2=0.5M(nit)v(nit)^2
therefore rms(ox)/rms(nit)=sqrt(m(nit)/(ox))=sqrt(14/16)=0.93

[omarsubei]

Wow. I see. THhnk you very much

[omarsubei]

I swear, if you solve this question, you're just a born genius! I've been trying it the whole day and I'm not getting the answer, which is 72.
I HATE Permutations and Combinations. Here it is:

"Mr Blue, Mr Black, Mr Green, Mrs White, Mrs Yellow and Mrs Red sit around a circular table for a meeting. Mr Black and Mrs White must not sit together.

Calculate the number of different ways these six people can sit at the table without Mr Black and Mrs White sitting together."
 

[crucio]

u sure the ans is 72? im gettin 144...lol 

[astarmathsandphysics]

Soppose mr black site down fist then mrs white can site in one of 3 possible seats - draw it!. The other 4 guests can sit in 4! different ways with respect to oder. 3x24 =72

[omarsubei]

Soppose mr black site down fist then mrs white can site in one of 3 possible seats - draw it!. The other 4 guests can sit in 4! different ways with respect to oder. 3x24 =72

Wait wait wait. I DID DRAW IT, a few million times too. Ya but what if Mr. Black changes his seat. He can also sit in six different places can't he. It's a permutation isn't it? Please explain more. There is actually a solution, but it's even more complex than yours:

"The number of different ways six people can sit around a circular table
is 5! = 120.   (M1)
The number of different ways these six people can sit around a circular
table with Mr Black and Mrs White together is 4! × 2 = 48.   (A1)
Therefore, the number of different ways these six people can sit around
a circular table with Mr Black and Mrs White NOT together is
120 – 48 = 72   "

Why can they sit in 5! ways, not 6!   ?

[omarsubei]

Oooooooh, wait I think I get it. Is it because it doesn't matter where Mr. Black sits first, because the question is asking about the different "ways" they can sit i.e. their positions with respect to each other?

[astarmathsandphysics]

Exactly. If it mattered there answer would be 6x72=432

[astarmathsandphysics]

You are making it soooooooooooooo compilated but it is exactly as I say.

[astarmathsandphysics]

Oooooooh, wait I think I get it. Is it because it doesn't matter where Mr. Black sits first, because the question is asking about the different "ways" they can sit i.e. their positions with respect to each other?

Exactly

[avrila]

Can you please help me with this:

1. Find the fourth vertex of the parallelogram:
A(2,1,0) B(3,2,-1) C(0,-1,1)

2. Find the shortest distance between point A (3,5,6) and line (x-7)/2=y-5=(z-12)/6

Thanks in advance...