CPhill

Good job, GL !!!

Your points are a mountin' up !!!

(But, you're still not gonna' catch me !!!....... LOL!!)

(Now...get back to that solo !!!)

Thank you for that, Stu.....I'm sure that will be very helpful for a lot of people on this site...."Thumbs Up" from me !!!

4x-7y=11

-5x+2y=14

OK, I'm going to use something called the "elimination" nethod to solve this. We're going to eliminate a variable (I'll choose "x") which will set up an equation in one variable that will be easy to solve.

Note that if we multiply the top equation by 5 on both sides and the bottom equation by 4 on both sides, we get the following system:

20x - 35y = 55

-20x + 8y = 56    

.......Now, if we just add these together, note how the "x's" "disappear!!"   So we have......

-27y = 111    .... divide by -27 on both sides, and we get

y = 111/-27   =   -37/9

Now using either one of the original equations - I'll use the second one - we can substitute -37/9 for y and find x.  So we have

-5x + 2(-37/9) = 14

-5x - 74/9 = 14       ... multiply through by 9 on both sides

-45x - 74 = 126      .....add 74 to both sides

-45x = 200             .....divide by -45 on both sides

x = 200/-45 = -40/9

So there are our solutions...x = -40/9  and y = -37/9

Not very pretty, is it??   ....but, that's the way it goes sometimes !!!

If you check these in the first original equation, you will see that they "work"  (In fact, they should "work" in all the equations!!!)

OK......let's see if we can find a pattern

Suppose we had three people.....the third person shakes hands with persons one and two....the second person then shakes hands with person one. Note that person  one doesn't have anyone left to shake hands with. So, that's three total handskakes.

What about four people?? The fourth person shakes hands with the other three, the third person shakes hands with persons one and two, the second person shakes hands with person one, and again, person one has no one left. So, that's a total of 3+2+1 = 6 

Look at the patttern so far.......

2 people = 1 hand shake

3 people = 2 + 1 handshakes = 3

4 people = 3 +  2 + 1 handshakes = 6

So...it appears that with "n" people, the number of handshakes is just the sum of the first "n-1" counting numbers. There is a "formula" for this given by:

n* (n-1) /2 

where n is the number of people...To see that it's true, note that the number of handshakes between 4 people are:

(4) * (3) / 2 = 12/2 = 6...just as we found.....

So....with 20 people, we'd need...     (20)*(19)/2 = 190 handshakes

So 78 handshakes won't be enough...

Hope this helps........

Actually....if you ask a "Physiques" question........we'll answer you in French.....

If you mean you want to find the inverse cosine, go to the calculator and hit the "2nd" button.....you will see the inverse cosine button labeled "acos." Make sure that you specify the correct mode that you want at the bottom left (either degrees or rads).......

 "Is" means "equal" 

55% = .55 in decimal form

"Of" means "multiply" 

"What number" means some variable (we'll call it "n")

So, putting all this together, we have.......

61,933.08 = .55 * n          .....divide both sides by .55.....

112,605.6 = n = "What number"

Wasn't this the one you did last night?? Remember the calculator has to be in radian mode.......

After you integrate, you should get

(5/3) [cos(-3) - cos(6)] = -3.25

Does that help??

Euclid proved that when 2^p -1 is prime, then 2^p-1(2^p -1) is a perfect number. Such a prime is known as a Mersenne prime.

For 2^p-1 to be prime, it is necessary that p be prime. (It doesn't work the other way....p might be prime, but 2^p-1 might not be.)

The 45th perfect number - discovered in 2008 - has over 22 million digits - obviously impractical to write that out, here !! (Note that this is the 45th "ranked" perfect number......this "rank" may change if smaller perfect numbers are discovered. It is known that this would have to occur after the 43rd perfect number.......thus, the "ranking" of the first 43 is correct.)

The Mersenne prime that generated the 45th perfect number is (2^37,156,667 - 1). So, the "formula" would be:

2^{37,156,667 -1} (2^37,156,667 - 1)

BTW....all the perfect numbers discovered so far are even. It is not known if any odd ones exist. If they do, they are greater than 10¹⁵⁰⁰ . (No...I don't know how this was proved !!)

Stu...your answer is "wrong" because 4.005 ISN'T a zero....look at my previous post...it's a pretty detailed explanation of the proceedure - in simple terms....