CPhill

You and 9 friends are waiting inline at a movie theater. You want to determine how many different orders you and your friends can stand in line. How many different arrangements are possible?

Well....notice that there qre 10 ways to choose the first person to stand in line, there are 9 ways to chooose the second person to stand in line, 8 eight ways to choose the third person, etc.

So we have

10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1 ways = 10 !    where the little " ! " is known as "factorial"

And 10 ! = 3,628,800 arrangements  (Quite a lot !!!) 

None......I ate all 6 while she wasn't looking.....

The ratio of the circumference of a circle "C"  to its diameter "d."

So........

π = C / d

Pi is an irrational number....no repeating decimal pattern has ever been found (there is none)

The value usually used in computations is either 3.14 or 22/7........

BTW......as of Oct 28, 2013, pi had been calculated to over 12 TRILLION digits !!!

(Someone has a lot of free time on their hands...... )

Hint.....we can write 35% as .35

......see if you can take it from there....

It is in "lowest terms" because 61 is a prime number (and it doesn't divide 115)....there's nothing to be done to reduce iit !!!

Check your sign in front of the "23"......It needs to be either a "+" or a " -"......an "=" doesn't make any sense....

how do you factorize -x^4+3x^3+x^2-3x

Ler's start by taking out any greatest common factor.  We could choose to take out an x or a -x. I'm going to do it the second way, because it makes any potential further factoring easier. So we have...

-x(x^3 - 3X^2 - x +3)  Notice, that because I took out  an  "-x," the signs in the parenthesis "reverse."

Let's see if we can factor the stuff in the parenthesis by "grouping."   We have..

x^2(x - 3) -1(x -3)....That's good....Now, take out the greatest common factor between these terms, (x-3), and write back what we have left...This gives

(x-3) (x^2 - 1)  Note that the second term is just a difference of two squares that we can further factor as (x-1) (x+1)

So, the stuff in the parenthesis factors as (x-3) (x-1) (x+1)

Now, putting everything together gives us....

-x[(x-3) (x-1) (x + 1)]

Note, some people might place the " - " in front of the leading "x" back inside the parenthesis. But, since the point of factoring is to usually find the "zeroes" of some polynomial by setting each factor to zero, it doesn't really matter. The " - " (which really represents " -1 ') would be divided away, anyway, during such a process.

Hope that helped........

The term "radius" implies that we want to find the area of a pentagon inscribed in a circle. We have 5 triangles. Using trigonometry, each triangle has an area = (1/2)*(r^2)*sin(72º).

And since we have 5 triangles, the total area = (5/2)(r^2)*sin(72º)

Also, if we know the length of a side, the total area is given by 1.7204*(s^2) where s is the side length.

Re: how to covert km/h to m/s?

I believe this is something known as "dimensional analysis"

Here's the metod of conversion.....Suppose that some object is traveling at 100 Km/Hr, and we want to convert this to m/s......So we have

(100 Km/ 1 Hr) x (1Hr / 3600sec) X (1000m / 1 Km)

Note that we equated 1 Hr with 3600 sec and 1Km with 1000m

Also, notice that the  "Hr" and the "Km"  units "cancel out" and we're left with

(100) X (1/3600 sec) x (1000 m)  = 27.78 m/s

To convert m/s to K/hr, we just reverse the process

(27.78m/1sec) x (1Km/1000m) x (3600sec/1Hr)

Note now that the "sec" and "m" units cancel out and we're left with

(27.78) x (1Km/1000)x (3600/Hr) = 100Km/Hr

As long as we equate units properly, the final result should be in terms of what we're after. Also, some conversions may require us to equate more things to get the correct answer.  For instance, if we wanted to convert Km/year to cm/sec, it would require additional conversions.

I hope this helps.....

Where x is negative....i.e., the 2nd and 3rd quadrants