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0!  is defined to be  1  so that certain formula work.

For example: the formula for permutations is:  _nP_r  is  n! / (n - r)!  

     which wouldn't work for ₅P₅  =  5! / (5 - 5)!  =  5! / 0!  unless  0!  is defined to be  1.

A problem that requires  ₅P₅  is:  How many different ways can you arrange 5 books on a bookshelf?

Since there are 5 ways to choose the first book, 4 ways to choose the second book, 3 ways to choose the third book, 2 ways to fourth books and 1 way to choose the last book, you get 5 x 4 x 3 x 2 x 1  =  120  =  5!.

Not a proof....but notice....

3! = 4!/4

2!  = 3!/3

1! = 2!/2

So....this would imply that

0!  = 1! / 1  = 1/1 = 1

I get (-2/3y). 

If you factor -1 from the parenthetical part in the denominator, I believe that you can now cancel part with the numerator. 

14/21 can be simplified by dividing both the numerator and denominator by 7    --->   2/3

y⁴/y⁵ can be simplified by dividing both the numerator and denominator by y⁴   --->   1/y

5 - 3y can be written as:  -1(-5 + 3y)  =  -1(3y - 5)

So:  (5 - 3y)/(3y - 5)  becomes  -1(3y - 5)/(3y - 5)  which is -1.

Putting these together, we have:  -1·(2/3)·(1/y)  =  -2/(3y)

Draw a right triangle.  The functions sine, cosine, tangent,  etc are the ratios between two of the sides. 

For example,  the sine of an angle is the ratio of the side opposite the angle over the hypotenese. 

Remember that in a right triangle the hypotenese is the longest side. 

Peanut butter. 

After review I see that the misinterpretation was due to a missing ^ after the 10 of each number.  My apologies. 

U can't...

None. 7.6994 E4 should be correct. 

(16)((x^2+1)^3))(1-3x^2)

The only thing that makes this 0 is found in the last term

We have

1 - 3x^2 = 0      add 3x^2  to both sides

1 = 3x^2          divide bpth sides by 3

1/3 = x^2          take the square root of both sides

±√(1/3)  = x  

And these are the two values that make this function = 0

COME ON, you people ANSWER ME!!! my math teechur iz soooo pist at me and im gonna fail my math class!!! how much, guys???

with swag cuz swag is life

3 million 

2 * (x - 10) = x   simplify

2x - 20  = x        add 20 to both sides and subtract x from both sides

x = 20

............................................................................................................................

thanks

We know the hypotenuse - 40 - and an angle = 60. And we're looking for the opposite side. The sine relates these......so we have

sine 60 = opp / 40

(√3/2) *40  = opp = 20√3 ft. = about 34.64 ft.

Define number a so that the straight that goes through points (-1,3) and (3,a). the straights slope is 2:3

So we have

[3 - a] / [-1 -3 ] = 2/3

[3 -a ] / -4 = 2/3     cross-multiply

3(3 -a) = -8    simplify

9 - 3a  = -8     subtract 9 from both sides

-3a  = -17        divide both sides by -3

a = 17/3

Use the formula x(2/3)=1 put your age in the Variable and solve, if they dont equal then youll never get married

Area is length times width, so length is Area divided by width.

A= (length)(width)

A÷(width)= length

Divide and multiply,  before you add and subtract.