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I haven't actually watched this clip but it is probably good and if it is not then there are others :)

It is quicker just to google things like this :)

Thanks Pyramid :)

Mmm   Thanks Pyramid, that is a really good question.  One that I will have problems answering but here goes :)

If you graph y=x!    (where x is a integer greater or equal to zero) you get a graph of points. 

If you draw a smooth curve between these points so that the graph is continuous then you will have all positive values of x (x>=1) and all values of y (y>=1) included. 

So now you can read 2.4! off the graph. 

The gamma functions has values outside this domain as well but i don't understand it well enough to explain those.

I don't think my explanation is very accurate.  But it probably gives you as much of an idea as I possess. :)

There is of course a proper formula for n! where n is not an integer but I am not going there. :/

A bag contains red marbles, white marbles, green marbles, and blue marbles. There are an equal number of red marbles and white marbles, and five times as many green marbles as blue marbles. There is a 35% chance of selecting a red marble first. What is the fewest possible number of green marbles in the bag?

I want to talk about this one a bit

There is a 35% chance of getting a red so there must be a 35% chance of getting a white.

35+35=70%

There is 100% chance that you will pick a marbles  and 70+30=100

SO  there must be a 30% chance that you will choose a blue or green marble.

and let the number of Blue marbles be B  the number of green marbles will be 5B     

B+5B=30%

6B=30%

Blue=5%

Green = 30-5=25%

so lets look at the ratios

Red: White: Green : blue

35  :35     :       25:    5

They are all divisable by 5

7    : 7      :      5   :   1

So the fewest number of green marbles is 5    

If you turn them both upside down so that they look like a 1 (ignoring the zero) and a 6, then three times the first plus three times the second will do it.

I think what you are calling a trapezoid I would call a trapezium.

Your formula is corect but this is how I think of it.

Area = average of the parallel sides x perpendicular height.

$$area = \frac{(a+b)}{2}\times h$$

Hi LooLoo  :)

These are 2 factorizations that you are supposed to memorized

$$\\\boxed{a^3-b^3 = (a- b)(a^2+ ab +b^2)}\\\\
\boxed{a^3+ b^3 = (a+ b)(a^2- ab +b^2)}$$

Now lets look at your question.        

   $$\\x^6+y^6\\\\
= (x^2)^3+(y^2)^3\\\\
= [(x^2)+(y^2)][(x^2)^2-(x^2y^2)+(y^2)^2]\\\\
= [(x^2)+(y^2)][(x^4-(x^2y^2)+(y^4)]\\\\
= [x^2+y^2][x^4-x^2y^2+y^4]\\\\$$

Never mind the whole works, just consider the phrase "to be or not to be" There are 18 characters (including the spaces).  Suppose the monkeys can type 18 characters a second and they only ever hit the 26 lower case letters of the English alphabet plus the space key.  Then there are 27^18 possibilities, so this many/18 seconds to get through them all (hence to guarantee getting the phrase). This many seconds is:

$${\frac{{{\mathtt{27}}}^{{\mathtt{18}}}}{\left({\mathtt{18}}{\mathtt{\,\times\,}}{\mathtt{3\,600}}{\mathtt{\,\times\,}}{\mathtt{24}}{\mathtt{\,\times\,}}{\mathtt{365}}{\mathtt{\,\times\,}}{\mathtt{1\,000}}\right)}} = {\mathtt{102\,439\,781\,348\,723.257\: \!530\: \!001\: \!284\: \!246\: \!6}}$$

Approximately 102439781348723 millenia.

Don't hold your breath!

.

If tan²(x) = 1/4 then tan(x) = ±1/2 so x = tan^-1(±1/2)

Use atan on the calculator on the home page here to find the values of x (atan is the same as tan^-1).  This will give you angles in the first and fourth quadrants, but there will also be solutions in the second and third quadrants (obtained by 180° ± x).

.

$${\frac{{\mathtt{0.5}}}{{\mathtt{100}}}} = {\frac{{\mathtt{1}}}{{\mathtt{200}}}} = {\mathtt{0.005}}$$

$${\mathtt{0.005}}{\mathtt{\,\times\,}}{\mathtt{7\,306\,483\,056}} = {\mathtt{36\,532\,415.28}}$$

1/3 (x- 13) > 14    mutiply both sides by 3

(x - 13) > 42      add13 to both sides

x >  55

I think you want to know the angle when the tanget  = 7//11.  For that, we can use the tangent inverse.

tan-1 (7/11) = about 32.47°    

This could also be a 3rd quadrant angle = 180 + 32.47 = 212.47°

0=10x^2-15x

we don't need the quad formula, here....just factor

0 = 5x(2x -3)     and setting both factors to 0, we have

5x = 0                               and            2x - 3 = 0

divide both sides by 5                      add 3 to both sides 

x = 0                                                   2x = 3

                                                         divide both sides by 2

                                                             x = 3/2

So...the solutions are......x = 0   and x = 3/2

Which two equations?

Alas, tis true!

If you mean

f(-2)=2x-3, then substutute -2 for x in 2x-3 to get -7.

We can't say.......but....since every permutation is possible.....it theoretically could be done.....

Unless.....you used some of Nauseated's monkeys........they are well-read with regard to both Shakespearean tragedies and comedies.......they could bang out something in a jiffy for you....!!!!

Hit the "2nd" button on the calculator and then the "atan"  key...

Mmmmm.........what about -15  and 4  ???

x = [-b ±√(b² - 4·a·c)] / (2·a)

Go to a calculus class and have a terrible teacher that teaches you nothing and gives you book work to do by yourself. Eventually you would get sick and tired of it and fail your class and your parents/ guardians would get angry with you, dus "k*****g" you to the point where you never see dayligt again. Or they go in because of your calculus grades and make a fool of you to everybody. Making you feel dead for the rest of the day... or perphaps a lifetime..... Therefore math is a k****r to the brain. 

Mental

Abuse

To

Health

math

When  x²  =  150     --->     x  =  ± √(150)     --->     x  =  ± √(25)√(6)  =  ± 5√(6)

You can use trigonometry.

If you know the values of the opposite side and the hypotenuse:  Angle  =  sin^-1(opposite/hypotenuse).

If you know the values of the adjacent side and the hypotenuse:  Angle  =  cos^-1(adjacent/hypotenuse).

If you know the values of the opposite side and the adjacent side:  Angle  =  tan^-1(opposite/adjacent).