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Challenge accepted;

$$3x = 60\\
x = \lim_{n->\infty} \begin{pmatrix}
\frac{27n^3+27n^2-27n+27}{\frac{27}{5}n^3+\frac{27}{4}n^2+\frac{27}{3}n+\frac{27}{2}} \\
27^{\frac{1}{n}}+((\frac{1}{n})!)
\end{pmatrix}
\sqrt{((cos(\frac{1}{4}\pi)+isin(\frac{1}{4} \pi))(cos(\frac{1}{4}\pi)-isin(\frac{1}{4} \pi))-e^{i\pi}-2(cos(\frac{3}{4}\pi)+isin(\frac{3}{4} \pi))^4)}\\
\mbox{ where }\begin{pmatrix}
m \\
r
\end{pmatrix} \mbox{ is the combination of m taken r}$$

which is the value of this radical sqrt (3 * 5 ^ ^

√(3*5) = √(15)

Esto es todo lo que podemos hacer. ¿Alguno de su problema de conseguir "cortado?"

(This is all we can do. Did some of your problem get "cut off??")

Who dares to question rosala??  .... How about  a little "fire," Alan (and reinout)...???

No mistake Chris, you are perfectly correct!

Perhaps x and 60 are angles in degrees.  Then x could be 140°, which means that 3x = 420° which is the same as 60° for many purposes (certainly as far as the trig functions are concerned)!

After looking at this again, let's analyze it to see if I blew a fuse (which is always a faint possibility)....I know that a tetrahedron can be put in a cube (as the picture indicates) and that it can be oriented in such a way as to produce a tetrahedron that is equal to (1/3) of the cube's volume, but I'm having second thoughts as to whether or not THIS pariticular orientation produces such a thing.

Let's call the side length of the cube, s. Notice that every edge length appears to be just √(s² + s²) = s√2. And the "formula" for the volume of a tetrahedron with edge length "a" is just

(a)³/(6√2)    ....so we have.....

(s√2)³/(6√2)  = [(s³)2√2] / [6√2] = 2s³/6 =

........s³/3 ..........

Mmmmm.........interesting!!

Did I make a mistake somewhere along the line??

HAHAHA!!!!!.....I love that one, Melody!!!

But, still.......THE GREAT AND POWERFUL OZ HAS SPOKEN!!!! .....Now, bring me the broomstick of the Wicked Witch of the West!!!.....Go!!!   .....Go!!!

Even though the function might not be defined in the sense of f(n) = 80n-275, it still maps R->R which even though it is an undefined function still has a domain and range. The question here is not whether or not this function has a domain and range, but rather whether it's a mathematical fallacy to have an undefined function.

Thank you Bertie, I didn't know you could remove the $$14-\lambda$$ as a common factor from a single column.

Seeing this definitely helps.

You're a hero 

x = (-(-20))

Boom!

thats impossible ! x has to be equal to 20 ! proof = 3x=60 so 3*20=60! i hope u might be knowing this from before ! 

we can factorize it through factor the common factor

for example there is a polynomial 3x^2+x+6y^2+2y

we can have a simple grouping first , put x in a group and y in another

(3x^2+x) (+6y^2+2y)

by extracting the common factor ,

we can see x(3x+1)+2y(3y+1)

as both x(3x+1) and 2y(3y+1) have the same factor(3y+1) still

we need to factorize it also and it will become (x+2y)(3y+1)

factorization is done!

there is another way also 

The space surrounding the tetrahedron consists of four, not three, congruent right-triangular pyramids Melody.

read it ! and thanks for the explaination !

thank u very much for the explanation of" from where light comes " ! i was really excited to know that ! thanks ! i would give u a thumbs up for this one !

Sun 8/6/14

Talk about the German site and congratulate Radix for becoming a moderator.

Radix is moderator for the German site. he has never posted on our site. 

This site runs forums in German, Spanish, French, English and Russian.
If you go to the bottom of any page you will see 5 two letter abbreviations. EN stands for English that is our version. DE stands for Deutsch which is German in German. Click on that and you will be transferred to the German site. That is where Radix hangs out. You will be logged out but you can log into the German site or you can came back here and log on again.

The fun continues.

@@ End of Day Wrap - Saturday 8/6/14   Sydney, Australia   Time 12:25 am (really Sunday morning)

Hi everyone,

Thank you Rosala, Zegroes and Reinout-g.  I really appreciate your and everyones support.  It means more to me than you will ever know.  I also seemed to have ended up with quite a few 'wrap' points. Thank you so much.

Rosala wanted to know how the light were projected on the buidings that I was talking about last night. They were laser lights and they were projected from large boxes, maybe 2.5metres cubed, that were unobtrusively placed behind the onlookers.  One of the very large buidings had a platform in front of its box and individuals were invited up to 'conduct' the lights.  The lights changed quite dramatically depending on their movements. They could also play table tennis with laser light b***s etc. a bit like how you can interact using an xbox.

Lots of great answers today from Kitty<3, CPhill, Rosala, reinout-g, Alan, Heureka, Sportslover, NinjaDevo, Bertie, Problem, zegroes, Bioschip, GoldenLeaf, and jjzamball.

#

Jjzamball became a member today.  Welcome to web2.0calc forum.  We hope you learn lots and like it here.

#

I really have to modify the way I care for this forum.  I have spent many hours just checking everything is answered and collecting all the names.  Once all the questions are answered to my satisfaction/capability collecting the names is easy enough, it is the answer checking and tidying that takes an enormous amount of time.  I also collect threads for this wrap as I go.  Does anyone have any suggestions on how I could do it differently or how someone else may be able to help?

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There is a sticky thread called “Information worth keeping or Developing.”

I refer to it most days.  It is full of addresses of threads that can be used over and over again.

It is not well organised and some of the older posts have info that will no longer display properly but it would be worthwhile for answerers to familiarise themselves with the newer posts.  I write a little description above each reference address.  You are encouraged to add your own post on the end.  Once you have one post you can usually edit it to include new addresses.  You do not need to make a new post every time.

Today I added two address.

1)  Square root in question verses Square root introduced in the working. (Written by Melody)

c = -1/3 (7*3 - 2)/(--2) +1 

c = -1/3 (21 - 2)/(2) +1 

c = -1/3*19/2 +1 

c = -19/3*2 +1 

c = -19/6 +6/6

c = -13/6

You need to define exactly what you mean by 'larger'.

You might take it to mean magnitude, (in which case -0.5 is as large as 0.5) or you might take CPhill's dollars argument or Melody's line that all negative numbers are smaller than all positive numbers.

As an alternative, in electrostatics there are things called point charges, and they can be positive or negative. So, if I have a positive point charge of +9 and a negative point charge of -40, which is the larger ? I would say that it was the -40, (but it comes down to a matter of definition).

Yes it is a choice thing.

Sythetic division is much quicker but I have to look up how to do it every time because I have used normal long division for years and i do not have a good memory.

However if you can remember it, it will make you faster and exams tend to be long so speed does matter.

Oh sorry, I thought i was answering the question - silly me.

----------------------------------

Here is a couple of you tube clips that will help.

Synthetic Division

Firstly there is no theta in the question but it is pretty obvious that you want the gradiant of the line and jjzamball has found that for your nicely.

the only comment I would make to jjzamball is that if you change one unit to another unit and you want your answer correct to 2 signif figures then the original unit should have more than 2 significant figures or you a likely to end up with too much rounding error.

It is just a little observation.

c = -13/6 because well i have to give a more detailed answer but i dont know what else to say because i just solved it so im just typing this so this stupid thing will accept my answer and im running out of ideas of what to type so im just typing what im thinking about that i have nothing left to type about so now ill try publishing again but in any case c equals -13/6.