Melody

A kite could have that.  

Thanks AELN

I think resource links like this are better than actual answers to specific problems. 

I would just suggest that you use the link button though. It just makes it easier for the user.

It cannot be simplified further.

Thanks very much guest for finding that.

My logic is actually the same both times. It is nice to know that I did learn something.

It was just a careless error this time.

I actually do not know where i got the 15 from, it obviously should have been 21.

So the denominator should be   21C4 = 5985

Answer       70/5985

LOL

Are you going to give me the address of where I answered it correctly?

That is not simplifying Helpmeeee, that is factorizing.

They are opposite in meaning.

The expression cannot be simplified.

However, Helpmee has shown you how to factories it.

Thanks very much.

The video did not really explain more but while I was watching it I had a light bulb moment.

I suddenly had insight into why it would work.

So yes, the video was both interesting and very helpful.   Thank you  HELPMEEEEE     

Now I just hope I can remember it for next time. :///

Thanks guest, that SYMBOLAB calculator site is super cool.

It gets the answer with working!

I've never done this type of question before and to be honest, although I can follow their algebra, I do not have a full understanding of what it is doing.

How do I interpret the relevance of discriminant of expressions like that one.

I also found the axis of symmetry of that expression and it gave me the equation of a hyperbola which does give the graph symmetry.

Super weird, super cool!

Can anyone off me more insight into the logic of this question, and the answer given by that calculator?

I am not good at presenting these but I'll show you what I would do.

\(\displaystyle\lim_{x→0} (((1 + sinx)cotx −e)cotx)\\ =\displaystyle \lim_{x→0} \left[ \left[ (1 + 0)\frac{cosx}{sinx} −e\right]\frac{cosx}{sinx}\right]\\ =\displaystyle \lim_{x→0} \left[ \left[\frac{cosx}{sinx} −e\right]\frac{cosx}{sinx}\right]\\ \\~\\ \rightarrow+\infty\)

Maybe Heureka or someone some other mathematician may like to tidy up my presentation.

Hi Loki,

Lets say the first digit is 1

it will be followed by 2,3,4,5     there will be 4! = 24 ways that these number can be arranged so that accounts for the smallest 24 numbers

If the first number is 2 followed by the others then again this will account for another 24 numbers.

so

25431 is the 48th number

31245 is the 49th

31254 is the 50th.

The question is not well worded but I think that is what is meant.