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Happy Birthday Dbg, I am sorry I am late!    

Happy birthday.....Dbg  !!!!

Okay,Melody.At first I would like to apologize for that.And thank you for spend your time to solve the question.

Now,I have to explain my question.I stated "if" at the begin of each questions.That mean you can not use the given in qustion 1 to solve qustion 2.

But if I did state "if" at the begin of the qustion ,like "$${\mathtt{OM}} = {\sqrt{{\mathtt{5}}}}$$,what is the length of PM?",then you can use it to solve question 2. and I stated if,so.......

Now,if you could only use the given in number two and the title,can you do qustion 2? 

That all looks good, Fiora.....!!!

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Like I said, I think there must be a translation problem :)

It doesn't matter, if you understand that is good.  

I did look at your graph but so far it does not make sense to me.   

the given in question one is not vaild, when you doing number two.

see my link on demos,https://www.desmos.com/calculator/a5dnftk4qi

I do not understand what you are trying to tell me Fiora.

(Neither does Civonamzuk or CPhill)

Perhaps there is a translation problem?

M can only be those 2 set points.  

And you have said that angle PON=30 degrees.

So if N lies on the interval PQ, there is only one point that N it can be.     

Thanks for my points     

(Sin 1 ) + 1/2  =    0.517452406437   if using degrees

(Sin 1)  + 1/2  =    1.341470984808   if using radians

The exact value   =    -1 / √3   or  -√3 / 3   .....{ if you prefer to "rationaloze" the denominator }.......

After extensive research and calculations, I'll have to agree with answer #1     Bravo!

The length of a day on earth is determined by the period of its spin on its axis and has nothinig to do with its volume.

I assume you are working in radians (and not degrees)    -0.57735026919

(15 - 12) !  * √16   +  5 =

(3) ! *  4    +   5   =

6  *  4   + 5    =

24   +   5    =

29

(x-2)(x-2)+4x =

x^2 - 4x + 4 + 4x =   {combine like terms}

x^2  + 4

No.Here is a graph from desmos:

4/3 times 3.14 = ?

2    +    2    =    4

$${{\mathtt{6}}}^{\left({\frac{{\mathtt{5}}}{{\mathtt{3}}}}\right)} = {\mathtt{19.811\: \!563\: \!493\: \!367\: \!764}}$$