Melody

I have a further question Heureka. 

$$\!\ \varphi(6) = 2. \qquad 1 \text{ and } 5 \\\\
6 = 2 \cdot 3\\
\!\ \varphi(6)}=6\cdot (1-\frac{1}{2})( 1-\frac{1}{3} )}=2$$

Now I do get why phi(6)=2

But what is it about from 6=2.3

What is the relvance of the brackets.  How can this be used on other examples?

Thank you Heureka,  that explains it beautifully 

$$\\V=\frac{4}{3}\pi*r^3\\
estimated\;r\;=21cm\qquad max\;r\;=21.05cm\\
$biggest error = max volume - estimated volume$\\
max\; error=\frac{4}{3}\pi*21.05^3-\frac{4}{3}\pi*21^3\\\\
max\; error=\frac{4}{3}\pi*(21.05^3-21^3)\\\\$$

$${\frac{{\mathtt{4}}}{{\mathtt{3}}}}{\mathtt{\,\times\,}}{\mathtt{\pi}}{\mathtt{\,\times\,}}\left({{\mathtt{21.05}}}^{{\mathtt{3}}}{\mathtt{\,-\,}}{{\mathtt{21}}}^{{\mathtt{3}}}\right) = {\mathtt{277.748\: \!730\: \!102\: \!649\: \!218\: \!5}}$$

max possible error approx  278  cm^3

almost :)

$$x=\pm\sqrt{2}$$

I am sorry but the question is wrong and so is your answer silver  

f(x)=-x^2-3x+1

find    f(-4)

f(-4)=-(-4)^2-3*-4+1 = -16+12+1=-3

$$\\tan(x+50)=cot(x )\\
tan(x+50)=tan(90-x )\\
x+50=90-x\\
2x=40\\
x=20\\$$

I expect there are other answers but that is one anyway.

I suspect that you have not interpreted this as intended silver27.

This is why people must learn to use brackets properly .   

maybe, if j = sqrt(-1)  then

$$\\e^{-2j}\\\\
=cos(-2)+isin(-2)\qquad $in radians$\\\\
\approx \;-0.4161-0.9093j$$

Could a mathematician please check this.   

Look in the sticky topics !!!!!

Thanks Chris, that is high praise.