Melody

[2nd] [acos]

arc cos is the same as inverse cos

$${\frac{{\mathtt{62.5}}}{{\mathtt{100}}}} = {\frac{{\mathtt{5}}}{{\mathtt{8}}}} = {\mathtt{0.625}}$$

I could do that in my head Chris but then I am a show off.  LOL

Here is another easier way and it works for all numbers ending in 5

25^2=2^2+2 then add 25 = 625

75^2 = 7^2+7 then add 25 = 5625

35^2=3^3+3 then add 25 = 1225

105^2=10^2+10 then add 25 = 11025

etc.

That is really easy to do in your head :)

Another great answer Brittany 

nice work BJ.

I have put your answer aside for the next wrap :)

Please can another mathematician check this answer. 

I'm not good at limits so my answer will probably be wrong but I always think I learn better if I get involved.

Lim x-> infinity of (e^x + x)^1/x

$$\\\displaystyle\lim_{x\rightarrow\infty}\;(e^x+x)^{1/x}\\\\
=\displaystyle\lim_{x\rightarrow\infty}\;\left(\frac{e^x}{1}\cdot \frac{(e^x+x)}{e^x}\right)^{1/x}\\\\
=\displaystyle\lim_{x\rightarrow\infty}\;\left[\left(1+ \frac{x}{e^x}\right)^{1/x}\cdot (e^x)^{1/x}\right]\\\\
=\displaystyle\lim_{x\rightarrow\infty}\;\left[\left(1+ \frac{x}{e^x}\right)^{1/x}\cdot e\right]\\\\
=\;e\times\;\left[\left(1+ 0}\right)^{1/x}\right]\\\\
=\;e$$

well the web2 calc will solve equations for you.

e.g

i enter

x^2-7=8             And the calc gives me the answer.  Isn't that nifty :)

$${{\mathtt{x}}}^{{\mathtt{2}}}{\mathtt{\,-\,}}{\mathtt{7}} = {\mathtt{8}} \Rightarrow \left\{ \begin{array}{l}{\mathtt{x}} = {\mathtt{\,-\,}}{\sqrt{{\mathtt{15}}}}\\
{\mathtt{x}} = {\sqrt{{\mathtt{15}}}}\\
\end{array} \right\} \Rightarrow \left\{ \begin{array}{l}{\mathtt{x}} = -{\mathtt{3.872\: \!983\: \!346\: \!207\: \!416\: \!9}}\\
{\mathtt{x}} = {\mathtt{3.872\: \!983\: \!346\: \!207\: \!416\: \!9}}\\
\end{array} \right\}$$

https://www.youtube.com/watch?v=O8ezDEk3qCg

19 computers and 23 peripheral graphics devices

I don't get this question.

The connections are not 1 to 1 since there are more peripheral devices than computers.

So some computers are connected  to more than 1 device. 

What is the maximum number of divices that a computer can connect to?

Can a peripheral connect to more than one computer?

Se my confusion.   

The answer could be really enormous depending on what the question really means .

Perhaps you mean the  [2nd] key ?