Alan

You might be thinking of the Fields medal.

They are different names for the same thing!

Expand sin(a+x) as a series in x:  

sin(a+x) = sin(a) + x*cos(a) + higher order terms involving multiples of x.

Similarly:

sin(a-x) = sin(x) - x*cos(a) + higher order terms

Therefore, sin(a+x) - sin(a-x) = 2x*cos(a) + higher order terms

(sin(a+x) - sin(a-x))/x = 2cos(a) + higher order terms.

The higher order terms all contain multiples of x, so when x goes to zero, these go to zero and we are left with:

$$\lim_{x \rightarrow 0}\frac{\sin(a+x)-\sin(a-x)}{x}=2\cos(a)$$

About 6000 are Torres Strait islanders, so 6000/8000 = 3/4 are islanders.  3/4 = 75%.

If you are looking for the number of possible combinations then there are 50 for the first tumbler; for each of these there are 50 for the second; for each of all of these there are 50 for the third.  Therefore in total there are 50*50*50 = 125000.

Fraction = 2.79/9

Percentage = fraction*100 = 2.79*100/9 = 279/9 = 31%

The first statement means if you are far away (an infinite distance) from a charged particle (say) then the electric potential due to that particle is insignificant (zero).

For the second statement I can't see the image - it only appears as an icon in my browser.

This can be solved in the Equations part of the calculator on the home page of this site.

$$\left({\mathtt{x}}{\mathtt{\,\small\textbf+\,}}{\mathtt{8}}\right){\mathtt{\,\times\,}}\left({\mathtt{x}}{\mathtt{\,\small\textbf+\,}}{\mathtt{2}}\right) = {\mathtt{279}} \Rightarrow \left\{ \begin{array}{l}{\mathtt{x}} = {\mathtt{\,-\,}}{\mathtt{3}}{\mathtt{\,\times\,}}{{\mathtt{2}}}^{\left({\frac{{\mathtt{5}}}{{\mathtt{2}}}}\right)}{\mathtt{\,-\,}}{\mathtt{5}}\\ {\mathtt{x}} = {\mathtt{3}}{\mathtt{\,\times\,}}{{\mathtt{2}}}^{\left({\frac{{\mathtt{5}}}{{\mathtt{2}}}}\right)}{\mathtt{\,-\,}}{\mathtt{5}}\\ \end{array} \right\} \Rightarrow \left\{ \begin{array}{l}{\mathtt{x}} = -{\mathtt{21.970\: \!562\: \!748\: \!477\: \!140\: \!6}}\\ {\mathtt{x}} = {\mathtt{11.970\: \!562\: \!748\: \!477\: \!140\: \!6}}\\ \end{array} \right\}$$

Possibly like this: