Alan

A missing side of what?  And what information do you have for whatever it is?

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Use N = 56e^k*t where t is the time in years from 1995 and k is an. as yet, unknown rate constant.

Find k from the 2002 data:   59 = 56e^k*7   (because 2002 - 1995 = 7)

Divide through by 56, take logs, then divide by 7 to get k = ln(59/56)/7

$${\mathtt{k}} = {\frac{{ln}{\left({\frac{{\mathtt{59}}}{{\mathtt{56}}}}\right)}}{{\mathtt{7}}}} \Rightarrow {\mathtt{k}} = {\mathtt{0.007\: \!455\: \!107\: \!595\: \!795\: \!7}}$$

In 2016 t = 2016 - 1995 = 21, so
N = 56e^0.007455*21

$${\mathtt{N}} = {\mathtt{56}}{\mathtt{\,\times\,}}{{\mathtt{e}}}^{\left({\mathtt{0.007\: \!455}}{\mathtt{\,\times\,}}{\mathtt{21}}\right)} \Rightarrow {\mathtt{N}} = {\mathtt{65.490\: \!604\: \!574\: \!065\: \!260\: \!8}}$$

or N ≈ 65 million

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I think GL has, very sensibly, first considered a single unit:

0.4*x + 0.7*(1-x) = 1

-0.3x +0.7 = 1

-0.3x = -0.1

x = 1/3

so, with 30L you simply require (1/3)*30 L

No doubt GL considered the lead up to the final equation too obvious to be worth spelling out!!

Here's a slightly different approach:

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Yes, they are true.  Examples, using the inbuilt calculator here:

$${\sqrt{{{\mathtt{5}}}^{{\mathtt{2}}}}} = {\mathtt{5}}$$

$${\sqrt{{\left(-{\mathtt{5}}\right)}^{{\mathtt{2}}}}} = {\mathtt{5}}$$

$${{\sqrt{{\mathtt{5}}}}}^{\,{\mathtt{2}}} = {\mathtt{5}}$$

$${{\sqrt{-{\mathtt{5}}}}}^{\,{\mathtt{2}}} = -{\mathtt{5}}$$

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If a and b are both negative then 

$$\sqrt a\times \sqrt b=\sqrt{-|a|}\times \sqrt{-|b|}=i^2\sqrt{|a|\times |b|}=-\sqrt{|a| \times |b|}$$

But

 $$\sqrt{a\times b}=\sqrt{-|a|\times -|b|}=\sqrt{|a|\times|b|}$$

i.e. the two are different, so not true when both are negative.

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Just use the calculator on the home page here.

$${{\mathtt{6.25}}}^{\left({\frac{{\mathtt{3}}}{{\mathtt{5}}}}\right)} = {\mathtt{3.002\: \!811\: \!084\: \!953\: \!578\: \!1}}$$

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A.  If you mean x + (1/x) = -1 then:

Multiply all terms by x:

x² + 1 = -x

Add x to both sides:

x² + x + 1 = 0

Solve:

$${{\mathtt{x}}}^{{\mathtt{2}}}{\mathtt{\,\small\textbf+\,}}{\mathtt{x}}{\mathtt{\,\small\textbf+\,}}{\mathtt{1}} = {\mathtt{0}} \Rightarrow \left\{ \begin{array}{l}{\mathtt{x}} = {\mathtt{\,-\,}}{\frac{\left({\sqrt{{\mathtt{3}}}}{\mathtt{\,\times\,}}{i}{\mathtt{\,\small\textbf+\,}}{\mathtt{1}}\right)}{{\mathtt{2}}}}\\
{\mathtt{x}} = {\frac{\left({\sqrt{{\mathtt{3}}}}{\mathtt{\,\times\,}}{i}{\mathtt{\,-\,}}{\mathtt{1}}\right)}{{\mathtt{2}}}}\\
\end{array} \right\} \Rightarrow \left\{ \begin{array}{l}{\mathtt{x}} = {\mathtt{\,-\,}}\left({\frac{{\mathtt{1}}}{{\mathtt{2}}}}{\mathtt{\,\small\textbf+\,}}{\mathtt{0.866\: \!025\: \!403\: \!785}}{i}\right)\\
{\mathtt{x}} = {\mathtt{\,-\,}}{\frac{{\mathtt{1}}}{{\mathtt{2}}}}{\mathtt{\,\small\textbf+\,}}{\mathtt{0.866\: \!025\: \!403\: \!785}}{i}\\
\end{array} \right\}$$

B.  If you mean (x + 1)/x = -1

Multiply both sides by x

x + 1 = -x

Add x to both sides

2x + 1 = 0

Subtract 1 from both sides

2x = -1

Divide both sides by 2

x = -1/2

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9a. Doesn't specify if 1-sided or 2-sided required (perhaps appendix F only has one set of values - don't know as we can't see it!).