Alan

Perhaps this picture will help.  A quarter of the largest square has been divided into four.  What fraction of the whole do you think the black square is?

See graph, but can't be sure from this!  Can you supply the URL that points to the place on the internet where you found this data?

 It's the etc. that's puzzling!  Other than that you have only three values to plot:

The oxygen concentration (in mg/L) is plotted against time (in seconds) here (the third column is just the total time in seconds).

Is there any limit on the number of books that can fit on a shelf? Is n>k? n<k? n=k?  Are all these allowed?

I assume cod is chemical oxygen demand.

You don't say what you mean by "per 15 seconds" etc.  Do you mean you take a measurement of dissolved oxygen, in mg/L, every 15 seconds and then average the values you collected during the two minute period? Then, for the next four minutes measure the oxygen every 30 seconds and average these values, etc?  If so, then I think I would plot the values against the middle of each time period.  That is, plot the first value at 1 minute, the second value at 4 minutes (the middle of the period from 2 minutes to (2+4) minutes) etc.

However, this might be a completely incorrect interpretation, so you need to provide more details of exactly what you are doing.

Your interpretation of the question makes sense, Reinout.  I'm glad I didn't think of that interpretation or it would have been my head that was spinning! 

Your constraints are inconsistent.

a) constrains x1 to be greater than zero; c) allows it to be zero.

b) constrains x2 to be greater than 1; d) allows it to be 1.

Which constraints apply?

First do tan^-1(2.64) (use 2nd atan on the calculator)

$$\underset{\,\,\,\,^{\textcolor[rgb]{0.66,0.66,0.66}{360^\circ}}}{{tan}}^{\!\!\mathtt{-1}}{\left({\mathtt{2.64}}\right)} = {\mathtt{69.253\: \!919\: \!724\: \!317^{\circ}}}$$

This is 69° plus a fraction of a degree.  Multiply the fraction by 60 to get minutes.

$${\mathtt{0.253\: \!919\: \!724\: \!317}}{\mathtt{\,\times\,}}{\mathtt{60}} = {\mathtt{15.235\: \!183\: \!459\: \!02}}$$

This gives 15' plus a fraction of a minute. Multiply the fraction by 60 to get seconds.

$${\mathtt{0.235\: \!183\: \!459\: \!02}}{\mathtt{\,\times\,}}{\mathtt{60}} = {\mathtt{14.111\: \!007\: \!541\: \!2}}$$ 

This is 14'' to the nearest second.  So the result is 69°15'14''

Tan is also positive in the 3rd quadrant, so you could add this angle to 180° to get the 3rd quadrant solution.

Well, if d = $4.75 then she will have $(56 - 6*4.75) left

$${\mathtt{56}}{\mathtt{\,-\,}}{\mathtt{6}}{\mathtt{\,\times\,}}{\mathtt{4.75}} = {\frac{{\mathtt{55}}}{{\mathtt{2}}}} = {\mathtt{27.5}}$$

She has $27.5 dollars left.

First draw a graph to see the likely value.

Looks like it might be x = -2.

Try x=2

 -2+6 = 4

0.5^-2 = 1/2^-2 = 2² = 4

So x = 2.

If you prefer a numerical approach rewrite the equation as 2^x = 1/(x+6)

Take log₂ of both sides

x = log2(1/(x+6))  ...(1)

Make an initial guess for x, say x = -1.  Plug this into the right-hand side of equation (1) to get a new estimate for x. Plug this new value into the right-hand side of equation (1) to get yet another estimate, and so on.  Repeat until you converge on a unique value.  In this case the process will converge on the number -2 in 9 or 10 iterations.