Alan

This is a question of Boolean logic, where the logic table for AND looks like:

Alternatively, think of AND as multiply, true as 1 and false as 0.

Your question, as you've stated it, is incomplete!  Does it have anything to do with the angles whose tangent is +1?

false

false

false

(On the grounds that you can't derive a true statement by "anding" a set of false ones, or a set containing a false one) ??

This simplifies as follows:

Multiply out the bracketed terms:

5*2*x + 5*8 - 5*5*x - 5*6

10x + 40 - 25x - 30

Collect like terms:

-15x +10

That's about it!

I suspect it should be in the following form (where n is a positive integer):

$$f(n)=\frac{(1+\sqrt5)^n-(1-\sqrt5)^n}{2^n \sqrt5}$$

This function generates the Fibonacci sequence, so the questioner is asking for the 54'th Fibonacci number.

$${\frac{\left({\left({\mathtt{1}}{\mathtt{\,\small\textbf+\,}}{\sqrt{{\mathtt{5}}}}\right)}^{{\mathtt{54}}}{\mathtt{\,-\,}}{\left({\mathtt{1}}{\mathtt{\,-\,}}{\sqrt{{\mathtt{5}}}}\right)}^{{\mathtt{54}}}\right)}{\left({{\mathtt{2}}}^{{\mathtt{54}}}{\mathtt{\,\times\,}}{\sqrt{{\mathtt{5}}}}\right)}} = {\mathtt{86\,267\,571\,271.999\: \!999\: \!999\: \!756\: \!697\: \!1}}$$

The calculator here has some problems with precision!  The answer should be 86267571272.

Just to illustrate that the function really does generate the numbers in the Fibonacci sequence here are the first 20 values calculated from it (n = 1, 2, 3, ..., 20) (from the third one onwards each one is the sum of the previous two).

9431 if you count from right to left, or 1349 if you count from left to right.

With the calculator on this site, if you press = after each stage you get the following:

On the other hand, if you use brackets at each stage and don't press = until the very end you get:

The small inaccuracy in the first arises because √6 is an irrational number and the calculator only stores it to a finite precision. 

Does the following formulation of the question help you rosala?

Mary is now 24 years old.

Ann is now A years old.

When Mary was A years old, Ann was B years old.

Mary is now 2*B years old.

How old is Ann now?

Do you mean the x-component?  If so, the x-component of a vector pointing south is zero, and the x-component of a vector of length 4m pointing in the direction 60° north of east is 4cos(60°)m or 2m (since cos(60°) is 1/2).

However, I might have misunderstood your question!