2(3x + 4) = 4x + 22 what is x
1 answer:
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Firstly, we'll fix the postions where the women will be. We have
forms to do that. So, we'll obtain a row like:
The n+1 spaces represented by the underline positions will receive the men of the row. Then,
Since there is no women sitting together, we must write that . It guarantees that there is at least one man between two consecutive women. We'll do some substitutions:
The equation (i) can be rewritten as:
We obtained a linear problem of non-negative integer solutions in (ii). The number of solutions to this type of problem are known:
[I can write the proof if you want]
Now, we just have to calculate the number of forms to permute the men that are dispposed in the row:
Multiplying all results:
First, lets note that 
. This leads us with the following problem:
Lets add sin on both sides, and we get:
Now if we divide with sin on both sides we get:
Now we can remember how cot is defined, it is (cos/sin). So we have:
Now take the inverse of cot and we get:
In general we have
, the reason we have to add pi times n, is because it is a function that has multiple answers, see the picture:
Lets add sin on both sides, and we get:
Now if we divide with sin on both sides we get:
Now we can remember how cot is defined, it is (cos/sin). So we have:
Now take the inverse of cot and we get:
In general we have