Melody

You have made a little error EP

The largest one is x+1   (not x+2)

Diagram 6

now use cosine formula to finish it.

I have done it and was going to present my answer but since it is a comptetition I should leave some for you to do.

Hint:  there is a square root in the answer.

Have fun :)

diagram 5

Diagram 4

Diagram 3

diagram 2

Your question was automatically  flagged because of the language that you used. It is not helpful in life to go around calling everything that you find difficult 'stupid'. The only think that it brings into question is your own intelligence.

Anyway I have unflagged it and will answer I hope you learn more from my answer than just how to cheat with minimum effort.

A proper thank you or polite feedback will be appreciated.

question

I will do a pictorial answer. There may be an easier way but then again the problem was not supposed to be easy.

I will also do it over several posts as I have found that too many pics in one post causes problems.

You should be able to follow but if you have specific question on specific diagrams feel free to ask.

Firstly you should sketch this and realize immediately that ABCD is a kite. You should also already know that the diagonals of a kite bisect each other at right angles.

Diagram 1

Lets see

\(n-2(n+1)!+6n!=3(n+1)\\ n-2n!(n+1)+6n!=3n+3\\ -2n!(n+1)+6n!=2n+3\\ n![-2(n+1)+6]=2n+3\\ n![-2n-2+6]=2n+3\\ n![4-2n]=2n+3\\ n!=\frac{2n+3}{-2n+4}\\ \)

if n=1       LHS=1     RHS=5/2 = 2.5

IF N=2      LHS=2     RHS=7/0  UNDEFINED

IF N=3      LHS=6      RHS=9/-2  = -4.5

For all higher integer values of n the right hand side will be negative so there are no solutions to this.

(unless i made some stupid algebraic error)

Did you give it a go already?

\(4 sec^2 x + 2 tan^2 x − 6 = 0\\~\\ hint:\\ sin^2x+cos^2x=1\\ \text { if i divide by }cos^2x \text{ then I get}\\ tan^2x+1=sec^2x \)

Now I did one of these for you just a moment ato so you should be able to finish it.

Hi Critical, 

In future could you please put only one question per post.

second question -

82+88+91+83 = 344

(344+F)/6   will give the score out of 100  (percentage)  

So if he scores a B in what range will F have to lie?

\(80\le \frac{344+F}{6}\le 89\)

Anyway, since only on is an outlier it must be the highest or the lowest one!

So if you totally guess you would have 50% chance of getting it right  :)

Also this means that you only need to check one end, it is either the one that you want or else it must be the one at the other end :)