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Happy to have been of help. As for the many answers, we'll just have to see.
Thank you for the explanation, that really helps. Actually there is no other question except for the 'derive e' line!
Actually I didn't (post 28) . But that doesn't mean you are wrong (what did the spreadsheet give you?).
Well there is a good reason why this happened.
It is incredible, thank you so much for this. I will definitely try create my own in the future for similar problems to check my work!
Oh yes. I had an expression for alpha e too and made the same mistake!
I didn't have the WHOLE expression over alpha (which =2), I left that out by mistake, sorry! So it does in fact equal 3! Yay!
I get it to equal 6 funnily enough, not 3 xD!
Oh no, for 'a' i am getting the trick correct in excel.
That excel trick is incredible. It actually holds for all 4 equations and gave 51 for my answer as you said, that is great that we can check with real numbers. I willt try it with new expression! Thank you!
This is absolutely incredible. Thank you so much. I should now be able to tackle the third part of the question. This has all been really helpful.
Oh yes. You might find the following helpful in checking your algebra.
then it works with numbers, so I think it is ok. I got a different expression because I kept in alpha g and gstar but not gamma and b.
Yes sorry, I meant phi, I need to revise the Greek alphabet
Really appreciate the help. Your method for the a expression is brilliantly intuitive and I have written that out in full. Thank you.