# Transform formula into another form

1. Feb 4, 2017

### fonseh

1. The problem statement, all variables and given/known data
I need help when changing the formula of the yellow circled part to red-circled part ...

2. Relevant equations

3. The attempt at a solution
I tried , but i didnt get what the author got .... Here's my working ... Which part of my working is wrong ?

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2. Feb 4, 2017

### Staff: Mentor

Moved to Calculus and Beyond section.
@fonseh, many helpers won't respond if the problem statement and work are shown only in attached images.

3. Feb 4, 2017

### haruspex

I cannot make sense of the text either. It looks quite wrong. Certainly a du has been omitted from the right hand side, and I cannot see how that 1-u term can appear. Perhaps the N exponent is in the wrong place. Maybe some approximation has been made, but that should be stated.
Your own working has y on the right instead of dy (=y0du).

4. Feb 4, 2017

### haruspex

The closest I can get is $\frac{y_0du}{S_0}[\left(1-\frac {1}{1-u^N}\right)$ $(1-(\frac{y_c}{y_0})^Mu^{-M})^{-1}]$.
If we use the binomial approximation for the last (...)-1 term, we get:
$\frac{y_0du}{S_0}[\left(1-\frac {1}{1-u^N}\right)$ $(1+(\frac{y_c}{y_0})^Mu^{-M})]$.
Multiplying the brackets out produces something quite close to the text. The remaining differences look like typos.

5. Feb 6, 2017

### fonseh

Can you show your working pls ? I tried it many times , but didnt get the red part , i gt (1-(1/u)^N ) instead

6. Feb 6, 2017

### fonseh

This is actually hydraulic formula , should i move it to another thread ? Or this is just purely mathematics derivation ? I'm not sure

7. Feb 7, 2017

### Staff: Mentor

It's fine here. The gist of the question is mathematical in nature.