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Re-arrangement!

Dekota

How the hell do you re-arrange: (X - x)/x = r

to : 1/X = (1-r)/x ?

given r is suffiecintly small.

Reply 1

Dekota

This is harder than physics! Can nobody do it? :frown:

Reply 2

ebinsc

(X-x)/x = r
X-x = rx
X = rx + x
X = x(r+1)

1/X = 1/[x(r+1)]
1/X = 1/x * 1/(r+1)

Taking 1/(r+1), and multiplying both parts of the fraction by (1-r) gives

1-r/(1-r²)

Now if r is sufficiently small, 1 - r² ≈ 1

Therefore

1/X = 1/x*(1-r)

1/X = (1-r)/x

As required

Reply 3

Aitch

Dekota

This is harder than physics! Can nobody do it? :frown:

only if I can start with r=(X-x)/X :biggrin:

Reply 4

Dekota

OMG thank you! I wish i would have done that in the exam - it was the first question and I couldn't do it! :eek:

Reply 5

Aitch

Dekota

OMG thank you! I wish i would have done that in the exam - it was the first question and I couldn't do it! :eek:

Which exam was this?

Reply 6

Dekota

Aitch

Which exam was this?

Numerical methods this morning. :frown:

And I missed a pile of questions at the end. :/

Reply 7

Esquire

Ebinsc, you are in year 11 and know numerical methods? :eek:

Reply 8

ebinsc

Esquire

Ebinsc, you are in year 11 and know numerical methods? :eek:

Well I did Maths IGCSE in Year 10, and so far have done the C1-C4 + S1 exams

Anyway, I did not even know that this was a "numerical methods" question. I just did a bit of algebraic manipulation, and it seemed quite obvious that
1 - r² ≈ 0 if r is small enough.

So I can really only do very basic "numerical methods" questions - I don't know much about it :wink: