Rearrange Formula to Make r^2 the Subject - Homework Help

[rad10k]

Homework Statement

I am trying to rearrange formula to make r^2 the subject.

Homework Equations

0.05=(2.88/4*1*0.018)(0.05^2-r^2)

The Attempt at a Solution

I tried to rearrage as :

0.05^2+0.05/2.88/4*0.018 then sqr root of the answer but I don't think it is correct
Please help

 

[haruspex]

0.05^2+0.05/2.88/4*0.018

There's at least one mistake, maybe more - can't be sure because you've left out parentheses.
Please post your individual individual steps, using parentheses as appropriate.

 

[rad10k]

Thank you for your reply,

(0.05^2+0.05)/(2.88/4*0.018)=r^2 this is what I had changed it to ...
thanks

 

[haruspex]

Thank you for your reply,

(0.05^2+0.05)/(2.88/4*0.018)=r^2 this is what I had changed it to ...
thanks

That looks worse!
You start with 0.05=(2.88/4*1*0.018)(0.05²-r²). Do you mean 0.05=(2.88/(4*1*0.018))(0.05²-r²) or 0.05=((2.88/4)*1*0.018)(0.05²-r²)?
Whichever, post your individual steps, just making one simple change at a time.

 

[rad10k]

Ok So I started with :

0.05=(2.88/4*1*0.018)(0.05^2-r^2)

I wish to make r^2 the subject so ,

I rearrange to make ;

r^2 = (0.05^2+0.05) / (2.88/4*1*0.018)

As the first two parentheses are multiply I change it to a divide.

I exchange r^2 with the 0.05 and used a plus instead of a minus in the formula.

 

[tiny-tim]

hi rad10k!

some people can do these things safely in their head

some people can't

you can't (you get confused about where to put the brackets)

you need to follow haruspex's advice …

just do one operation at a time​

(and not just this question, but always, including in the exam, or you'll make mistakes and lose marks!)

 

[rad10k]

This is the equation :

u={∆P/4.Lμ}(R^2-r^2)
and I wish to find r^2 but a unsure how to rearrange it I thought maybe;

r^2=u/{∆P.Lμ}(R^2 ) ??

 

[tiny-tim]

why are you not following our advice?

do it in steps, ie one operation at a time!

the first step would be

u = {∆P/4.Lμ}(R²-r²)

u/{∆P/4.Lμ} = (R²-r²)​

 

[rad10k]

u = {∆P/4.Lμ}(R2-r2)

u/{∆P/4.Lμ} = (R2-r2)

This was arrived by dividing both sides by {∆P/4.Lμ} and cancelling on the right to leave (R2-r2) on its own .

So then do I need to subtract R2 from both sides cancelling out R2 on the right leaving;

u/{∆P/4.Lμ} - R2 = -r2 ?

I apologise but I am rubbish at rearranging

 

[haruspex]

I am rubbish at rearranging

But see how much better you do when you take smaller steps!

 

[tiny-tim]

I apologise but I am rubbish at rearranging

then you need to practise!

(caution: you'll always be a bit rubbish,

so no matter how much practice you get, and how good you think you've become,

you must always do it one step at a time, so that in the pressure of the exam:

i] you're less likely to make a mistake

ii] if you do make a mistake, at least the examiner can see it's a silly error, and only take off one mark! )

 

[rad10k]

Thanks guys :)