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

In summary, Homework Equations show that r^2 is the subject of an equation. You try to rearrange the equation to make r^2 the subject, but you get confused and make a mistake.

## 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

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.

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

(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.

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.

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!)

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 ) ??

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)​

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

I am rubbish at rearranging
But see how much better you do when you take smaller steps!

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! )

Thanks guys :)

## 1. How do I rearrange a formula to make r^2 the subject?

To rearrange a formula to make r^2 the subject, you need to isolate r^2 on one side of the equation. This can be done by using inverse operations, such as addition, subtraction, multiplication, or division, to cancel out any terms that are not r^2. Once r^2 is on its own on one side of the equation, the formula is rearranged to have r^2 as the subject.

## 2. What is the purpose of rearranging a formula to make r^2 the subject?

Rearranging a formula to make r^2 the subject allows you to solve for the value of r more easily. In many scientific calculations, r^2 is a crucial parameter and having it as the subject of the formula makes it easier to manipulate and use in further calculations.

## 3. Can I rearrange any formula to make r^2 the subject?

Yes, most formulas can be rearranged to make r^2 the subject. However, some formulas may be too complex to manipulate and may require advanced mathematical techniques to rearrange. It is important to have a good understanding of algebra and mathematical operations to successfully rearrange a formula.

## 4. Are there any specific steps to follow when rearranging a formula to make r^2 the subject?

Yes, there are some general steps that can be followed when rearranging a formula to make r^2 the subject. These include identifying all terms that contain r^2, isolating r^2 on one side of the equation, and performing inverse operations to cancel out any other terms. It is also important to be careful with signs and to simplify the equation as much as possible.

## 5. Can I check if I have correctly rearranged the formula to make r^2 the subject?

Yes, you can always check your work by substituting the value of r from the original formula into your rearranged formula and ensuring that both sides of the equation are equal. You can also use a calculator to verify the values of r^2 before and after rearranging the formula.

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