Rearrange equation[resolved]

[Pino]

Ok my maths skills are ok, but i stuggle with re-arranging formulas.

= 4 πr – (10000r / r(cubed))


I'm trying to re-arrange that to get a value of r, π = pi().

If anyone could show me the way to do it step by step i would appriciate it.

Thanks

[RobDog888]

Well, lets see how much I can correctly remember my algebra.

Lets put it into complete formula syntax.

0 = 4(pi)r - (10000r / r^3)

Now since the equation is balanced properly we need to shift the variables to one side leaving one on one side for
solving its value.

So far you probably already know this.

[RobDog888]

Next we need to simplify so we can solve for r.

0 = 4(pi)r - (10000r / r^3)
becomes

0 = 4(3.1415)r - (10000 / r^3)
becomes

0 = 12.566r - (10000 / r^3)
becomes

0 = 12.566r - (10000)
...................-------
.....................r^3

[RobDog888]

Next if I still am remembering correctly (someone correct me if I am wrong) we can do like so...

Move half to other side changing its sign
(10000)...12.566r
------- = -------
..r^3..........1

Then cancel out one r on each side
(10000)...12.566
------- = ------
..r^2..........1

[RobDog888]

Then we can cross-multiply to remove the division.

10000 = 12.566r^2

Then divide by 12.566 on each side to isolate the r so we can colve it.
10000....r^2
------ = ----
12.566.....1

Which then gives us

795.7981~ = r^2

Then we can take the square root of each side.
28.209~ = r

Then switch to make it the proper order.
r = 28.209~

w00t w00t, I remembered

[opus]

RobDog888, you missed one "r" in the second line!
And the cancleing out of r in your third post was not correct, you have to do the same on each side of the =!
0 = 4(pi)r - (10000r / r^3)
delete one r in the second part
0 = 4(pi)r - (10000 / r^2)
add the second part to shift it to the other side
(10000 / r^2)= 4(pi)r
multiply by r^2
1000=4(pi)r^3
divide by 4(pi)
1000/(4(pi))=r^3
which is
79.5774715....=r^3
and now take the cubic root, and you have it:
r=4,301270069.........

[sql_lall]

remember....dividing by r can be dangerous if r is zero

[RobDog888]

Doh!!!

opus, how could you cancel out r and r^3 from just one element of the equation and not reduce the other element?

Told you "lets see how much I can correctly remember my algebra"

[opus]

The part of the equation was (1000*r)/r^3, if you divide just this part by r, the result will not change, so it comes to 1000/r^2. Sorry but I don't have the correct wording for that in english. It's the same as reducing (2*3)/(3*3) to 2/3.


and for sql_lall: yes never ever forget the dammed division by Zero, but I don't put it into code, I just gave the conversion of the formula.

[RobDog888]

Thanks for the refresher opus. Its been more years then I care to say but I was actually surprised at the
amount I remembered.

[Dreamlax]

You lot need to lay off the Pepsi and espressos and get a bit of sleep I think.

0 = 4(pi)r - (10000r / r³)

Remove common factor:
0 = 4(pi)r - (10000 / r²)

Rearrage:
4(pi)r = 10000 / r²

Multiply both sides by r²:
4(pi)r³ = 10000

Divide both sides by 4(pi):
r³ = 10000 / 4(pi)

Cube root both sides:
r = (10000 / 4(pi))^1/3

r is approximately 9.2668054481521281461060217862479

Opus, what happened when 10000 became 1000? Typo?

[opus]

Oh, well .........
Maybe it's the age.