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•  » Extremely complicated change of a volume formula

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## Topic review (newest first)

krassi_holmz
2005-12-31 22:13:35

Plot:

krassi_holmz
2005-12-31 22:10:57

I was right from the begining!
If x=Root[a == b x^2 + c x^3,1](means the first root of f(x)) then Im[x]->0!

krassi_holmz
2005-12-31 21:23:07

But we have conditions for a,b and c:

krassi_holmz
2005-12-31 21:11:28

Simplifyed:

krassi_holmz
2005-12-31 21:09:20

Real solutions:

krassi_holmz
2005-12-31 21:04:34

I'll try something...

krassi_holmz
2005-12-31 21:01:36

Simplified:

krassi_holmz
2005-12-31 20:59:51

I'm sorry. Actually this runction has three roots.
1-real and 2-complex.
Here's it's roots:

fizzled
2005-12-31 11:18:30

#### krassi_holmz wrote:

Yes, I can, but it's ugly:
a=bx^3+cx^2

Hi krassi_holmz,

THANK YOU VERY, VERY MUCH for this transformation!!

I tried the formula immediately. But unfortunately it does not work for my a, b and c; excel does not calculate square roots from negative values!
My values are:

0,0448036323381  < a < 12,132000000000
b = 0,2135347303000
c = 1,7159763313610

applied to your result of a=bx³+cx² shown above.
I am helpless again.
Do you know if there is a solution to this problem??

Thanks again in advance!

krassi_holmz
2005-12-30 10:14:21

Yes, I can, but it's ugly:
a=bx^3+cx^2

fizzled
2005-12-30 10:02:29

Can somebody change this formula: V = ar² + br³ into r = ...   ???

Thank you for your help.

John E. Franklin
2005-12-28 10:01:21

Sounds good.  I think with result from post #13 and your #14, you might be almost there, though it might be
a little messy.  And I hope this reduction idea is all right.  I think it is.

fizzled
2005-12-28 09:57:50

My ideas were:

h1 = h*s1/s
b1 = b*s1/s
c1 = c*s1/s

(theorem on intersecting lines)

John E. Franklin
2005-12-28 09:57:49

So the volume of the front slice to correct for the reduction would be:

(L-c)((s-s1)/s)h1b1

John E. Franklin
2005-12-28 09:51:09

Okay, tack on the front a slice of thickness (s - s1)/s

The reason I say this is because if s1=8 and s=9, then the new proportion is 8/9,
so then the part we need to add to the reduced length is 1/9th.
So (9-1)/8, hence (s-s1)/s