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#1 2005-12-30 12:10:31
- snyy
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Equation Problem.. t=??
a = x0 * (1-t)³ + x1 * 3 * t * (1-t)² + x2 * 3 * t² * (1-t) +x3 * t³
if x0 = 138, x1=116, x3= 171, x4=198 while t=0.01
then a =137.934235
but for now, i want to find t, i have the all the value of x0,x1,x2,x3 and a. so how to reverse the formula so that i can find t??
thanks..
#2 2005-12-30 12:26:50
- krassi_holmz
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Re: Equation Problem.. t=??
It would be something very VERY ugly.
And probably it's complexity will make it useless.
IPBLE: Increasing Performance By Lowering Expectations.
#3 2005-12-30 12:43:00
- John E. Franklin
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Re: Equation Problem.. t=??
Code:
a = x0 * (1-t)³ + x1 * 3 * t * (1-t)² + x2 * 3 * t² * (1-t) +x3 * t³
1-2t+t^2(1-t) 1-2t+t^2 3x2(t^2-t^3) x3t^3
3x1 (t-2t^2+t^3) | |
1-2t+t^2 | | |
-t +2t^2 -t^3 | | |
-------------- v v v
x0(1-3t+3t^2-t^3)
(-x0+3x1-3x2+x3)t^3 + (3x0-6x1+3x2)t^2 + (-3x0+3x1)t + x0
I don't know what to do next to this cubic equation.Imagine for a moment that even an earthworm may possess a love of self and a love of others.
#4 2005-12-30 12:59:16
- John E. Franklin
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Re: Equation Problem.. t=??
Code:
I found a method to possibly get close to an answer. a = (-x0+3x1-3x2+x3)t^3 + (3x0-6x1+3x2)t^2 + (-3x0+3x1)t + x0 Get t on left side, and put a on right, leave t^3 and t^2 on right side. -(-3x0+3x1)t = (-x0+3x1-3x2+x3)t^3 + (3x0-6x1+3x2)t^2 + x0 - a Divide by -(-3x0+3x1) t = (-1/(-3x0+3x1)) ((-x0+3x1-3x2+x3)t^3 + (3x0-6x1+3x2)t^2 + x0 - a ) Make a guess at t and plug it into the t^3 and t^2 and solve right side of equation. Take answer and put it back in again. Repeat until you appear to be getting closer and closer to last result. I don't know if this will work, but I just read this on a web page about solving a cubic.
Imagine for a moment that even an earthworm may possess a love of self and a love of others.
#5 2005-12-30 13:09:36
- krassi_holmz
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Re: Equation Problem.. t=??
ax^3+bx^2+cx+d=0
Here's the real solution:
Last edited by krassi_holmz (2005-12-30 13:10:46)
IPBLE: Increasing Performance By Lowering Expectations.
#6 2005-12-30 13:11:26
- krassi_holmz
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Re: Equation Problem.. t=??
I told you it will be ugly.
IPBLE: Increasing Performance By Lowering Expectations.
#8 2005-12-30 19:19:28
- krassi_holmz
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Re: Equation Problem.. t=??
OK,Here is the answer direct from the original equation:
Last edited by krassi_holmz (2005-12-30 19:20:30)
IPBLE: Increasing Performance By Lowering Expectations.
#9 2005-12-30 21:40:06
- MathsIsFun
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Re: Equation Problem.. t=??
Ye Gods!
You did better than this guy:
"The physicists defer only to mathematicians, and the mathematicians defer only to God ..." - Leon M. Lederman
#10 2005-12-31 02:54:50
- John E. Franklin
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Re: Equation Problem.. t=??
snyy wrote:
sorry, don't really understand how you do this.
can show me how you get this formula (-x0+3x1-3x2+x3)t^3 + (3x0-6x1+3x2)t^2 + (-3x0+3x1)t + x0 ??
from x0(1-3t+3t^2-t^3) + 3x1 (t-2t^2+t^3) + 3x2(t^2-t^3) + x3t^3
Method used is similar to this example:
(A+B)C + (A+B)D
See how I am skipping a step and not writing it down.
This is the equivalent.
(C+D)A + (C+D)B
The step I didn't ever write down is because you just organize by
jumping around and choosing the A's first, and the B's second.
But it would be:
AC + BC + AD + BD
Then get the A's on the left, and B's on the right.
Imagine for a moment that even an earthworm may possess a love of self and a love of others.