23 Apr 11
Does anyone remember how to solve for x in this equation, I can't remember how to do it?
[10 (x)^9] - [9 (x)^10] = 0.75
The answer is 0.9036 but the prof does not say how to get it. Here is his only explanation:
The 75th percentile is the value of x for which
F(x) = 0.75
0.75 = 10(x)9 – 9(x)10
x » .9036
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24 Apr 11
Originally posted by mlpriorIm going with pylanka, just use some form of approximation method (I used Newtons method) to solve the polynomial. Since the powers are pretty large, to avoid a wild goose chase,I'd make sure you have a pretty accurate visual representation of the function in the range to get your first approximation.
Does anyone remember how to solve for x in this equation, I can't remember how to do it?
[10 (x)^9] - [9 (x)^10] = 0.75
The answer is 0.9036 but the prof does not say how to get it. Here is his only explanation:
The 75th percentile is the value of x for which
F(x) = 0.75
0.75 = 10(x)9 – 9(x)10
x » .9036
P(x) = -9*x^10+10*x^9-.75 = 0
Recap of Newtons method:
x(n+1) = x(n) - f(x(n))/f'(x(n))
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25 Apr 11
Originally posted by mlpriorBut the real question is what are you going to do when something like this comes along in the real world? I maybe being a bit melodramatic, but he/she gave you the problem to address a serious disconnect between theory and practicality/reality, such that you may be better prepared to bridge the gap when you come upon it in the future.
OK thanks.
I'm not going to worry about it then, it was just in one of the homework questions. I don't think the professor would actually put something like that on a test anyway.
Thanks everyone!
Just a thought.
25 Apr 11
Originally posted by joe shmoI think the only human way to find the answer would be to plot it.
But the real question is what are you going to do when something like this comes along in the real world? I maybe being a bit melodramatic, but he/she gave you the problem to address a serious disconnect between theory and practicality/reality, such that you may be better prepared to bridge the gap when you come upon it in the future.
Just a thought.
Since complex polynomial equations are not the point of the class, I don't feel like I need to spend a whole lot of time on it, especially since there is a lot of other material I could be studying and I have already spent a lot of time on this one problem.
I do see your point though. If I came across something like this in real life, I would probably contact my old statistics professor. 🙂
25 Apr 11
Originally posted by EladarI have a TI-86 but don't have the manual, maybe I can find the directions online.
Get your graphing calculator out.
Type the left side into y1. Type the right side into y2, then use the calculator's interset function to solve. TI command should be 2nd-trace-5-enter-enter-enter.
As long as the solution is on the screen, it will find it.
25 Apr 11
4 edits
Originally posted by mlpriorWhilst you're playing around with graphing calculators and such; assuming you don't have money to burn grab yourself a copy of maxima 5.24 (poor man's mathematica but it's actually pretty good, and is actually the distant ancestor of the likes of maple and mathematica)
I have a TI-86 but don't have the manual, maybe I can find the directions online.
http://sourceforge.net/projects/maxima/files/
Also grab yourself a copy of Scilab (free clone of MATLAB - not quite as efficient but again, it's pretty good)
http://www.scilab.org/products/scilab/download
Then use these instead to do your plotting and root finding (and whatever else) - save the batteries on your TI :]
As for your OP, another pencil & paper approach might to perturb a trial solution x=1 with a small value a; i.e. evaluate 10(1+a)^9 -9(1+a)^10 = 3/4 and when you expand it you'll have a different degree 10 polynomial where you know already that the higher order terms are neglible (since |a| is small) and so you can throw some of these away - say up the the 4th power of a perhaps, and play around with that instead.
25 Apr 11
Originally posted by AgergFor equation solving or substitutes for graphic calculators, Wolfram Alpha is a pretty good site (see KN's post). No need to install software.
Whilst you're playing around with graphing calculators and such; assuming you don't have money to burn grab yourself a copy of maxima 5.24 (poor man's mathematica but it's actually pretty good, and is actually the distant ancestor of the likes of maple and mathematica)
http://sourceforge.net/projects/maxima/files/
Also grab yourself a copy of Scilab (free ...[text shortened]... to do your plotting and root finding (and whatever else) - save the batteries on your TI :]