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15:20 <wally345> Hi, how to solve these equation with maxima ?  65-sqrt(400-x^2)=sqrt(2500-x^2); 
16:34 <rtoym> wally345: If solve doesn't find an answer, I'd square both sides, rearrange, square again, ask solve for the answer, and then check for extraneous ones.
16:39 <rtoym> Oh, don't need to square again.  After the first squaring, solve produces 2 roots.
16:51 <wally345> rtoym:  Hi
16:51 <wally345> thx
16:51 <wally345> i thought maxima can do this kind of stuff easily
16:52 <wally345> also having problems with integrals
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17:17 <rtoym> Solve is not that smart.
17:17 <rtoym> What kind of integral problems?
17:18 <wally345> the equation above are two intersecting circles
17:19 <wally345> i have to calc the intersection area with integrals
17:19 <wally345> between 0 and the solution of the above equation 
17:20 <wally345> maple said its 11.52....
17:20 <wally345> this is the x value of intersection point
17:21 <rtoym> maxima produced two solutions to the equation.  I think they're both right.
17:22 <wally345> so in need something like "int(f(x) dx [0..11.52]
17:22 <wally345> there are 2 intersection points
17:22 <wally345> and 1 area
17:22 <wally345> the area i have to find out
17:23 <rtoym> Are the centers of the circles on the y axis?
17:23 <wally345> zes
17:24 <rtoym> Did you draw a picture?  I think once you have a picture, you'll know what to do.
17:24 <wally345> the question is given as two radii (20 and 50) and a centerdistance of 65
17:24 <wally345> i did 
17:25 <rtoym> The area you want is kind of an eye shape.   Find the equation for the upper part of the eye and the equation for the lower part, as a function of x.
17:27 <rtoym> Once you've formulated that, ask maxima to evaluate the integral.  If maxima can't do that, then maybe I can help.
17:27 <rtoym> Is this a homework problem?
17:27 <wally345> yes, the upper is sqrt(400/x^2) and the lower is -sqrt(2500-x%2)+65
17:28 <wally345> no, its no homework problem
17:28 <wally345> i want to test some pc/math apps
17:28 <rtoym> Not homework?  Ok.
17:29 <wally345> maple do it easily but i like opensource and so i wanted to trz maxima
17:29 <rtoym> Well, the integral is then integrate(upper-lower,x,-11.52,11.52);
17:29 <wally345> actuallz have wxmaxima and the TeXmacs installed
17:29 <wally345> octave too, but i didnt tried this yet
17:30 <wally345> 11,52
17:30 <wally345> but now we need the area under the upper and lower function in the range from 0 to 11,52
17:30 <rtoym> The upper curve, sqrt(400/x^2) is not a part of a circle.
17:31 <wally345> the difference is the half of the "eye"-area
17:31 <wally345> 400-x^2
17:31 <wally345> its the radius  20^2
17:32 <rtoym> Yes, of course, but that's not what you wrote. :-)
17:32 <wally345> sorry
17:34 <rtoym> Ok, maxima says the value (1/2 area) is (800*asin(3*sqrt(399)/104)+5000*asin(3*sqrt(399)/26)-75*sqrt(399))/4 = 38.99 or so.
17:35 <wally345> may zou paste your int-command here please ?
17:37 <wally345> sorry i have little troubles with y and z , chnaging from german to us keyboard 
17:47 <wally345> .
17:49 <rtoym> Basically integrate(upper-lower,x,0,15*sqrt(399)/26);   
17:49 <wally345> when i do float(%), numer; on zour above expression i got some "%i"
17:49 <wally345> is this a result of the 3rd root
17:49 <wally345> something imaginary _
17:49 <rtoym> Where upper is sqrt(400-x^2) and lower is -sqrt(2500-x^2)+65.  The 15*sqrt(399)/26 is one of the roots solve found.
17:50 <rtoym> Oops.  Mis-copy.  It's asin(3*sqrt(399)/260).
17:52 <wally345> ic
17:52 <rtoym> Does that answer match what maple says?  I hope so.
17:53 <wally345> yes, but i can not reproduce it on mz maxima
17:53 <wally345> which version do you use ?
17:53 <rtoym> 5.11.  Shouldn't matter much, though.
17:54 <wally345> i agree
17:54 <rtoym> integrate(sqrt(400-x^2)-(-sqrt(2500-x^2)+65),x,0,15*sqrt(399)/26);
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18:01 <wally345_> rtoym:  soory , was dc
18:02 <wally345_> do you see the results from maxima i pasted
18:02 <wally345_> ?
18:03 <wally345_> (%i1) integrate(sqrt(400-x^2)-(-sqrt(2500-x^2)+65),x,0,15*sqrt(399)/26);
18:03 <wally345_>                   3 sqrt(399)              3 sqrt(399)
18:03 <wally345_>          800 asin(-----------) + 5000 asin(-----------) - 75 sqrt(399)
18:03 <wally345_>                       104                      260
18:03 <wally345_> (%o1)    -------------------------------------------------------------
18:03 <wally345_>                                        4
18:05 <wally345_> How to let maxima calc the resulkt from this ?  something near 38.9....
18:14 <rtoym> float(%o1)
18:14 <rtoym> Or %o1,numer
18:17 <wally345_> he calcs this already a few minutes, is this possible ? or it hangs 
18:19 <rtoym> No, that's not right.  I should return instantly.
18:19 <wally345_> so anything is wrong 
18:20 <rtoym> Don't know.
18:20 <rtoym> Try this:  float(asin(3*sqrt(399)/104))
18:20 <wally345_> ok
18:20 <wally345_> mom
18:21 <wally345_> the same problem
18:21 <wally345_> no output
18:22 <rtoym> Don't forget the semicolon ;
18:23 <wally345_> yes the semicolon
18:23 <rtoym> Does it work now?
18:24 <wally345_> for your last float yes
18:24 <wally345_> now trz the big one
18:24 <rtoym> float(%o1); doesn't give an answer right away?
18:24 <rtoym> It works for me.
18:26 <wally345_> it works now :)
18:27 <wally345_> i have no idea whats the problem was, i usually apply the semicolon always (i hope at least
18:28 <wally345_> thank you very much, so i see i do not make a fundamental mistake with maxima
18:30 <wally345_> can you recommend a good tutorial ?
18:41 <wally345_> another question to the above method
18:42 <wally345_> you recommended integrate(upper - lower)
18:43 <wally345_> is this the same as integrate (upper) - integrate(lower) ?
18:57 <rtoym> There are some tutorials on maxima's website.  Pretty good, I think.
18:57 <rtoym> integrate(upper-lower) is, of course, the same as integrate(upper)-integrate(lower).
18:57 <rtoym> And maxima does that itself, anyway, I think.
18:58 <wally345_> ok, i have to learn a lot 
18:58 <wally345_> thx
18:59 <wally345_> :)
18:59 <rtoym> Good luck.  If you have problems, ask here, or, even better, ask on the mailing list.
19:00 <wally345_> ok, i will remeber this invitation
19:01 <wally345_> wish you a nice evening
19:01 <wally345_> here is alreadz 7pm
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