PKMLmXńB–Hmimetypetext/x-wxmathmlPKMLmXQdBV55 format.txt This file contains a wxMaxima session in the .wxmx format. .wxmx files are .xml-based files contained in a .zip container like .odt or .docx files. After changing their name to end in .zip the .xml and eventual bitmap files inside them can be extracted using any .zip file viewer. The reason why part of a .wxmx file still might still seem to make sense in a ordinary text viewer is that the text portion of .wxmx by default isn't compressed: The text is typically small and compressing it would mean that changing a single character would (with a high probability) change big parts of the whole contents of the compressed .zip archive. Even if version control tools like git and svn that remember all changes that were ever made to a file can handle binary files compression would make the changed part of the file bigger and therefore seriously reduce the efficiency of version control wxMaxima can be downloaded from https://github.com/wxMaxima-developers/wxmaxima. It also is part of the windows installer for maxima (https://wxmaxima-developers.github.io/wxmaxima/). If a .wxmx file is broken but the content.xml portion of the file can still be viewed using an text editor just save the xml's text as "content.xml" and try to open it using a recent version of wxMaxima. If it is valid XML (the XML header is intact, all opened tags are closed again, the text is saved with the text encoding "UTF8 without BOM" and the few special characters XML requires this for are properly escaped) chances are high that wxMaxima will be able to recover all code and text from the XML file. PKMLmXé "ö‹ö‹ content.xml Kedvenc Matematikai KĂ­sĂ©rleteim Alapok Halmazok Ă©s fĂŒggvĂ©nyek SzĂĄmok HatĂĄrĂ©rtĂ©k DifferenciĂĄlszĂĄmĂ­tĂĄs IntegrĂĄlszĂĄmĂ­tĂĄs LineĂĄris algrebra TöbbvĂĄltozĂłs fĂŒggvĂ©nyek Metrikus terek DiffereciĂĄlszĂĄmĂ­tĂĄs LineĂĄris operĂĄtorok normĂĄja Feladat Feladat Feladat Feladat kill(all); (%o0) done F:cos(t)^2+(3*sin(t)+2*cos(t))^2; (%o27)

3*sin

t

+2*cos

t

2
+cos

t

2
ratsimp(%); (%o28) 9*sin

t

2
+12*cos

t

*sin

t

+5*cos

t

2
Ft:diff(F,t); (%o29) 2*

3*cos

t

−2*sin

t

*

3*sin

t

+2*cos

t

−2*cos

t

*sin

t

solve(Ft); (%o43) [sin

t

=−

10−1

*cos

t

3
,sin

t

=

10+1

*cos

t

3
]
%/cos(t); (%o44) [sin

t

cos

t

=−10−13,sin

t

cos

t

=10+13]
trigsimp(%); (%o45) [sin

t

cos

t

=−10−13,sin

t

cos

t

=10+13]
trigreduce(%); (%o46) [tan

t

=−10−13,tan

t

=10+13]
ee:float(%), numer; (%o47) [tan

t

=−0.7207592200561265,tan

t

=1.387425886722793]
solve(ee[1]); rat: replaced 0.7207592200561265 by 26995669/37454490 = 0.7207592200561268solve: using arc−trig functions to get a solution.Some solutions will be lost.(%o48) [t=−atan

2699566937454490

]
float(%), numer; (%o49) [t=−0.6245228861991274] subst(%,F); (%o50) 0.6754446796632413 solve(ee[2]); rat: replaced −1.387425886722793 by −14510839/10458821 = −1.387425886722796solve: using arc−trig functions to get a solution.Some solutions will be lost.(%o53) [t=atan

1451083910458821

]
float(%), numer; (%o54) [t=0.9462734405957703] subst(%,F); (%o55) 13.32455532033675 sqrt(%); (%o56) 3.650281539872884 Feladat Feladat Feladat DefinĂ­ciĂł PĂ©lda PĂ©lda Sima görbĂ©k ÖsszegszabĂĄly LĂĄncszabĂĄly KoordinĂĄtafĂŒggvĂ©nyek differenciĂĄlhatĂłsĂĄga ParciĂĄlis derivĂĄltak KözĂ©pĂ©rtĂ©k-egyenlƑtlensĂ©g KövetkezmĂ©ny KövetkezmĂ©ny TĂ©tel MegjegyzĂ©s PĂ©ldĂĄk Feladat Feladat Feladat Feladat Feladat Feladat Feladat Feladat Feladat Feladat BevezetƑ pĂ©lda FĂŒggvĂ©nysorozat tagonkĂ©nti differenciĂĄlĂĄsa Feladat MagasabbrendƱ derivĂĄltak MagasabbrendƱ derivĂĄltak Ă©s parciĂĄlis derivĂĄltak kapcsolata A mĂĄsodik derivĂĄlt, mint bilineĂĄris lekĂ©pezĂ©s A magasabbrendƱ derivĂĄltak, mint multilineĂĄris lekĂ©pezĂ©sek Young tĂ©tele PĂ©lda Feladat Feladat C^m-lekĂ©pezĂ©sek Feladat Taylor-formula maradĂ©ktag nĂ©lkĂŒl Taylor-formula valĂłs Ă©rtĂ©kƱ fĂŒggvĂ©nyekre MegjegyzĂ©s Implicit fĂŒggvĂ©ny tĂ©tel Feladat kill(all); (%o0) done e1:x1*exp(x3+x4)-2*x3*x4-1; (%o1) x1*%ex4+x3−2*x3*x4−1 sublis([x1=1,x2=2,x3=0,x4=0],e1); (%o2) 0 e2:x2*exp(x3-x4)+x3/(1+x4)-2*x1; (%o3) x2*%ex3−x4+x3x4+1−2*x1 sublis([x1=1,x2=2,x3=0,x4=0],e2); (%o5) 0 e13:diff(e1,x3); e14:diff(e1,x4); e23:diff(e2,x3); e24:diff(e2,x4); (%o6) x1*%ex4+x3−2*x4(%o7) x1*%ex4+x3−2*x3(%o8) x2*%ex3−x4+1x4+1(%o9) −x2*%ex3−x4−x3

x4+1

2
sublis([x1=2,x2=1,x3=0,x4=0],[[e13,e14],[e23,e24]]); (%o10) [[2,2],[2,−1]] Feladat kill(all); (%o0) done e:x^2-x*y+2*y^2+x-y-1=0; (%o1) 2*y2−x*y−y+x2+x−1=0 sublis([x=0,y=1],e); (%o3) 0=0 ey:diff(lhs(e),y); (%o7) 4*y−x−1 sublis([x=0,y=1],ey); (%o8) 3 depends(y,x); (%o9) [y

x

]
ep:diff(e,x); (%o16) 4*y*

dd*x*y

−x*

dd*x*y

−dd*x*y−y+2*x+1=0
epp:diff(ep,x); (%o17) 4*y*

d2d*x2*y

−x*

d2d*x2*y

−d2d*x2*y+4*

dd*x*y

2
−2*

dd*x*y

+2=0
Feladat kill(all); (%o0) done e:x^2+2*y^2+3*z^2+x*y-z-9=0; (%o1) 3*z2−z+2*y2+x*y+x2−9=0 sublis([x=1,y=-2,z=1],e); (%o2) 0=0 depends(z,[x,y]); (%o3) [z

x,y

]
ex:diff(e,x); (%o10) 6*z*

dd*x*z

−dd*x*z+y+2*x=0
exx:diff(%,x); (%o11) 6*z*

d2d*x2*z

−d2d*x2*z+6*

dd*x*z

2
+2=0
ey:diff(e,y); (%o12) 6*z*

dd*y*z

−dd*y*z+4*y+x=0
eyx:diff(%,x); (%o13) 6*

dd*x*z

*

dd*y*z

+6*z*

d2d*x*d*y*z

−d2d*x*d*y*z+1=0
eyy:diff(ey,y); (%o14) 6*z*

d2d*y2*z

−d2d*y2*z+6*

dd*y*z

2
+4=0
Feladat etc. Feladat Feladat Inverz fĂŒggvĂ©ny tĂ©tel MegjegyzĂ©s Feladat Feladat SzĂ©lsĆ‘Ă©rtĂ©k szĂŒksĂ©ges feltĂ©tele LokĂĄlis szĂ©lsĆ‘Ă©rtĂ©k mĂĄsodrendƱ elĂ©gsĂ©ges feltĂ©tele LokĂĄlis szĂ©lsĆ‘Ă©rtĂ©k magasabbrendƱ elĂ©gsĂ©ges feltĂ©tele Feladat kill(all); (%o0) done e:2*x^3-3*x^2+2*y^3+3*y^2; (%o1) 2*y3+3*y2+2*x3−3*x2 ex:diff(e,x); (%o2) 6*x2−6*x ey:diff(e,y); (%o3) 6*y2+6*y s:solve([ex,ey],[x,y]); (%o5) [[x=0,y=0],[x=1,y=0],[x=0,y=−1],[x=1,y=−1]] exx:diff(ex,x); (%o6) 12*x−6 exy:diff(ex,y); (%o7) 0 eyy:diff(ey,y); (%o8) 12*y+6 sublis(s[1],[[exx,exy],[exy,eyy]]); (%o9) [[−6,0],[0,6]] sublis(s[2],[[exx,exy],[exy,eyy]]); (%o13) [[6,0],[0,6]] sublis(s[3],[[exx,exy],[exy,eyy]]); (%o14) [[−6,0],[0,−6]] sublis(s[4],[[exx,exy],[exy,eyy]]); (%o15) [[6,0],[0,−6]] Feladat etc. Feladat Feladat Lagrange-elv: feltĂ©teles szĂ©lsĆ‘Ă©rtĂ©k keresĂ©se FeltĂ©teles szĂ©lsĆ‘Ă©rtĂ©k mĂĄsodrendƱ elĂ©gsĂ©ges feltĂ©tele SzĂ©lsĆ‘Ă©rtĂ©k-szĂĄmĂ­tĂĄs PĂ©lda PĂ©lda Feladat kill(all); (%o0) done F:(x^2-6*x)*(y^2-4*y); (%o1)

x2−6*x

*

y2−4*y

Fx:diff(F,x); (%o2)

2*x−6

*

y2−4*y

Fy:diff(F,y); (%o3)

x2−6*x

*

2*y−4

solve([Fx,Fy],[x,y]); (%o4) [[x=0,y=0],[x=0,y=4],[x=6,y=0],[x=6,y=4],[x=3,y=2]] subst(3,x,F); (%o10) −9*

y2−4*y

subst(2,y,%); (%o11) 36 subst(2*t,y,F); (%o5)

4*t2−8*t

*

x2−6*x

f:subst(t,x,%); (%o6)

t2−6*t

*

4*t2−8*t

subst(0,t,f); (%o12) 0 subst(4,t,f); (%o13) −256 plot2d(f,[t,0,4]); (%o7) [/tmp/maxout100361.gnuplot_pipes] ft:diff(f,t); (%o8)

2*t−6

*

4*t2−8*t

+

8*t−8

*

t2−6*t

solve(ft,t); (%o14) [t=3−3,t=3+3,t=0] etc. Feladat (1) kill(all); (%o0) done f:5*x-2*y-1; (%o9) −2*y+5*x−1 F:f+λ*(25*x^2+4*y^2-50); (%o10)

4*y2+25*x2−50

*λ−2*y+5*x−1
Fx:diff(F,x); (%o2) 50*x*λ+5 Fy:diff(F,y); (%o3) 8*y*λ−2 solve(Fx,λ); (%o4) [λ=−110*x] e1:subst(%,Fy); (%o5) −4*y5*x−2 e2:diff(F,λ); (%o6) 4*y2+25*x2−50 sol:algsys([e1,e2],[x,y]); (%o7) [[x=−1,y=52],[x=1,y=−52]] subst(sol[1],f); (%o11) −11 subst(sol[2],f); (%o12) 9 (2) etc. Feladat kill(all); (%o0) done F:x*y+λ*(x^2+y^2-1); (%o1)

y2+x2−1

*λ+x*y
Fx:diff(F,x); (%o2) 2*x*λ+y Fy:diff(F,y); (%o4) 2*y*λ+x solve(Fx,λ); (%o12) [λ=−y2*x] e1:subst(%,Fy); (%o13) x−y2x e2:diff(F,λ); (%o14) y2+x2−1 sol:algsys([e1,e2],[x,y]); (%o20) [[x=−12,y=12],[x=12,y=−12],[x=−12,y=−12],[x=12,y=12]] 1/2; (%o22) 12 Feladat etc. Feladat etc. Feladat F:x*y*z+λ*(x+y+z-5)+ÎŒ*(x*y+y*z+z*x-8); (%o28)

y*z+x*z+x*y−8

*Ό+

z+y+x−5

*λ+x*y*z
Fx:diff(F,x); (%o29)

z+y

*Ό+λ+y*z
Fy:diff(F,y); (%o30)

z+x

*Ό+λ+x*z
Fz:diff(F,z); (%o31)

y+x

*Ό+λ+x*y
Fl:diff(F,λ); (%o32) z+y+x−5 Fm:diff(F,ÎŒ); (%o33) y*z+x*z+x*y−8 e1:solve(Fx,λ); (%o35) [λ=

−z−y

*Ό−y*z]
e2:subst(e1,Fy); (%o36)

z+x

*Ό+

−z−y

*Ό−y*z+x*z
e3:subst(e1,Fz); (%o37)

−z−y

*Ό+

y+x

*Ό−y*z+x*y
e4:solve(e2,ÎŒ); (%o38) [ÎŒ=−z] e5:subst(e4,e3); (%o41) −

−z−y

*z−

y+x

*z−y*z+x*y
ratsimp(%); (%o42) z2+

−y−x

*z+x*y
algsys([e5,Fl,Fm],[x,y,z]); (%o43) [[x=2,y=1,z=2],[x=43,y=73,z=43],[x=1,y=2,z=2],[x=73,y=43,z=43]] Feladat etc. Feladat etc. Feladat etc. Feladat Parametrizáljuk a határt! Feladat Parametrizáljuk a határt! Feladat f:x+y^2/(4*x)+z^2/y+2/z; (%o44) z2y+2z+y24*x+x fx:diff(f,x); (%o45) 1−y24*x2 fy:diff(f,y); (%o46) y2*x−z2y2 fz:diff(f,z); (%o47) 2*zy−2z2 algsys([fx,fy,fz],[x,y,z]); (%o48) [[x=−

−1

34
*%i
2
,y=−

−1

14
,z=−

−1

14
*%i],[x=−%i*%i2,y=−

−1

14
,z=−%i],[x=0,y=0,z=0],[x=12,y=1,z=1],[x=−12,y=−1,z=−1],[x=−%i2,y=−%i,z=%i],[x=%i2,y=%i,z=−%i]]
Feladat etc. Feladat etc. Feladat Parametrizáljuk a határt! Feladat etc. Feladat etc. Feladat etc. Feladat Ha a vektor hossza r, akkor a bal oldal r^4, a jobb legfeljebb a^2*r^2, így a megoldásokra r korlátos. etc. Feladat (1) f:x/y; (%o49) xy fx:diff(f,x); (%o50) 1y fxx:diff(fx,x); (%o51) 0 fy:diff(f,y); (%o52) −xy2 fyy:diff(fy,y); (%o53) 2*xy3 fyyy:diff(fyy,y); (%o54) −6*xy4 t:1+(x-1)-(x-1)*(y-x)/2+(x-1)*(y-1)^2/3-(y-1)+(y-1)^2-(y-1)^3; (%o55)

1−x

*

y−x

2
−y−

y−1

3
+

x−1

*

y−1

2
3
+

y−1

2
+x+1
(2) etc. Feladat (1) f:x^3+x*y+y^2-3*x-3*y; (%o56) y2+x*y−3*y+x3−3*x fx:diff(f,x); (%o57) y+3*x2−3 fy:diff(f,y); (%o58) 2*y+x−3 s:algsys([fx,fy],[x,y]); (%o60) [[x=−73−112,y=73+3524],[x=73+112,y=−73−3524]] subst(s[1],f); (%o61)

73+35

2
576
−

73−1

*

73+35

288
−73+358+73−14−

73−1

3
1728
float(%), numer; (%o62) −1.654268202073866 subst(s[2],f); (%o63)

73+1

3
1728
−

73−35

*

73+1

288
−73+14+73−358+

73−35

2
576
float(%), numer; (%o64) −3.098046612740949 (2) etc. Lagrange-szorzĂłk Lagrange-elv: feltĂ©teles szĂ©lsĆ‘Ă©rtĂ©k keresĂ©se, egyenlƑtlensĂ©geket is tartalmazĂł feltĂ©telrendszer KövetkezmĂ©ny ElvĂĄlasztĂĄsi tĂ©tel Farkas-lemma KövetkezmĂ©ny PrimĂĄl-duĂĄl feladatpĂĄr Feladat Nyeregpont tĂ©tel A lineĂĄris programozĂĄs fƑtĂ©tele ApproximĂĄciĂł A Newton-mĂłdszer KvĂĄzi Newton-mĂłdszer Feladat kill(all); (%o0) done Pontos: algsys([x^2+y^2,x^2-y^2],[x,y]); (%o1) [[x=0,y=0]] LĂĄsd a következƑ feladatot. Feladat kill(all); (%o0) done Pontos: algsys([x+y-3,x^2+y^2-9],[x,y]); (%o1) [[x=3,y=0],[x=0,y=3]] Newton: f(x):=matrix([x[1]+x[2]-3],[x[1]^2+x[2]^2-9]); (%o2) f

x

:=x1+x2−3x12+x22−9
m(x):=matrix([1,1],[2*x[1],2*x[2]]); (%o19) m

x

:=112*x12*x2
x:[2,4]; (%o4) [2,4] mm:m(x); (%o5) 1148 mmi:invert_by_lu(mm); (%o6) 2−14−114 d:-mmi.f(x); (%o7) −13414 x:x+args(transpose(d))[1]; (%o8) [−54,174] mm:m(x); (%o9) 11−52172 mmi:invert_by_lu(mm); (%o10) 1722−111522111 d:-mmi.f(x); (%o11) 8588−8588 x:x+args(transpose(d))[1]; (%o12) [−2588,28988] mm:m(x); (%o13) 11−254428944 mmi:invert_by_lu(mm); (%o14) 289314−221572531422157 d:-mmi.f(x); (%o15) 722527632−722527632 x:x+args(transpose(d))[1]; (%o16) [−62527632,8352127632] float(%), numer; (%o17) [−0.02261870295309786,3.022618702953098] MĂłdosĂ­tott Newton: x:[2,4]; (%o22) [2,4] m0:m(x); (%o25) 1148 m0i:invert_by_lu(m0); (%o27) 2−14−114 d:-m0i.f(x); (%o28) −13414 x:x+args(transpose(d))[1]; (%o29) [−54,174] d:-m0i.f(x); (%o30) 8532−8532 x:x+args(transpose(d))[1]; (%o31) [4532,5132] d:-m0i.f(x); (%o33) −2295204822952048 x:x+args(transpose(d))[1]; (%o34) [5852048,55592048] d:-m0i.f(x); (%o35) −3252015838860832520158388608 x:x+args(transpose(d))[1]; (%o36) [−8558558388608,260216798388608] float(%), numer; (%o37) [−0.1020258665084838,3.102025866508484] FĂ©kezett Newton: σ:0.01; (%o41) 0.01 1-σ; (%o42) 0.99 ρ:0.5; (%o43) 0.5 x:[2,4]; (%o39) [2,4] mm:m(x); (%o40) 1148 mmi:invert_by_lu(mm); (%o45) 2−14−114 ff:f(x); (%o46) 311 ffnn:ff[1][1]^2+ff[2][1]^2; (%o47) 130 α:1.0; (%o48) 1.0 d:args(transpose(-mmi.ff))[1]; (%o51) [−134,14] xx:x+α*d; (%o52) [−1.25,4.25] fff:f(xx); (%o53) 0.010.625 fffnn:fff[1][1]^2+fff[2][1]; (%o54) 10.625 (fffnn-ffnn)/α/ffnn; (%o55) −0.9182692307692307 x:x+α*d; (%o56) [−1.25,4.25] etc. Broyden: x:[2,4]; (%o57) [2,4] A:m(x); (%o97) 1148 Ai:invert_by_lu(A); (%o98) 2−14−114 ff:f(x); (%o99) 311 d:args(transpose(-Ai.ff))[1]; (%o100) [−134,14] fff:f(x+d); (%o101) 0858 dnn:d[1]^2+d[2]^2; (%o102) 858 A:(fff-ff-A.transpose(matrix(d))).matrix(d)/dnn; (%o103) 00−13414 Ai:invert_by_lu(A); expt: undefined: 0 to a negative exponent. −− an error. To debug this try: debugmode(true); Kapcsolat minimumfeladatokkal Nelder-Mead-mĂłdszer minimumfeladatokra Az irĂĄny menti csökkentĂ©s mĂłdszere KvĂĄzi Newton-mĂłdszerek minimalizĂĄlĂĄsra Feladat LĂĄsd a következƑ feladatot. Feladat Pontos: kill(all); (%o0) done F:(x^2+y-11)^2+(y^2+x-7)^2; (%o12)

y2+x−7

2
+

y+x2−11

2
Fx:diff(F,x); (%o13) 2*

y2+x−7

+4*x*

y+x2−11

Fy:diff(F,y); (%o14) 4*y*

y2+x−7

+2*

y+x2−11

algsys([Fx,Fy],[x,y]); (%o15) [[x=3.584428223844282,y=−1.848126535626535],[x=−2.80511811023622,y=3.131312515247621],[x=−3.779310344827586,y=−3.283185840707964],[x=3,y=2],[x=0.08667750491999658,y=2.884254431699687],[x=−0.1279613466334164,y=−1.953714981729598],[x=−0.2708445885107149,y=−0.9230384807596201],[x=−3.0730257571469,y=−0.08135304590138556],[x=3.38515406162465,y=0.07385188249896566]] Nelder-Mead: kill(all); (%o0) done α:1.0; (%o1) 1.0 ÎČ:2.0; (%o2) 2.0 Îł:0.5; (%o3) 0.5 ÎŽ:0.5; (%o4) 0.5 Δ:0.1; (%o5) 0.1 F(x):=(x[1]^2+x[2]-11)^2+(x[2]^2+x[1]-7)^2; (%o6) F

x

:=

x12+x2−11

2
+

x22+x1−7

2
x0:[4,2]; x1:[2,2]; x2:[2,4]; (%o7) [4,2](%o8) [2,2](%o9) [2,4] F0:F(x0); F1:F(x1); F2:F(x2); (%o10) 50(%o11) 26(%o12) 130 xa:(x0+x1+x2)/3.0; (%o13) [2.666666666666666,2.666666666666666] Fa:(F0+F1+F2)/3.0; (%o14) 68.66666666666667 ((F0-Fa)^2+(F1-Fa)^2+(F2-Fa)^2)/3; (%o15) 1976.888888888889 y:xa+α*(xa-x2); (%o16) [3.333333333333333,1.333333333333333] F(y); (%o17) 5.654320987654321 z:xa+ÎČ*(xa-x2); (%o18) [3.999999999999999,−4.440892098500626*10−16] F(z); (%o19) 33.99999999999997 x2:y; (%o20) [3.333333333333333,1.333333333333333] F2:F(x2); (%o21) 5.654320987654321 x0; x1; x2; (%o22) [4,2](%o23) [2,2](%o24) [3.333333333333333,1.333333333333333] F0; F1; F2; (%o25) 50(%o26) 26(%o27) 5.654320987654321 xa:(x0+x1+x2)/3.0; (%o28) [3.11111111111111,1.777777777777777] Fa:(F0+F1+F2)/3.0; (%o29) 27.21810699588477 ((F0-Fa)^2+(F1-Fa)^2+(F2-Fa)^2)/3; (%o30) 328.4984335043778 y:xa+α*(xa-x0); (%o31) [2.222222222222221,1.555555555555555] F(y); (%o32) 25.86587410455727 x0:y; (%o33) [2.222222222222221,1.555555555555555] F0:F(x0); (%o34) 25.86587410455727 x0; x1; x2; (%o35) [2.222222222222221,1.555555555555555](%o36) [2,2](%o37) [3.333333333333333,1.333333333333333] F0; F1; F2; (%o38) 25.86587410455727(%o39) 26(%o40) 5.654320987654321 xa:(x0+x1+x2)/3.0; (%o41) [2.518518518518518,1.629629629629629] Fa:(F0+F1+F2)/3.0; (%o42) 19.17339836407053 xa:(x0+x1+x2)/3.0; ((F0-Fa)^2+(F1-Fa)^2+(F2-Fa)^2)/3; (%o43) 91.38572484740236 y:xa+α*(xa-x1); (%o44) [3.037037037037036,1.259259259259258] F(y); (%o45) 5.918658891579704 x1:y; (%o46) [3.037037037037036,1.259259259259258] F1:F(y); (%o47) 5.918658891579704 x0; x1; x2; (%o48) [2.222222222222221,1.555555555555555](%o49) [3.037037037037036,1.259259259259258](%o50) [3.333333333333333,1.333333333333333] F0; F1; F2; (%o51) 25.86587410455727(%o52) 5.918658891579704(%o53) 5.654320987654321 xa:(x0+x1+x2)/3.0; (%o54) [2.864197530864197,1.382716049382715] Fa:(F0+F1+F2)/3.0; (%o55) 12.47961799459709 y:xa+α*(xa-x0); (%o56) [3.506172839506172,1.209876543209875] F(y); (%o57) 10.38663757920144 w:xa+Îł*(xa-x0); (%o58) [3.185185185185184,1.296296296296295] F(w); (%o59) 4.750894266720111 x0:w; (%o60) [3.185185185185184,1.296296296296295] F0:F(w); (%o61) 4.750894266720111 etc. Feladat etc. BelsƑ pont mĂłdszerek
PKMLmXńB–HmimetypePKMLmXQdBV55 5format.txtPKMLmXé "ö‹ö‹ ’content.xmlPK§±’