{VERSION 5 0 "IBM INTEL NT" "5.0" }
{USTYLETAB {CSTYLE "Maple Input" -1 0 "Courier" 0 0 0 0 255 1 0 0 0 0 
1 0 0 0 0 1 }{CSTYLE "2D Math" -1 2 "Times" 0 1 0 0 0 0 0 0 2 0 0 0 0 
0 0 1 }{CSTYLE "2D Output" 2 20 "" 0 1 0 0 255 1 0 0 0 0 0 0 0 0 0 1 }
{PSTYLE "Normal" -1 0 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 
2 2 1 1 1 1 }1 1 0 0 0 0 1 0 1 0 2 2 0 1 }{PSTYLE "Maple Output" 0 11 
1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }3 3 0 -1 -1 -1 
0 0 0 0 0 0 -1 0 }{PSTYLE "R3 Font 0" -1 256 1 {CSTYLE "" -1 -1 "Couri
er" 1 11 128 0 128 1 2 1 2 2 2 2 1 1 1 1 }1 1 0 0 0 0 1 0 1 0 2 2 0 1 
}{PSTYLE "R3 Font 2" -1 257 1 {CSTYLE "" -1 -1 "Courier" 1 11 0 128 
128 1 2 1 2 2 2 2 1 1 1 1 }1 1 0 0 0 0 1 0 1 0 2 2 0 1 }}
{SECT 0 {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "restart;" }}}{EXCHG 
{PARA 0 "" 0 "" {TEXT -1 25 "   Umstellen von Formeln:" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 27 "l1:=solve(3-B*(3-2*c)=1,c):" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 27 "l2:=solve(2*A-1/(3-c)=1,c):
" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 29 "l3:=solve(2*A*(1/2*c-1)
=1,c):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 28 "g1:=U=2*Pi*r+r: s
olve(g1,r):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 31 "g2:=O=2*a*b+
b*c+2: solve(g2,a):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 29 "g3:=
A=3*(a+2*b): solve(g3,b):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
29 "g4:=B=4/(a+2*b): solve(g4,b):" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 31 "g5:=B=4/a-(1-c)/b: solve(g5,b):" }}}{EXCHG {PARA 0 "
" 0 "" {TEXT -1 65 "   Gleichungssystem mit 2 Unbekannten erzeugen, L
\366sungen vorgeben" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "d1:=3*x-4*y:
" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "d2:=6*x+5*y:" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 34 "x1:=-3: y1:=4: # L\366sungen
 vorgeben" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "r1:=subs(x=x1,
y=y1,d1):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "r2:=subs(x=x1,
y=y1,d2):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "glg1:=d1=r1:" 
}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "glg2:=d2=r2:" }}}{EXCHG 
{PARA 0 "" 0 "" {TEXT -1 43 "   L\366sen des Gleichungssystems (Kontro
lle):" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 32 "lsg:=solve(\{glg1,glg2\},
\{x,y\}):\n\n" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 34 "Gleichungssystem
 mit 3 Unbekannten" }{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 14 "d1:=2*x-3*y+z:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 
1 0 14 "d2:=x-2*y-3*z:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "d
3:=2*x+y-2*z:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 42 "x1:=-2: y1
:=1: z1:=0:  # L\366sungen vorgeben" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 28 "r1:=subs(x=x1,y=y1,z=z1,d1):" }}}{EXCHG {PARA 0 "> " 
0 "" {MPLTEXT 1 0 29 "r2:=subs(x=x1,y=y1,z=z1, d2):" }}}{EXCHG {PARA 
0 "> " 0 "" {MPLTEXT 1 0 29 "r3:=subs(x=x1,y=y1,z=z1, d3):" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "glg1:=d1=r1:" }}}{EXCHG {PARA 0 "> \+
" 0 "" {MPLTEXT 1 0 12 "glg2:=d2=r2:" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 12 "glg3:=d3=r3:" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 45 "
     L\366sen des Gleichungssystems (Kontrolle):" }}{PARA 0 "> " 0 "" 
{MPLTEXT 1 0 38 "lsg:=solve(\{glg1,glg2,glg3\},\{x,y,z\}):\n" }}}
{EXCHG {PARA 0 "" 0 "" {TEXT -1 47 "     quadratische Gleichung,  L
\366sungen vorgeben" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 7 "x1:=-1:" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "x2:=1/2:" }}}{EXCHG {PARA 0 "
> " 0 "" {MPLTEXT 1 0 22 "expand((x-x1)*(x-x2)):" }}}{EXCHG {PARA 0 ">
 " 0 "" {MPLTEXT 1 0 9 "restart:\n" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 
-1 24 "     Exponentialfunktion" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 
1 0 12 "g:=x->a*q^x:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "glg
1:=g(1)=30:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "glg2:=g(2)=7
0:" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 31 "    L\366sen des Gleichungs
systems" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 33 "lsg:=evalf(solve(\{glg1,
glg2\}),6):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 29 "g:=unapply(s
ubs(lsg,g(x)),x):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 29 "plot(g
(x),x=0..10,y=0..300):\n" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 29 "     \+
   Abstand zweier Punkte" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 32 
"x1:=4: y1:=-1:  x2:=-3:  y2:=-6:" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 36 "d:=sqrt(    (x2-x1)^2+(y2-y1)^2   );" }}{PARA 11 "" 
1 "" {XPPMATH 20 "6#>%\"dG*$\"#u#\"\"\"\"\"#" }}}{EXCHG {PARA 0 "> " 
0 "" {MPLTEXT 1 0 10 "d1:=x2-x1:" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 10 "d2:=y2-y1:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
9 "restart:\n" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "restart:" }
}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 18 "   Einsetz\374bungen:" }}{PARA 
0 "> " 0 "" {MPLTEXT 1 0 14 "term:=1/x+x^2:" }}}{EXCHG {PARA 0 "> " 0 
"" {MPLTEXT 1 0 23 "subs(x=2*sqrt(3),term):" }}}{EXCHG {PARA 0 "" 0 "
" {TEXT -1 29 "   Gleichungen h\366heren Grades" }}{PARA 0 "> " 0 "" 
{MPLTEXT 1 0 31 "k:=expand( (x-3)*(x+2)*(x-5) ):" }}}{EXCHG {PARA 0 ">
 " 0 "" {MPLTEXT 1 0 14 "gl:=expand(k):" }}}{EXCHG {PARA 0 "" 0 "" 
{TEXT -1 5 "     " }{MPLTEXT 1 0 24 "# solve(gl,y):\n\nrestart;" }}}
{EXCHG {PARA 0 "" 0 "" {TEXT -1 111 " Aufgaben zum Thema Pythagoras,\n
   f\374r ein rechtwinkliges Dreieck sind gegeben:\n\n1. Aufgabe\nL
\344nge der Katheten " }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 6 "k1:=a:" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 19 "k2:=4:\nassume(a>0):" }}}
{EXCHG {PARA 0 "" 0 "" {TEXT -1 21 "L\344nge der Hypotenuse:" }}{PARA 
0 "> " 0 "" {MPLTEXT 1 0 29 "c:=simplify(sqrt(k1^2+k2^2)):" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 21 "restart;\nassume(a>0):" }}}{EXCHG {PARA 0 "" 0 "" 
{TEXT -1 32 "2. Aufgabe\nL\344nge einer Kathete\n " }{MPLTEXT 1 0 13 "
k1:=sqrt(2):\n" }{TEXT -1 20 "L\344nge der Hypotenuse" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "c:=3*sqrt(3):" }}}{EXCHG {PARA 0 "
" 0 "" {TEXT -1 26 "L\344nge der zweiten Kathete:" }}}{EXCHG {PARA 0 "
> " 0 "" {MPLTEXT 1 0 29 "k2:=simplify(sqrt(c^2-k1^2)):" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "\nrestart;" }}}{EXCHG {PARA 0 "" 0 "
" {TEXT -1 61 "3. Aufgabe\nL\344nge einer Kathete a\nHypotenusenabschn
itt p\n     " }{MPLTEXT 1 0 5 "a:=3:" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 5 "p:=2:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "h:
=sqrt(a^2-p^2):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "q:=solve
(h^2=x*p,x):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "b:=sqrt(h^2
+q^2):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 7 "c:=q+p:" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "\n\nrestart;" }}}{EXCHG 
{PARA 0 "" 0 "" {TEXT -1 54 "      F\374r die Erstellung von Aufgaben \+
zum Thema Terme," }}{PARA 0 "" 0 "" {TEXT -1 78 "      z. B. f\374r ei
nen Quader 2 Kantenl\344ngen und die Gesamtkantenl\344nge vorgeben" }}
{PARA 0 "" 0 "" {TEXT -1 46 "      gesucht ist die dritte Kantenl\344n
ge.\n    " }}{PARA 0 "" 0 "" {TEXT -1 11 "     W\374rfel" }}{PARA 0 ">
 " 0 "" {MPLTEXT 1 0 6 "a:=18:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 
1 0 19 "Oberflaeche:=6*a^2:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
13 "Volumen:=a^3:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 19 "Kanten
laenge:=12*a:" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 12 "    Rechteck" }}
{PARA 0 "> " 0 "" {MPLTEXT 1 0 7 " a:=12:" }}}{EXCHG {PARA 0 "> " 0 "
" {MPLTEXT 1 0 7 " b:=14:" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}
{PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "Flaeche:=a*b:" }}}{EXCHG {PARA 0 ">
 " 0 "" {MPLTEXT 1 0 16 "Umfang:=2*(a+b):" }}}{EXCHG {PARA 0 "> " 0 "
" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 6 "Quader" }}
{PARA 0 "> " 0 "" {MPLTEXT 1 0 6 "a:=18:" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 6 "b:=16:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 6 "c:
=13:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "Volumen:=a*b*c:" }}
}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 29 "Oberflaeche:=2*(a*b+a*c+b*c
);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%,OberflaecheG\"%g9" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "Kantenlaenge:=4*a+4*b+4*c:" }}}
{EXCHG {PARA 0 "" 0 "" {TEXT -1 6 "Trapez" }}{PARA 0 "> " 0 "" 
{MPLTEXT 1 0 6 "a:=17:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 6 "b:
=14:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 5 "h:=8:" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 18 "Trapez:=(a+b)/2*h:" }}}}{MARK "70 2
 0" 42 }{VIEWOPTS 1 1 0 1 1 1803 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }