{VERSION 5 0 "IBM INTEL NT" "5.0" } {USTYLETAB {CSTYLE "Maple Input" -1 0 "Courier" 0 0 0 0 1 1 0 1 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 0 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 "Warning" -1 7 1 {CSTYLE "" -1 -1 "Courier" 1 10 0 0 255 1 2 2 2 2 2 1 1 1 3 1 }1 1 0 0 0 0 1 0 1 0 2 2 0 1 }{PSTYLE "Maple Output" -1 11 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 1 1 1 }3 3 0 0 0 0 1 0 1 0 2 2 0 1 }{PSTYLE "Maple Plot" -1 13 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 1 1 1 }3 1 0 0 0 0 1 0 1 0 2 2 0 1 }{PSTYLE "R3 Font 0 " -1 256 1 {CSTYLE "" -1 -1 "Courier" 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 21 "restart: with(plots) :" }}{PARA 7 "" 1 "" {TEXT -1 50 "Warning, the name changecoords has b een redefined\n" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 11 " Recycling" } }{PARA 0 "" 0 "" {TEXT -1 106 " Aus einem trapezf\366rmigen Blechst \374ck A(0/0), B(x2/0), C(x2/y2) und D(0/y1) werden Rechtecke geschni tten." }}{PARA 0 "" 0 "" {TEXT -1 143 " Gesucht ist das Rechteck mit \+ maximalem Fl\344cheninhalt.\n (Das Trapez muss die angegebene Form ha ben, obere Begrenzung mit negativer Steigung.)" }}{PARA 0 "" 0 "" {TEXT -1 1 " " }}{PARA 0 "" 0 "" {TEXT -1 52 " Gerade durch D(0/y1) \+ und C(x2/y2) " }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 28 "x1: =0 : " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 29 "y1:= 5: " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 28 "x2:= 8: " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 141 "y2:= 1: \+ \n Trapez:=(y1+y2)/2*x2;\n\n polygonplot([[0,0], [x2,0], [x 2,y2], [0, y1], [0,0]]); " }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%'Trap ezG\"#C" }}{PARA 13 "" 1 "" {GLPLOT2D 352 352 352 {PLOTDATA 2 "6#-%)PO LYGONSG6#7'7$$\"\"!F)F(7$$\"\")F)F(7$F+$\"\"\"F)7$F($\"\"&F)F'" 1 2 0 1 10 0 2 9 1 4 2 1.000000 45.000000 45.000000 0 0 "Curve 1" }}}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 43 "g1:=solve((y1-y2)/(x1-x2)=(y 1-y)/(x1-x),y):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 27 "g:=unapp ly(simplify(g1),x);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"gGf*6#%\"xG 6\"6$%)operatorG%&arrowGF(,&*&#\"\"\"\"\"#F/9$F/!\"\"\"\"&F/F(F(F(" }} }{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 62 "A:=unapply(x*g(x),x);\n\nNu llstellen:=evalf(fsolve(A(x)=0,x),3);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"AGf*6#%\"xG6\"6$%)operatorG%&arrowGF(*&9$\"\"\",&*&#F.\"\"#F.F- F.!\"\"\"\"&F.F.F(F(F(" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%,Nullstell enG6$$\"\"!F'$\"#5F'" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 19 "plo t(A(x),x=0..x2);" }}{PARA 13 "" 1 "" {GLPLOT2D 496 496 496 {PLOTDATA 2 "6%-%'CURVESG6$7S7$$\"\"!F)F(7$$\"3ELLLLBxV5E$F-$\"3mn\\TB%Qtd\"!#<7$$\"3MLLLLAKn\\F-$\"3GGy\"em*GgBF57$$ \"3=LLLLc$\\o'F-$\"3vJF57$$\"3)emmm^&Q%R)F-$\"3I<7Kx&F57$$\"3\")*****\\[A4]\"F5$ \"3u62,s#G#yjF57$$\"3wmmm'3Q\\n\"F5$\"3?O+DO;)>(pF57$$\"3OLLLB6@G=F5$ \"3S.o#4mx)puF57$$\"3&)******f-w+?F5$\"3gmB+\"\\!G-!)F57$$\"3%******** *y,u@F5$\"3@%zR_e7p])F57$$\"3)*******RP)4M#F5$\"3!\\!y_ki\"['*)F57$$\" 3ILLL=Zg#\\#F5$\"3Qoyt]W[c$*F57$$\"3cmmmEn*Gn#F5$\"3#Gk?w<&H#z*F57$$\" 3Tmmm1xiDGF5$\"3)p@*\\c_g85!#;7$$\"3!)*****\\9!H.IF5$\"3%RHZx[d10\"F[q 7$$\"3Immm1:bgJF5$\"3]'o=?Y@33\"F[q7$$\"3<+++X@4LLF5$\"3/lp954266F[q7$ $\"31+++N;R(\\$F5$\"3V,;20%3r8\"F[q7$$\"3wmmm;4#)oOF5$\"3U\"z/C6)Rh6F[ q7$$\"3jmmm6lCEQF5$\"3_m7VP^6\"=\"F[q7$$\"3ELLL$G^g*RF5$\"3cn^r[Vg*>\" F[q7$$\"3oKLL=2VsTF5$\"3u&3-UXcd@\"F[q7$$\"3f*****\\`pfK%F5$\"36%f7m9% GF7F[q7$$\"3!HLLLm&z\"\\%F5$\"3hf'4wT'3P7F[q7$$\"3s******z-6jYF5$\"3.; z#eEDVC\"F[q7$$\"3<******4#32$[F5$\"3')H>\\9qc[7F[q7$$\"3O*****\\#y'G* \\F5$\"3_))Rgcu**\\7F[q7$$\"3G******H%=H<&F5$\"3!oJG3'\\][7F[q7$$\"35m mm1>qM`F5$\"3+&o$oJ()RW7F[q7$$\"3%)*******HSu]&F5$\"3Y&z'4<_7P7F[q7$$ \"3'HLL$ep'Rm&F5$\"35z?\"RRdzA\"F[q7$$\"3')******R>4NeF5$\"3$=N(es58:7 F[q7$$\"3#emm;@2h*fF5$\"32$GV6_)Q+7F[q7$$\"3]*****\\c9W;'F5$\"3-$zSg$p ?#=\"F[q7$$\"3Lmmmmd'*GjF5$\"3-/9b*\\#ph6F[q7$$\"3j*****\\iN7]'F5$\"33 V:\"*zXJP6F[q7$$\"3aLLLt>:nmF5$\"3mQ0*[@I56\"F[q7$$\"35LLL.a#o$oF5$\"3 )pY$)=i.83\"F[q7$$\"3ammm^Q40qF5$\"3mE/IK*z*[5F[q7$$\"3y******z]rfrF5$ \"3nH5mQ:y;5F[q7$$\"3gmmmc%GpL(F5$\"3Aw2@%p#Qp(*F57$$\"3/LLL8-V&\\(F5$ \"3')y:>DST'Q*F57$$\"3=+++XhUkwF5$\"3a=-#*emT]*)F57$$\"3=+++:o " 0 " " {MPLTEXT 1 0 48 "A1:=unapply(diff(A(x),x),x): # Oberstufe\n" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 123 "x_A_max:=fsolve(A1(x)=0, x): # Oberstufe\n\nx_A_max:=evalf((Nullstellen[1]+Nullstellen[ 2])/2,3); # Mittelstufe" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%( x_A_maxG$\"$+&!\"#" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 33 "Flaec he_max:=evalf(A(x_A_max),4);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%,Fla eche_maxG$\"%]7!\"#" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 65 "Verschnitt_in_Prozent:=evalf (100*(Trapez-Flaeche_max)/ Trapez,4);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%6Verschnitt_in_ProzentG$\"%#z%!\"#" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 37 "Tabelle:=seq(evalf(A(n),4),n=0..8);\n\n" }}{PARA 11 " " 1 "" {XPPMATH 20 "6#>%(TabelleG6+$\"\"!F'$\"%+X!\"$$\"\")F'$\"%]5!\" #$\"#7F'$\"%]7F/F0F-F+" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}}}{MARK "15 0 0" 0 } {VIEWOPTS 1 1 0 1 1 1803 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }