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(Y OR N)"A ANS$T ANS$"N"7000Z v$ " COEFFICIENT MATRIX"|. 8 B I1ML J1MV K8J7` K)SS(I,J);j Jt u ~ I  " INVERSE OF COEFFICIENT MATRIX"OLUTIONS."#PAUSE11500:PAUSE-7040V"THE SYSTEM HAS A UNIQUE SOLUTION."s"LET'S SEE WHAT IT IS."PAUSE11500:PAUSEI1NX(I)B(I)II1N"X(";I;") = ";X(I)I"THE COEFFICIENT MATRIX I1N."X(";I;") = ";(100X(I))1005&I;0N5PRMMN7000w:"TO FIND OTHER SOLUTIONS, TYPE 'Y'"D"OTHERWISE TYPE 'N' "NANS$XANS$"N"1900]K1N_X(K)0bKg1585l7000 "THE SYSTEM HAS NO SN S(T)0T"PCN17360LPC1NMS(PC)S(PC)A(PR,L)X(L)TLjX(PC)B(PR)S(PC)sRPRIPC111X(I)01790RR1LI1NS(I)S(I)A(R,L)X(L)LX(I)B(R)S(I)I400015OLUTIONS. LOOK AT THE ARRAY AND"N"DECIDE HOW MANY ARBITRARY ASSIGNMENTS"v""CAN BE MADE. ENTER THIS NUMBER."},Z1Y1Z6"NOW TYPE THE SUBSCRIPT I AND THE VALUE"@"X(I) OF AN ASSIGNMENT."JI,X(I)^Y--SOLVINGT1PIVOT." PR,PC 3000" , 40005 &350; ` "WE PROCEED TO FIND SOLUTIONS."f y xPRMMN1500 }PRMMN2200 IPR1M B(I)02000 I --CHOOSE PARAMETERS  "THE SYSTEM HAS INFINITELY MANY"!"SCHELON FORM? (Y OR N)"; rF$0 |F$"Y"12006 d "IS A ROW INTERCHANGE NEEDED? (Y OR N)";n ANS$ ANS$"N"500  "WHICH ROWS DO YOU WANT TO INTERCHANGE?" K1,K2 5000 4000  "ENTER THE ROW AND COLUMN OF THE Y TO BEGIN"+ )"THE SOLUTION PROCEDURE.";3 *G$9 ,^ @"WE NOW PERFORM ELEMENTARY ROW" J"OPERATIONS ON THE AUGMENTED MATRIX." KPAUSE11500:PAUSE O Q4000 T V W ^"IS THE AUGMENTED MATRIX IN" c h"REDUCED ROW EYPE 'GO'"  K$ + 7N)"*"6 I1MA J1NM A(I,J)[ MN225n SS(I,J)A(I,J) JIE(I,J)1 K7J6 K)A(I,J); J B(I) 7N)"* ";B(I) 7N)"*" I "12 &"TYPE 'GO' WHEN YOU ARE READS A(I,J) AND THE " ZB d"CONSTANTS B(I) ARE LOCATED IN DATA"H nr x"STATEMENTS BEGINNING AT LINE 6000."x "TO SEE THE AUGMENTED MATRIX OF THE" "SYSTEM, WITH THE CONSTANTS SEPARATED" "FROM THE COEFFICIENTS BY *'S, T  I110 X(I)0% I1I110=J110JA(I,J)0QJXIaM,NmI110xS(I)0 I("WITH THIS PROGRAM WE SOLVE A SYSTEM"2<"OF ";M;" LINEAR EQUATIONS IN ";N;" UNKNOWNS."F P"THE COEFFICIENT          ٽΨةٽΨةѤٽΨةΠ 20, 30, 40, 50 IN...." M "THEN TYPE 'RUN 2100' AND PRESS 'RETURN'."a F(T)1(T)2g d5LE:"PAUSE11000:PAUSE'30009` PAUSE15000De PAUSEJj Tl 2415Zo `t  "DO YOU WANT A DIFFERENT SCALE?"  "THE CURRENT SCALE IS ";S CG$  CG$"NO"ī1950 "TYPE '2100 S =...'"  " USING 10,139,79279,79 ^I139279S/`I,78I,806bI@f3000RpJ06.28.05ju((J)).001ī2230vzRF(J)XSR(J)YSR(J)XX139Y79YX0X279Y0Y159ī2230X,YJ22"HERE IS THE FUNCTION RU"THEN TYPE 'RUN 2100' AND PRESS 'RETURN'."X" NOTE:IF THERE IS A POSSIBILITY OF"" ZERO IN A DENOMINATOR OR A NEGATIVE"" NUMBER UNDER A RADICAL, INSERT A TEST"" AT LINE NUMBER 2165 AND GO TO 2230." 4S209>H"M$!M$"YES"ī50'-Z"THE CURRENT FUNCTION IS LISTED BELOW:"`j3000p"ENTER YOUR FUNCTION OF THE ANGLE T. TYPE:"" 3000 DEF FN F(T) ="" FOLLOWED BY YOUR RULE IN BASIC.",   139,0139,159/ 0,79279,79A J139279SXP J,78J,80W Jj J1390(SX)y J,78J,80 J J79159SY 138,J140,J J J790(SY) "138,J140,J #J "DO YOU WANT TO DO ANOTHER GRAPH?IS ";SX 9 "THE CURRENT VERTICAL SCALE SY IS ";SY? k "YOUR CHOICES ARE 10, 20, 30, 40, 50."q  "TYPE '515 SX =...:SY =...'"  " WITH YOUR CHOICES IN ... AND ...."  "THEN TYPE 'RUN 510' AND PRESS 'RETURN'." X,Y lI v225 "HERE IS THE FUNCTION RULE."N PAUSE11000:PAUSEW 560p PAUSE15000:PAUSEv  680   "DO YOU WANT DIFFERENT SCALES?"  CH$ CH$"NO"ī1950  "THE CURRENT HORIZONTAL SCALE SX ,B SEPARATED BY A COMMA.)" 0 SX10:SY109 A,BG WIDTHBAY N(WIDTH)SXj &DLTAWIDTHNt +1000 0F(X)X(X3)(X2) :I0N ?XAIDLTA DZF(X) IXSXX139 KX0X279ī620 NYSY(Z)79 PY0Y159ī620 X"IF YOU WANT A DIFFERENT FUNCTION, TYPE:"/ K " 560 DEF FN F(X) ="Q "FOLLOWED BY YOUR FUNCTION RULE IN BASIC" "THEN TYPE 'RUN 500' AND PRESS 'RETURN'."   "WHAT X-INTERVAL DO YOU WANT?"  "(ENTER Ai 25d"SO YOU WANT TO PLOT A GRAPH. WOULD YOU";i^n"PREFER RECTANGULAR OR POLAR"dsx"CO-ORDINATES? (JUST ANSWER R OR P.)"}ANS$ANS$"P"ī2000"THE CURRENT FUNCTION IS GIVEN BELOW:"560)      ٽٽѤٽΠ (F$,D)DEN(D$)"FNUMDEN( AONE MOMENT PLEASE"0$(4);"BLOAD CHAIN, A520"A.520"CIRCLE"| SUBROUTINE TO ACCEPT FRACTIONAL VALUES OF INPUTI1(F$)(F$,I,1)"/"ĂII(F$)4060F(F$)4120N$(F$,I1)NUM(N$)D(F$)ID$ASE""\ (4);"BLOAD CHAIN, A520"5f 520"PARABOLA"m ROUTINE TO CALL UP HYPERBOLA PART OF PROGRAM :22:"ONE MOMENT PLEASE" (4);"BLOAD CHAIN, A520" 520"HYPERBOLA" ROUTINE TO CALL UP CIRCLE PART OF PROGRAM:22:"GAIN!"%& SCND2āI11000:I:3020/0 3070b ROUTINE TO CALL UP LINE PART OF PROGRAM :22:"ONE MOMENT PLEASE" (4);"BLOAD CHAIN, A520" 520"LINE"H ROUTINE TO CALL UP PARABOLA PART OF PROGRAMR :22:"ONE MOMENT PLEF GRAPHS :10$ SCND2ė:21R "1 LINE 2 PARABOLA 3 HYPERBOLA"q "4 CIRCLE 5 ELLIPSE" SCND23070 :"TYPE THE NUMBER OF YOUR CHOICE:" CHOICE$ CHOICE(CHOICE$) CHOICE3300,3400,3500,3600,50 :"TRY A WANT IT ON THE SAME AXES WITH"@Z "THE OTHER GRAPH(S)? (Y/N)"Hd N$ei N$"N"SCND0:::3000vn N$"Y"3000s "TRY AGAIN!":2660x 3000 ::12 "THANK YOU; END OF PROGRAM." I13000:I : ALLOWS FOR CHOICES O YY0YY1592550 XX,YY$ X< 23:31:" "e 19::"'RETURN' TO CONTINUE";A$:o :21 "DO YOU WANT ANY MORE GRAPHS DRAWN?"( "(Y/N)"2 N$7 N$"N"2700< N$"Y"2630A "TRY AGAIN!":2610F :21P "DO YOU3513454 FOR BOTH EQUATIONS; SEE 520 AND 530I>RADAA(XBB)2YHRAD02550lRYCCDDRAD.5\XXX135:YYY80fXX0XX2692300pYY0YY1592300zXX,YYYCCDDRAD.5 XXX135 YYY80 XX0XX2692550"THE NO. OF UNITS BETWEEN MARKS ON THE"b"X-AXIS = ";10XCHNG;" AND ON THE Y-AXIS = ";10YCHNGz:31:"GRAPHING":SCND2:x"THAT ORDER? PRESS ";::"RETURN";::" WHEN DONE." ROUTINE USED TO GRAPH THE EQUATIONS7X1:1120"tXCHNG10:YCHNG10:1210,~:21["HOW MANY UNITS WOULD YOU LIKE TO ASSIGN""BETWEEN MARKS ON THE X-AXIS? ";::"RETURN":XCHNG:XCHNG10XCHNG"FOR BETWEEN THE MARKS ON THE Y-AXIS?"YCHNG:YCHNG10YCHNG:21'Y:X,YX526910-$Y7585:X,Y:Y,X5.21F8SCND21210sB"CURRENTLY EACH MAJOR MARK ON BOTH THE"L"X-AXIS AND Y-AXIS ARE ONE UNIT. DO YOU"V"WANT THIS CHANGED? (Y/N)"`Y$eY$"Y"1150jY$"N"1140o"TRY AGAIN!"BYCHNG(AXCHNG)YELLIP2AA(BXCHNG)2:BBHXCHNG:CCKYCHNG:DDAYCHNG(BXCHNG)c2000 SUBROUTINE TO DRAW AXIS FOR ALL EQUATIONS USEDSCND21210::30,80269,80:135,0135,159Y015910X130140:X, AGAIN!", SCND2āI12000:I::21:3805 410? 1000G 23 ELLIP1ĺ"(X-";H$;")^2/";A$;"^2 + (Y-";K$;")^2/";B$;"^2 = 1" ELLIP2ĺ"(X-";H$;")^2/";B$;"^2 + (Y-";K$;")^2/";A$;"^2 = 1"ELLIP1AA(AXCHNG)2:BBHXCHNG:CCKYCHNG:DDAT IS THE VALUE OF A (1/2 THE MAJOR"O "AXIS) AND B (1/2 THE MINOR AXIS) IN" "THAT ORDER? PRESS ";::"RETURN";::" WHEN DONE." A$,B$:F$A$:4000 AF:F$B$:4000 BF ABAB480 ::"SORRY A MUST BE > OR = B.": "TRY 6:8:200:SCND2Ģ21I @"GIVE THE VALUES OF THE X-COORDINATE (H)"w J"AND THE Y-COORDINATE (K) OF THE CENTER" T"IN THAT ORDER. PRESS ";::"RETURN";::" WHEN DONE." ^H$,K$:F$H$:4000 hHF:F$K$:4000 rKF::SCND2ė:21$ |"WH1". "2 (X-H)^2 / B^2 + (Y-K)^2 / A^2 = 1"Q "3 OOPS! NEITHER OF THESE."] ELLIP$q ELLIP(ELLIP$) ELLIP300,300,3000 ::"TRY AGAIN!" SCND2āI11000:I::60 170 , FOR BOTH FORMS OF THE EQUATION OF AN ELLIPSE"- P"AN ELLIPSE, IT CAN BE WRITTEN IN THE"\ Z"FORM OF THE FOLLOWING. INDICATE WHICH:"o d::"NOTE:": n11:7:"(X-H)^2 IS THE COMPUTER'S WAY OF" x"WRITING '(X-H) SQUARED'.": I11000:I:255 "1 (X-H)^2 / A^2 + (Y-K)^2 / B^2 = *( ROUTINE TO GRAPH AN ELLIPSE8 START150e::"THE PROGRAM GRAPH CHECK IS NEEDED""FIRST. I'LL LOAD IT NOW.":(I12000:I:(4);"RUN GRAPH CHECK"2:7:200<SCND2Ģ21:140 F" IF THE GRAPH OF YOUR EQUATION IS      ٽثڍٽثڍѤٽثڢΠ S OF INPUTI1(F$)0(F$,I,1)"/"ĂIBI(F$)4060NF(F$)X4120iN$(F$,I1)wNUM(N$)D(F$)ID$(F$,D)DEN(D$)FNUMDEN :22:"ONE MOMENT PLEASE"6 (4);"BLOAD CHAIN, A520"J 520"HYPERBOLA"t ROUTINE TO CALL UP ELLIPSE PART OF PROGRAM~:22:"ONE MOMENT PLEASE"(4);"BLOAD CHAIN, A520"520"ELLIPSE"  SUBROUTINE TO ACCEPT FRACTIONAL VALUEOMENT PLEASE"+ (4);"BLOAD CHAIN, A520": 520"LINE"qH ROUTINE TO CALL UP PARABOLA PART OF PROGRAMM :22:"ONE MOMENT PLEASE"R (4);"BLOAD CHAIN, A520"\ 520"PARABOLA" ROUTINE TO CALL UP HYPERBOLA PART OF PROGRAM : SCND230706 :"TYPE THE NUMBER OF YOUR CHOICE:"C CHOICE$Y CHOICE(CHOICE$)| CHOICE3300,3400,3500,50,3700 :"TRY AGAIN!"& SCND2āI11000:I:30200 3070 ROUTINE TO CALL UP LINE PART OF PROGRAM.  :22:"ONE MN$"Y"3000$x "TRY AGAIN!":26600 ::12R "THANK YOU; END OF PROGRAM."c I13000:Ik : ALLOWS FOR CHOICES OF GRAPHS :10 SCND2ė:21 "1 LINE 2 PARABOLA 3 HYPERBOLA" "4 CIRCLE 5 ELLIPSE" :21. "DO YOU WANT ANY MORE GRAPHS DRAWN?";( "(Y/N)"C2 N$T7 N$"N"2700e< N$"Y"2630~A "TRY AGAIN!":2610F :21P "DO YOU WANT IT ON THE SAME AXES WITH"Z "THE OTHER GRAPH(S)? (Y/N)"d N$i N$"N"SCND0:::3000 n XXX135 YYY80- XX0XX2692550C YY0YY1592550N XX,YYX 2550h PNT12552o Xy PNT0 KK0KK1592560 HHRR0HHRR2692560 HHRR,KK 23:31:" " 19::"'RETURN' TO CONTINUE";A$: ^.5, SEE 250 &HRADAA(XBB)26RRAD02546FTPNT12140PUPNT1fVKK0KK1592140XHHRR0HHRR2692140ZHHRR,KK\YCC(RAD)fXXX135:YYY80pXX0XX2692190zYY0YY1592190XX,YYYCC(RAD) N'T BE GRAPHED HERE IF"=2"THE AXES ARE DIFFERENT SCALES!"T<I15000:I:2580 ROUTINE USED TO GRAPH THE EQUATIONS7X1351344 EQUATION FOR A CIRCLE> Y = K*YCHNG - ((X+&-((XCHNG*YCHNG*R^2) - (X - H*XCHNG)^2)"X-AXIS = ";10XCHNG;" AND ON THE Y-AXIS = ";10YCHNGP:31:"GRAPHING":]SCND2: THIS PROGRAM WILL NOT GRAPH CORRECTLY FOR A CIRCLE IF THE X-AXIS AND Y-AXIS ARE NOT THE SAME SCALE.:21::"SORRY":(21:7:"A CIRCLE CA YOU LIKE TO ASSIGN"H"BETWEEN MARKS ON THE X-AXIS? ";::"RETURN":bXCHNG:XCHNG10XCHNG"FOR BETWEEN THE MARKS ON THE Y-AXIS?"YCHNG:YCHNG10YCHNG:21SCND2:XCHNGYCHNG1300"THE NO. OF UNITS BETWEEN MARKS ON THE"8, B"CURRENTLY EACH MAJOR MARK ON BOTH THE"[ L"X-AXIS AND Y-AXIS ARE ONE UNIT. DO YOU"| V"WANT THIS CHANGED? (Y/N)" `Y$ eY$"Y"1150 jY$"N"1140 o"TRY AGAIN!":1120 tXCHNG10:YCHNG10:1210 ~:21"HOW MANY UNITS WOULDHNG:KKKYCHNG80 2000Z  SUBROUTINE TO DRAW AXIS FOR ALL EQUATIONS USEDk SCND21210v ::3 0,80269,80:135,0135,159 Y015910 X130140:X,Y:X,Y X526910 $Y7585:X,Y:Y,X .21 8SCND21210K$,R$ F$H$:4000) HF:F$K$:4000= KF:F$R$:4000K RF:1000} 23:"(X-";H$;")^2 + (Y-";K$;")^2 = ";R$;"^2" AAXCHNGYCHNGR2:BBHXCHNG:CCKYCHNG  TO GRAPH THE LEFT AND RIGHT POINT OF THE CIRCLE HHHXCHNG135:RRRXC" N$::N$"N"3000( N$"Y"155@ "TRY AGAIN!":145M 14:200| "GIVE THE VALUES OF THE X-COORDINATE (H)" "AND THE Y-COORDINATE (K) OF THE CENTER," "AND RADIUS (R) IN THAT ORDER. ";::"RETURN": SCND0ĺ" ":255 H$,". P"CIRCLE, IT CAN BE WRITTEN IN THE FORM"] Z"OF:":" (X-H)^2 + (Y-K)^2 = R^2" d:"IS THIS TRUE OF YOUR EQUATION? (Y/N)" nI1500:I:255 x:"NOTE:": 15:7:"(X-H)^2 IS THE COMPUTER'S WAY OF" "WRITING '(X-H) SQUARED'.& ROUTINE TO GRAPH A CIRCLE6 START150c::"THE PROGRAM GRAPH CHECK IS NEEDED""FIRST. I'LL LOAD IT NOW.":(I12000:I:(4);"RUN GRAPH CHECK"2:9:200<SCND2Ģ21:160 F" IF THE GRAPH OF YOUR EQUATION IS A     ̠ٽΨح٩ٽΨح٩ѤٽΨح٩Π SE"> SUBROUTINE TO ACCEPT FRACTIONAL VALUES OF INPUTMI1(F$)d(F$,I,1)"/"ĂIvI(F$)4060F(F$)4120N$(F$,I1)NUM(N$)D(F$)ID$(F$,D)DEN(D$)FNUMDEN , ROUTINE TO CALL UP CIRCLE PART OF PROGRAMO:22:"ONE MOMENT PLEASE"m$(4);"BLOAD CHAIN, A520"~.520"CIRCLE"t ROUTINE TO CALL UP ELLIPSE PART OF PROGRAM~:22:"ONE MOMENT PLEASE"(4);"BLOAD CHAIN, A520"520"ELLIP ROUTINE TO CALL UP LINE PART OF PROGRAMG :22:"ONE MOMENT PLEASE"e (4);"BLOAD CHAIN, A520"t 520"LINE"H ROUTINE TO CALL UP PARABOLA PART OF PROGRAMR :22:"ONE MOMENT PLEASE"\ (4);"BLOAD CHAIN, A520"f 520"PARABOLA"0 PARABOLA 3 HYPERBOLA"7 "4 CIRCLE 5 ELLIPSE"H SCND23070q :"TYPE THE NUMBER OF YOUR CHOICE:"~ CHOICE$ CHOICE(CHOICE$) CHOICE3300,3400,50,3600,3700 :"TRY AGAIN!"& SCND2āI11000:I:30200 3070( GRAPH(S)? (Y/N)"d N$5i N$"N"SCND0:::3000Fs N$"Y"3000_x "TRY AGAIN!":2660k ::12 "THANK YOU; END OF PROGRAM." I13000:I : ALLOWS FOR CHOICES OF GRAPHS :10 SCND2ė:21 "1 LINE 2:" "5 19::"'RETURN' TO CONTINUE";A$:? :21i "DO YOU WANT ANY MORE GRAPHS DRAWN?"v( "(Y/N)"~2 N$7 N$"N"2700< N$"Y"2630A "TRY AGAIN!":2610F :21P "DO YOU WANT IT ON THE SAME AXES WITH"Z "THE OTHER E 580RAD(XAA)2BB)RAD02550<YCCDDRAD.5RXXX135:YYY80h XX0XX2692340~ YY0YY1592340 XX,YY$ YCCDDRAD.5 XXX135 YYY80 XX0XX2692550 YY0YY1592550 XX,YY X  23:31HE EQUATIONS7#X1351346HYPERB32100IHYPERB42200~ FOR XY = K; Y = K*XCHNG*YCHNG/X, SEE 360 X02550YAAX 25004 FOR HYPERB = 3; SEE 580>RAD(XAA)2BBH2220 FOR HYPERB = 4; SEG-"FOR BETWEEN THE MARKS ON THE Y-AXIS?"GYCHNG:YCHNG10YCHNGQ:21~"THE NO. OF UNITS BETWEEN MARKS ON THE""X-AXIS = ";10XCHNG;" AND ON THE Y-AXIS = ";10YCHNG:31:"GRAPHING":SCND2:  ROUTINE USED TO GRAPH TWANT THIS CHANGED? (Y/N)""`Y$3eY$"Y"1150DjY$"N"1140]o"TRY AGAIN!":1120ytXCHNG10:YCHNG10:1210~:21"HOW MANY UNITS WOULD YOU LIKE TO ASSIGN""BETWEEN MARKS ON THE X-AXIS? ";::"RETURN":XCHNG:XCHNG10XCHNND21210::340,80269,80:135,0135,159DY015910]X130140:X,Y:X,YmX526910$Y7585:X,Y:Y,X.218SCND21210B"CURRENTLY EACH MAJOR MARK ON BOTH THE"L"X-AXIS AND Y-AXIS ARE ONE UNIT. DO YOU"V""^2 - (X-";H$;")^2/";B$;"^2 = 1"hDHYPERB3AAHXCHNG:BB(AXCHNG)2:CCKYCHNG:DDBYCHNG(AXCHNG)NHYPERB4AAHXCHNG:BB(BXCHNG)2:CCKYCHNG:DDAYCHNG(BXCHNG)X2000 SUBROUTINE TO DRAW AXIS FOR ALL EQUATIONS USED SCSE AXIS) AND B (1/2 THE CONJUGATE"U "AXIS) IN THAT ORDER? PRESS ";::"RETURN":l A$,B$:F$A$:4000 AF:F$B$:4000 BF 1000 &23 0HYPERB3ĺ"(X-";H$;")^2/";A$;"^2 - (Y-";K$;")^2/";B$;"^2 = 1" :HYPERB4ĺ"(Y-";K$;")^2/";A$;ATE (H)"6 "AND THE Y-COORDINATE (K) OF THE CENTER"s "IN THAT ORDER. PRESS ";::"RETURN";::" WHEN DONE." H$,K$:F$H$:4000 HF:F$K$:4000 KF::SCND2ė:21 SCND2ė:21 "WHAT IS THE VALUE OF A (1/2 THE TRANS-"" "VER:SCND2Ģ218 @"WHAT IS THE VALUE OF THE CONSTANT K?"e E"PRESS ";::"RETURN";::" WHEN DONE."~ J255:K$:F$K$:4000 TKF:1000 ^23:"XY = ";K$ hAAKXCHNGYCHNG r2000 :8:200:SCND2Ģ21 "GIVE THE VALUES OF THE X-COORDINNE OF THESE"4 "3 (X-H)^2/A^2 - (Y-K)^2/B^2 = 1"\ "4 (Y-K)^2/A^2 - (X-H)^2/B^2 = 1"i HYPERB$ HYPERB(HYPERB$) HYPERB300,3000,400,400 ::"TRY AGAIN!" SCND2āI11000:I::60 170 , FOR XY = K 6:12:200ION IS A"4 P"HYPERBOLA, IT CAN BE WRITTEN IN THE"c Z"FORM OF THE FOLLOWING. INDICATE WHICH:"v d::"NOTE:": n11:7:"(X-H)^2 IS THE COMPUTER'S WAY OF" x"WRITING '(X-H) SQUARED'.": I11000:I:255 "1 XY = K 2 OOPS! NO) ROUTINE TO GRAPH A HYPERBOLA9 START150f::"THE PROGRAM GRAPH CHECK IS NEEDED""FIRST. I'LL LOAD IT NOW.":(I12000:I:(4);"RUN GRAPH CHECK"2:7:200<SCND2Ģ21:255:140 F" IF THE GRAPH OF YOUR EQUAT            (N$)D(F$)I"D$(F$,D)0DEN(D$)>FNUMDEND (ART OF PROGRAM-~:22:"ONE MOMENT PLEASE"K(4);"BLOAD CHAIN, A520"]520"ELLIPSE" SUBROUTINE TO ACCEPT FRACTIONAL VALUES OF INPUTI1(F$)(F$,I,1)"/"ĂII(F$)4060F(F$)4120N$(F$,I1)NUMGRAM# :22:"ONE MOMENT PLEASE"A (4);"BLOAD CHAIN, A520"U 520"HYPERBOLA" ROUTINE TO CALL UP CIRCLE PART OF PROGRAM:22:"ONE MOMENT PLEASE"$(4);"BLOAD CHAIN, A520".520"CIRCLE"t ROUTINE TO CALL UP ELLIPSE P,3500,3600,3700$ :"TRY AGAIN!"C& SCND2āI11000:I:3020M0 3070 ROUTINE TO CALL UP LINE PART OF PROGRAM :22:"ONE MOMENT PLEASE" (4);"BLOAD CHAIN, A520" 520"LINE" ROUTINE TO CALL UP HYPERBOLA PART OF PRO ALLOWS FOR CHOICES OF GRAPHS0 :10B SCND2ė:21p "1 LINE 2 PARABOLA 3 HYPERBOLA" "4 CIRCLE 5 ELLIPSE" SCND23070 :"TYPE THE NUMBER OF YOUR CHOICE:" CHOICE$ CHOICE(CHOICE$) CHOICE3300,50TRY AGAIN!":2610F :21GP "DO YOU WANT IT ON THE SAME AXES WITH"hZ "THE OTHER GRAPH(S)? (Y/N)"pd N$i N$"N"SCND0:::3000n N$"Y"3000x "TRY AGAIN!":2660 ::12 "THANK YOU; END OF PROGRAM." I13000:I :&5 YYY80$ XX0XX2692550: YY0YY1592550E XX,YYL Xd 23:31:" " 19::"'RETURN' TO CONTINUE";A$: :21 "DO YOU WANT ANY MORE GRAPHS DRAWN?"( "(Y/N)"2 N$7 N$"N"2700< N$"Y"2630A "EEX)\RAD02550*fY(AARAD.5)BB@pXXX135:YYY80VzXX0XX2692200lYY0YY1592200wXX,YYY(AARAD.5)BB2500 Y = A*YCHNG/XCHNG^2*X^2 + B*YCHNG/XCHNG*X + C*YCHNG, SEE 420YAAX2BBXCC XXX13ROUTINE USED TO GRAPH THE EQUATIONS*7:X135134]4 EQUATIONS FOR PARABOLASo>PARAB12220H Y = (-B*YCHNG/XCHNG +&- (B*YCHNG/XCHNG)^2 - 4*A*YCHNG/XCHNG^2*(C*YCHNG - X)^.5) / (2*A*YCHNG/XCHNG^2) SEE 470 & 480RRADCCDD(XCHNG:XCHNG10XCHNGD"FOR BETWEEN THE MARKS ON THE Y-AXIS?"^YCHNG:YCHNG10YCHNGh:21"THE NO. OF UNITS BETWEEN MARKS ON THE""X-AXIS = ";10XCHNG;" AND ON THE Y-AXIS = ";10YCHNG:31:"GRAPHING":SCND2:# E UNIT. DO YOU"1V"WANT THIS CHANGED? (Y/N)"9[Y$J`Y$"Y"1150[eY$"N"1140tj"TRY AGAIN!":1115tXCHNG10:YCHNG10:1210~:21"HOW MANY UNITS WOULD YOU LIKE TO ASSIGN""BETWEEN MARKS ON THE X-AXIS? ";::"RETURN": EQUATIONS USED SCND21210+ ::3K 0,80269,80:135,0135,159[ Y015910t X130140:X,Y:X,Y X526910 $Y7585:X,Y:Y,X .21 8SCND21210 B"CURRENTLY EACH MAJOR MARK ON BOTH THE"L"X-AXIS AND Y-AXIS ARE ONCHNG:CCCYCHNG 2000:  FOR X = AY^2 + BY + Cc 23:"X = ";A$;"Y^2 + ";B$;"Y + ";C$ AABYCHNGXCHNG:BB2AYCHNGXCHNG2 CC(BYCHNGXCHNG)2:DD4AYCHNGXCHNG2:EECYCHNG 2000  SUBROUTINE TO DRAW AXIS FOR ALLESS ";::"RETURN";::" WHEN DONE.":2557 JA$,B$,C$G TF$A$:4000[ ^AF:F$B$:4000o hBF:F$C$:4000w rCF |1000 PARAB2450  FOR Y = AX^2 + BY + C 23:"Y = ";A$;"X^2 + ";B$;"X + ";C$ AAAYCHNGXCHNG2:BBBYCHNGX2 + BY + C"- "3 OOPS! NEITHER OF THESE"9 PARAB$M PARAB(PARAB$)e PARAB300,300,3000| ::"TRY AGAIN!" SCND2āI11000:I::60 170 ,:11:200:SCND2Ģ21 6"WHAT IS THE VALUE OF A, B, AND C IN") @"THAT ORDER? PRON IS A"7 P"PARABOLA, IT CAN BE WRITTEN IN THE FORM"a Z"OF THE FOLLOWING. INDICATE WHICH:"t d::"NOTE:": n11:7:"X^2 IS THE COMPUTER'S WAY OF" x"WRITING 'X SQUARED'.": I11000:I:255 "1 Y = AX^2 + BX + C" "2 X = AY^F( ROUTINE TO GRAPH A PARABOLA8 START150e::"THE PROGRAM GRAPH CHECK IS NEEDED""FIRST. I'LL LOAD IT NOW.":(I12000:I:(4);"RUN GRAPH CHECK"2:7:200<SCND2Ģ21:255:140 F" IF THE GRAPH OF YOUR EQUATI           # ""SACRAMENTO, CALIFORNIA 95821"4 -X12000:XH 2:D$;"BRUN EZ"e d COLLECTED BY TED PERRYR3000@ SUBROUTINE TO ACCEPT FRACTIONAL VALUES OF INPUTOI1(F$)f(F$,I,1)"/"ĂIxI(F$)4060F(F$)4120N$(F$,I1)NUM(N$)D(F$)ID$(F$,D)DEN(D$)FNUMDEN D CHAIN, A520"$520"CIRCLE"Ut ROUTINE TO CALL UP ELLIPSE PART OF PROGRAMt~:22:"ONE MOMENT PLEASE"(4);"BLOAD CHAIN, A520"520"ELLIPSE"<:21::"SORRY BUT THIS PART OF THE PROGRAM":" ISN'T DONE YET.":FI11000:I::\ 520"PARABOLA"I ROUTINE TO CALL UP HYPERBOLA PART OF PROGRAMh :22:"ONE MOMENT PLEASE" (4);"BLOAD CHAIN, A520" 520"HYPERBOLA" ROUTINE TO CALL UP CIRCLE PART OF PROGRAM :22:"ONE MOMENT PLEASE"(4);"BLOAOICE:" CHOICE$) CHOICE(CHOICE$)L CHOICE50,3400,3500,3600,3700a :"TRY AGAIN!"& SCND2āI11000:I:30200 3070H ROUTINE TO CALL UP PARABOLA PART OF PROGRAMM :22:"ONE MOMENT PLEASE"R (4);"BLOAD CHAIN, A520"" "THANK YOU; END OF PROGRAM."3 I13000:I; :c ALLOWS FOR CHOICES OF GRAPHSm :10 SCND2ė:21 "1 LINE 2 PARABOLA 3 HYPERBOLA" "4 CIRCLE 5 ELLIPSE" SCND23070 :"TYPE THE NUMBER OF YOUR CH" 2 N$7 N$"N"2700+< N$"Y"2630DA "TRY AGAIN!":2610NF :21zP "DO YOU WANT IT ON THE SAME AXES WITH"Z "THE OTHER GRAPH(S)? (Y/N)"d N$i N$"N"SCND0:::3000n N$"Y"3000s "TRY AGAIN!":2660x 3000 ::12/XCHNG*X+B*YCHNG, SEE 430'pYAAXBB4 XXX135A YYY80W XX0XX2692550m YY0YY1592550x XX,YY X 23:31:" " 19::"'RETURN' TO CONTINUE";A$: :21 "DO YOU WANT ANY MORE GRAPHS DRAWN?"( "(Y/N)HING":SCND2:B ROUTINE USED TO GRAPH THE EQUATIONSI7YX135134x4 EQUATIONS FOR LINES>LINE22150H Y = (C*XCHNG*YCHNG-A*X*YCHNG)/(B*XCHNG), SEE 285.RY(AABBX)CC\LINE12500f Y = M*YCHNGTHE X-AXIS? ";::"RETURN":7XCHNG:XCHNG10XCHNGc"FOR BETWEEN THE MARKS ON THE Y-AXIS?"}YCHNG:YCHNG10YCHNG:21"THE NO. OF UNITS BETWEEN MARKS ON THE""X-AXIS = ";10XCHNG;" AND ON THE Y-AXIS = ";10YCHNG:31:"GRAPH THE"5L"X-AXIS AND Y-AXIS ARE ONE UNIT. DO YOU"VV"WANT THIS CHANGED? (Y/N)"^`Y$oeY$"Y"1150jY$"N"XCHNG10:YCHNG10:1210t"TRY AGAIN":1120~:21"HOW MANY UNITS WOULD YOU LIKE TO ASSIGN""BETWEEN THE MARKS ON SUBROUTINE TO DRAW AXIS FOR ALL EQUATIONS USEDE SCND21210P ::3p 0,80269,80:135,0135,159 Y015910 X130140:X,Y:X,Y X526910 $Y7585:X,Y:Y,X .21 8SCND21210B"CURRENTLY EACH MAJOR MARK ON BOT |F$B$:4000 BF" 1000@ 23:"Y = ";M$;" X + ";B$` AAMYCHNGXCHNG:BBBYCHNGj 2000  FOR X = C (B=0) CCC CCA D1000 NXXCXCHNG135 X23:A"X = ";CC ]620 b7:XX,0XX,159 l25604  GYCHNG:BBAYCHNG:CCBXCHNG' "2000B , FOR Y = MX + BL 6:11\ @SCND2Ģ21 J"GIVE THE VALUE OF THE SLOPE (M) AND THE" T"Y-INTERCEPT (B) IN THAT ORDER. (PRESS " Y:"RETURN";::" WHEN DONE.)" ^M$,B$ hF$M$:4000 rMF00:I::60 120/ FOR AX + BY = C9 :11I SCND2Ģ21t "WHAT IS THE VALUE OF A, B, AND C IN" "THAT ORDER? (PRESS ";::"RETURN";::" WHEN DONE.)" A,B,C B0500 1000 23:"";A;"X + ";B;"Y = ";C AACXCHN"LINE, IT CAN BE WRITTEN IN THE FORM OF"Q Z"THE FOLLOWING. INDICATE WHICH:": d255:"1 AX + BY = C 2 Y = MX + B n"3 OOPS! NEITHER OF THESE. xLINE$ LINE(LINE$) LINE200,300,3000 ::"TRY AGAIN!" SCND2āI110 ROUTINE TO GRAPH A LINE/ START150\::"THE PROGRAM GRAPH CHECK IS NEEDED""FIRST. I'LL LOAD IT NOW.":(I12000:I:(4);"RUN GRAPH CHECK"2:9:200<SCND2Ģ21:100F" IF THE GRAPH OF YOUR EQUATION IS A"( P      1822&27,2413!&13,1524/&24,2715=&15,1727K& 27,2418c&15);"MATH SERIES"t&N03000:Nz&& %15)"HOWARD JENSEN"% >%12)"PIONEER HIGH SCHOOL":D%$J%XP%bW%g2e%l12,2911s%v11,2029%29,1220%20,1112%7%0,3937%18,1314%14,1713%13,1517%17,1415%13,1819%19,2215&13,5)"S2 (X2=";X2;")";29)"S3 (X3=";X3;")"4 P$(X3)C (P$)4ĺI 2S2)100000030)(1000000S3)1000000+ TI ^(N10)N10NN1:300S hNN1 r"TYPE 'N' TO STOP. TO SEE 10 MORE TERMS" t"(YOU'VE SEEN ";N1;"), JUST RETURN."; |Z$ Z$"N"490 1000 300  ' 1)"S1 (X1=";X1;")";10. "ENTER A, THE CENTER OF THE INTERVAL";5 A^ "ENTER 3 VALUES OF X : X1, X2, X3";l X1,X2,X3v "1000 ,CN1N /T1CN(X1A)N:S1S1T1 2T2CN(X2A)N:S2S2T2 5T3CN(X3A)N:S3S3T3% J2)(1000000S1)100000016)(1000000 SEE" A; F"THAT CONVERGENCE IS FASTER FOR VALUES OF"f P"X NEAR A. CN IS CURRENTLY GIVEN BY"o d300 n"TO CHANGE CN, TYPE LINE 300 AS FOLLOWS:" } " 300 CN = ..." "TYPE RUN 200 TO CONTINUE." N1 S10:S20:S3K 6"THIS PROGRAM COMPUTES PARTIAL SUMS OF A"<i"POWER SERIES OF YOUR CHOICE. YOU MAY"o#("CHOOSE THE CENTER A OF THE INTERVAL OF"-2"CONVERGENCE AND 3 VALUES OF X AT WHICH"7 <"TO COMPUTE PARTIAL SUMS. YOU WILL    90279,90:140,0140,159$60$70,5180,80C$90,160180,80U$180,80260,5[$d$(6)$"========================================"$:$19)"SLOPES"$::$"========================================"$:21)"BY"$M AGAIN OR KEY TO RETURN TO MENU.";:16368,0I#Z$:(Z$)13Ĭ\#(Z$)27906v#104,8:103,1:2048,0#:(4);"RUN MENU":##3#1,90279,90:140,0140,159#6#1,120180,0#1,150220,0###3$1,YED WORKING WITH YOU":A$;", AND I AM LOOKING FORWARD":"TO SEEING YOU AGAIN.""z:"NOW LEAVE ME ON AND RETURN TO YOUR CLASSAND WORK ON THE ASSIGNMENT GIVEN YOU.""((37)5)"10);"GOOD BYE ";A$;"."5#23:"PRESS THE KEY TO RUN PROGRAE SLOPES ARE 3/5 AND -5/3 WHICH ARE OPPOSITE RECIPROCALS."B!RK!W865!\"THAT'S RIGHT ";A$;". THE SLOPES":"ARE 3/5 AND -5/3 WHICH ARE OPPOSITE RECIPROCALS."!a40::2!f:"THIS COMPLETES TODAY'S LESSON ON SLOPE."!kN"p"I HAVE ENJOLAR." 40::28 %"ARE THESE LINES PERPENDICULAR?"@ *:_ /"LINE 1: (2,6) AND (7,3)" 4"LINE 2: (-3,1) AND (O,6)" 9: >(37):"ANSWER EITHER Y OR N =>"; @Q$:Q$""830 C H(Q$)89860";16368,0P$:P$""755 "YOU CAN ALSO USE SLOPE TO TELL IF LINES ARE PERPENDICULAR."O40:::2"IT TURNS OUT ";A$;", THAT":"IF THE SLOPES OF THE TWO LINES ARE OPPOSITE RECIPROCALS, THEN THE LINES WILL BE PERPENDICULAR.":B"IN OTHER WORDS--IF THE :"SLOPES ARE DIFFERENT AND THE LINES ARE NOT PARALLEL. LINE 1 HAS A SLOPE OF 2 AND LINE 2 HAS THE SLOPE 1/2."z670:"GOOD, THE SLOES ARE 2 AND 1/2, SO THE LINES ARE NOT PARALLEL.":"YOU ARE DOING WELL, ";A$40::2950:24@RALLEL.""X"HOW ABOUT THESE?":D]"LINE 1: (11,-4) AND (17,8)"eb"LINE 2: (-5,-2) AND (7,4)"mg:l(37):"ARE THESE LINES PARALLEL? (Y/N) =>";p16368,0qW$:W$""620r(W$)78650s(W$)89620q{:"SORRY ";A$;", THE"PAUSE12000:PAUSE $ 21J "TO DO ANOTHER GRAPH, TYPE 'GO'"T ANS$f ANS$"GO"10l J,78J,82 J J0150S0 138,J142,J7 J> 1N TT0T1DTZ &XF(T)f 0YG(T)p :XSXz DYSY NSXX140 XSY80Y b(X)139ī650 l(Y)79ī650 vSX,SYSX1,SY T 400 PAUSE12000:PAUSE 410  6# @"TYPE 'RUN 400' TO START) J/ hH F(T)5(T)(5T)a G(T)5(T)(5T)j T00u T16.3~ N15 S10 WT1T0 DTW(5N) TT0  2 0,80279,80 140,0140,159:141,159141,0 J0270S  AND n"SCALE FACTOR."# x::M "HIT 'RETURN' FOR MORE INSTRUCTIONS.e (16384)127ī140s 16368,0{ : "THE CURRENT VALUES ARE" 400,450 "ENTER THE DESIRED FUNCTIONS AND "VALUES ON THE APPROPRIATE LINE NUMBERSm 2"THIS PROGRAM WILL PLOT A GRAPH]("WHEN X AND Y ARE GIVEN BY PARAMETRIC2"EQUATIONS X = F(T), Y = G(T)."<::F"YOU CAN CHOOSE THE FOLLOWING"P:Z"X,Y,INITIAL T VALUE,LAST T VALUE, d"NUMBER OF POINTS PLOTTED,    z#???Xñ   Ƞ ӠӠԠ ح٠ҠӠ$Р ӠҠӠŠ  ŠŠ Šӱ ӲҠӠؠ Ӡ"ŠϠҠ ɭȠڠŠΠҠ ٽؠٽؠѤٽؠΠRE DONE."# 3,4 '2E FORM: M,N FIRST,FOLLOWED"!L"BY EACH ROW OF COEFFICIENTS AND THE"R~"CORRESPONDING CONSTANTS. CHANGE THE""DATA STATEMENTS BEGINNING AT 6000.""THEN TYPE 'RUN'."G$G$"YES"109999 (#"WE AlG$"Y "7040+vPAUSE11500:PAUSE1`"TO DO ANOTHER PROBLEM WITH STORED DATA,"f"TYPE 'YES'. IF YOU WANT TO USE YOUR""OWN DATA, TYPE 'NO', PRESS RETURN,""THEN TYPE 'LIST 6000,6100'""TO SEE TH,2,6,2,-4,0,0,6,0,2,-4,-6,-18,0*p 4,5 Bz 10,2,3,4,5,10 W 6,7,8,9,10,200p 11,12,13,14,15,300 16,-17.34,18,19,20,400  3,4 2,3,6,1,5 20,30,60,5,19 10,15,8,16,5X"HAVE YOU SEEN ENOUGH? (Y OR N)"bG$ 1 , 1, 1,0 ,0 4,4,2,3,-1,1,10,1,5,1 ,-2,25,-1,2,2,-3,15,3,1,-3,4 ,-5  4,3,2,4,7,10,-3,2,6,20,6,-2,7,30,8,4,1,40  5,5,1,1,-2,1,3,1,3,2,-4,-3,-9,3,2,-1,2,2,6g :936("AMG GRADES 7-12": D$(13)(4)A5^"GRAPHING AND PLOTTING":"EDUCATIONAL PROGRAMS FOR THE APPLE"15"COLLECTED AND DISTRIBUTED BY": :"APPLE FOR THE TEACHER & ABC SOFTWARE "!"2331 RAINBOW AVE" AXES SETUP%:: CLEAR THE SCREEN;:6: BLUE LINESU0,80279,80: X-AXISq140,0140,159: Y-AXIS X-AXIS SCRIBE MARKS$I1313:14010I,7814010I,82:I. Y-AXIS SCRIBE MARKS8I77:138,8010I142,8010I:IB7DIANDEGK8X(RADIAN)RXA:Y(RADIAN)R67YA:30ADEGXFL0:1:K3.14180gDEG0360xRADIANDEGKX(RADIAN)RXL:Y(RADIAN)R67YL:30DEG24:"DO YOU WANT ANOTHER EXAMPLE (Y OR N)";:Z$Z$"Y"11  YJ6XAXL:YAYL:XBXK:YBYK:XCXJ:YCYJ:J910:342TLI1XL1XA:YLYA:440rLI2XLXA:YL1YA:440LI3XLYA:YLXA:440XL1YA:YL1XAFL0:5:22:" PRE-IMAGE (ORANGE) IMAGE (GREEN)"K3.14180DEG0360 RA:XAX3:YAY3:385!~X3X1ī390=XCX3:YCY3:XAX1:YAY1MXXCXA.2qY(YCYA)(XCXA)(XXC)YC:30}X:397Y3Y1YCY1:YAY3YYCYA.2XX3:30YJ910J90:500FL0:1:X1XL:Y1YL:X2XK:Y2YK:X3XJ:Y3XX1:30dY=hFL0:X2X3XBX3:YBY3:XCX2:YCY2:365MjX2X3ī370ikXBX2:YBY2:XCX3:YCY3ymXXBXC.2nY(YCYB)(XCXB)(XXB)YB:30oX:380rY2Y3YBY3:YCY2tYYBYC.2vXX2:30xY|FL0:X3X1XCX1:YCY10:5:X1XA:X2XB:X3XC:Y1YA:Y2YB:Y3YCYU22:" PRE-IMAGE (ORANGE) IMAGE (GREEN)"|VX1X2XAX2:YAY2:XBX1:YBY1WFL0XX1X2ī350ZXXAXB.2\Y(YBYA)(XBXA)(XXA)YA:30]X:360^Y1Y2YAY2:YBY1`YYAYB.2 bLI1310@3XL1XA:YLYA:XK1XB:YKYB:XJ1XC:YJYC:340N6LI2320;XLXA:YL1YA:XKXB:YK1YB:XJXC:YJ1YC:340@LI3330EXLYA:YLXA:XKYB:YKXB:XJYC:YJXC:340JXL1YA:YL1XA:XK1YB:YK1XB:XJ1YC:YJ1XC)TFLXXA:30Y " FL0:1MXLXKVXL:XLXK:XKV:VYL:YLYK:YKV]XLXKī285mXXLXK.2Y(YKYL)(XKXL)(XXL)YL:30X:500500YLYKVYL:YLYK:YKV"YYLYK.2%XXL:30'Y*500,FI2404 1YA:YL1XA:XK1YB:YK1XBVFL0:5:22:" PRE-IMAGE (ORANGE) IMAGE (GREEN)"XAXBVXA:XAXB:XBV:VYA:YAYB:YBVXXAXB.2XAXBī258Y(YBYA)(XBXA)(XXA)YA:30X:265YAYBVYA:YAYB:YBVYYAYB.2 200 FL0< 21:" REFLECTING LINE (PURPLE) IS Y=-X"Q X13.913.9.1` Y1X:30g Xu FI1300 LI1XL1XA:YLYA:XK1XB:YKYB:240 LI2XLXA:YL1YA:XKXB:YK1YB:240 LI3XLYA:YLXA:XKYB:YKXB:240XL1140,0140,159* LI1āH12000:H:200c LI2Ģ21:"REFLECTING LINE(PURPLE)=HORIZONTAL AXIS"z LI2ē0,80279,80 LI2āH12000:H:200 LI4190 FL0:21:" REFLECTING LINE (PURPLE) IS Y=X" X13.913.9.1 YX:30 X:THE LINE Y=-X"::; "PLEASE CHOOSE 1, 2, 3, OR 4:";:LIj LI5ĺ"YOU MADE AN INVALID CHOICE.":129| P$"Y"İ1000 P$"N"ĉ:: 21:2 GRAPHING THE REFLECTING LINE LI1Ģ21:"REFLECTING LINE(PURPLE) = VERTICAL AXIS" LI1 1, 2, OR 3:";:FI$ n:FI1İ30004 pFI2İ3100D qFI3İ3200x tFI4ĺ"YOU HAVE MADE AN INVALID CHOICE.":101 x:"THE POSSIBLE LINES OF REFLECTION ARE:" |:"1. THE VERTICAL AXIS" ~"2. THE HORIZONTAL AXIS":"3. THE LINE X=Y" "4. Y 2(XN0)(XN279)ı/ <(YN0)(YN159)ıE FFL0ēXN,YN:FL1S PXN,YN:z d DECIDE ON FIGURE TO BE REFLECTED e f"THE FIGURES THAT CAN BE REFLECTED ARE:" g:"1. A SEGMENT":"2. A TRIANGLE" h"3. A CIRCLE":: i"PLEASE CHOOSE_ LINE REFLECTIONS  :P"THIS PROGRAM WILL REFLECT A FIGURE OVER ""A LINE DRAWN ON THE COORDINATIZED PLANE":::"DO YOU WANT THE AXES DISPLAYED (Y OR N)?";P$:100 GRAPHING OF FUNCTION ROUTINE (XN14010X:YN8010     ٽٽѤٽΠTHE RADIUS MUST BE BETWEEN .5 AND 7.5."- W "GIVE THE LENGTH OF THE RADIUS:";:R] )CENTER AND"3 " THE LENGTH OF THE RADIUS.":k "THE FIRST COORDINATE MUST BE BETWEEN -13 AND 13."q  "THE SECOND COORDINATE MUST BE BETWEEN -7 AND 7.":  "GIVE THE COORDINATES OF THE CENTER:";:XA,YA ' :"THE LENGTH OF DINATES OF THE SECOND"0; " VERTEX:";:XB,YBY? "GIVE THE COORDINATES OF THE THIRD"s@ " VERTEX:";:XC,YCyD  CIRCLE-CENTER AND RADIUS :"YOU HAVE CHOSEN A CIRCLE.": "NOW YOU MUST CHOOSE THE COORDINATES "  " OF THE E THE COORDINATES OF"6# " THE THREE VERTICES."::p& "THE FIRST COORDINATE MUST BE BETWEEN -13 AND 13.":+ "THE SECOND COORDINATE MUST BE BETWEEN -7 AND 7.":0 "GIVE THE COORDINATES OF THE FIRST"1 " VERTEX:";:XA,YA: "GIVE THE COORUST BE BETWEEN -7 AND 7.":^ "GIVE THE COORDINATES OF THE FIRST ENDPOINT:";:XA,YA: "GIVE THE COORDINATES OF THE SECOND ENDPOINT:";:XB,YB  TRIANGLE-COORDINATES! :"YOU HAVE CHOSEN A TRIANGLE":" "NOW YOU MUST CHOOS gW'  `^ :F Y %^LǏLZ^[_\Z][`1''I8Mt_=gH?J QVQT_ɕ%[^ZZ\[]^Z_[ 0W Г J1  @)ȹ@)ȹ@) q P^ɠ 0   qL MW'WП < XX QLiLLs4       DECIDING ON COORDINATES OF ENDPOINTS OF THE SEGMENT\ :"YOU HAVE CHOSEN A SEGMENT": "NOW YOU MUST CHOOSE THE COORDINATES OF" "THE TWO ENDPOINTS.":: "THE FIRST COORDINATE MUST BE BETWEEN -13 AND 13.": "THE SECOND COORDINATE M***************- * *K  * SAN MATEO COUNTY *i  * OFFICE OF EDUCATION *  * & *  * COMPUTER-USING *  * EDUCATORS *  * *  * SOFTSWAP *[! MIDPOINT SUMMER 1981. h PROGRAM HELPS USER UNDER-STAND AND USE THE MIDPOINTx FORMULA.~ APPLE II  HOWARDS JENSEN  PIONEER HIGH SCHOOL REVISION BY C.EDWARDS ********NES ACTIVATED BY LINE 3859W SET UP FOR SILENTYPELY(4);"PR#1":s\12529,128: MAKE UNI-DIRECTIONALa12524,0: MAKE BLACK ON WHITEf12525,32: SET HI-RES PAGE 1p(17): PRINT ITu(4);"PR#0"z9A1A1A39A396 BLANK OLD POSITIONG0:A1,B1:3_ PLOT NEW POSITIONh A,Bq630 A7A:BB19240* CHANGE SCALE TO REFLECT HGR (280 BY 192)4::> ASYMPTOTE DRAWERHH,0H,191:7:R HARD COPY ROUTI (40X60)(b USING L R U D AND FBl:3:20,20:A20:B20JvA$XA1A:B1BoA$"U"BB1:710A$"D"BB1:710A$"L"AA1:710A$"R"AA1:710A$"F"800 KEEP ON THE LO-RES SCREENB1B1B39B3DEF FNNUM(X)=(X-1)*(X+2)6"70 DEF FNDEN(X)=X*(X-7)@"RUNT::"REMEMBER:&"60 DEF FNNUM(X)=";::" LEGAL BASIC EXPRESSION0:"70 DEF FNDEN(X)=";::" LEGAL BASIC EXPRESSION::"RUN":DX POSITIONING THE ORIGIN ON THE SCREENENTS OF POLYNOMIALS)V"DEFINE YOUR FUNCTION IN TERMS OF NUMERATOR AND DENOMINATOR."FOR EXAMPLE, IF YOU WISH TO GRAPH THE FOLLOWING:" (X-1)(X+2)"Y = ----------" X(X-7):"YOU WOULD TYPE THE FOLLOWING:":"60 OTTOM QUARTER OF THE GRAPH*wI13000:>|16302,0:A$:OA$"P"İ850W:"DO YOU WANT TO SHIFT THE ORIGIN OR CHANGE THE SCALE?";A$(A$,1)"Y"90:"DIRECTIONS FOR RATIONAL FUNCTIONS":"(RATIONAL FUNCTIONS AR QUOTI350 1YNUM(X)* 6YNUM(X)D:VBYSw @ TRANSFORM THE REAL Y VALUE TO HGR AND SEE IF IT IS STILL ON THE SCREEN JV191V0350 TH,V ^H c h"HIT P FOR HARD COPY i"ANY OTHER KEY TO CONTINUEr THIS POKE WILL DISPLAY THE B:A2,VA2,V:% ACTUAL GRAPHING2 H0279b  TRANSFORM THE HGR COLOR TO THE REAL VALUEz X(HA)S:DDEN(X)  INSERT SPECIAL CHECKS FOR FORBIDDEN VALUES HERE WITH :GOTO350 " DRAW THE VERTICAL ASYMPTOTES IF NECESSARY ,D0Ē3:830:ARK ON THE AXIS FOR EACH UNIT"* :7V AXIS, WITH THE REAL ORIGIN AT (A,B)p 0,B279,B:A,0A,191 HASH MARKS EEVERY UNIT ON THE AXIS HA279S:H,B2H,B2: HA0S:H,B2H,B2: VB191S:A2,VA2,V: VB0SS ALLOWS THE USER TO SELECT WHICH AREA OF THE GRAPH TO VIEW] x620: TO POSITION THE ORIGINw S WILL BE THE SCALE DETAIL INCREASES AS S INCREASES 21:"AFTEER THE BOTTOM HALF OF THE GRAPH IS FINISHED, HIT ANY KEY."! "THERE IS A HASH M> IF YOU HAVE NO DENOMINATOR FUNCTION~ Z:"THERE ARE 280 HORIZONTAL DOTS ON THE SCREEN. HOW MANY DOTS/UNIT DO YOU WANT?";S d21:"INDICATE THE INTENDED LOCATION OF THE ORIGIN BY MOVING THE CURSOR WITH THE L R U D KEYS. FINISHED = F"; n THI % GRAPHING RATIONAL FUNCTIONS : BY RON CARLSONK MICRO 31:7f( A FEW SIMPLE MODS BY- GEORGE DORNER, HARPER COLLEGE2<440: THE NUMERATOR FUNCTION GOES HEREF THE DENOMINATOR FUNCTION GOES HERE% P DEF FN DEN(X)=1 >     E"Y(1) =";*FZ$:Z$""Ģ(37):325LG90:FLAG1Ģ(37):958:325XHB(Z$)gJ"X(2) =";KZ$:Z$""Ģ(37):330L90:FLAG1Ģ(37):958:330MC(Z$)O"Y(2) =";PZ$:Z$""Ģ(37):335Q90:FLAG1Ģ(37):958:335RND (11+-3)/2 = 4"'8,8);"SO MIDPOINT IS (6,4)."x6:"NOW YOU GIVE ME TWO POINTS AND I'LL FIND THE MIDPOINT.";"PRESS THE KEY AFTER EACH POINT."@"X(1) =";AZ$:Z$""Ģ(37):320B90:FLAG1Ģ(37):958:320CA(Z$)"26);"( (X(1)+X(2))/2,(Y(1)+Y(2))/2 )"::j"========================================"s900| :2"HERE'S AN EXAMPLE:""IF A =(5,11) AND B=(7,-3), THEN THE MID-POINT OF SEGMENT AB IS:""5)"(5+7)/2 = 6 AR TO FIND A MIDPOINT, YOU MUST FIRST ADD THE X-COORDINATES AND DIVIDE BY TWO AND THEN ADD THE Y-COORDINATES AND DIVIDE BY TWO.":"IN OTHER WORDS, WE COULD USE THE FORMULA:"((37)3)"======================================== WELL, YOU LOOK LIKE SOMEONE ELSE I KNOW........I'M STILL GLAD TO SEE YOU."V 180 :"I'M GLAD YOU CAME BACK TO SEE ME, ";A$ :"TODAY'S LESSON IS ON FINDING THE MIDPOINT OF A SEGMENT." 900 665 :2"IN ORDEZ1ĂZ aFLAG1:* x:910::590::46 }A$(20)d "HELLO, I'M APPLE.":"WHAT'S YOUR NAME"; A$:A$""(A$)11ė:4:130 :"HAVEN'T I WORKED WITH YOU BEFORE?"; 16368,0 B$:B$""145 B$"Y"170 B$"N"144M :"OHAY BE COPIED*+  *FOR EDUCATIONAL USE &*I *MAY NOT BE SOLD.COPY-*g ! *RIGHT 1981 CUE,INC * " *********************** P16384:120 ZFLAG0 [Z1(Z$):Z1$(Z$,Z,1) \(Z1$)48(Z1$)5795 ]Z: _Z1$"."ĂZ `Z1$"-"  * *;  * 333 MAIN STREET *Y  * REDWOOD CITY *w  * CA 94063 *  *(415)364-5600 EX 4401*  * *  * *  ***********************  *PROGRAM M ROGER MALCOLM( KEWANEE HIGH= 1101 E. 3RD STU& KEWANEE, IL 61443[0 a: gD mN sX RALL EQUATIONS USED ::3= 0,80269,80:135,0135,159M Y015910f X130140:X,Y:X,Yv X526910 $Y7585:X,Y:Y,X . COMMENTS AND SUG- GESTIONS ARE WEL- COME. MAIL TO  M ]:22:"ONE MOMENT PLEASE"> b(4);"BLOAD CHAIN, A520"O l520"CIRCLE"  ROUTINE TO CALL UP ELLIPSE PART OF PROGRAM :22:"ONE MOMENT PLEASE" (4);"BLOAD CHAIN, A520" 520"ELLIPSE"  SUBROUTINE TO DRAW AXIS FOR 22:"ONE MOMENT PLEASE"5 (4);"BLOAD CHAIN, A520"H 520"PARABOLA"  ROUTINE TO CALL UP HYPERBOLA PART OF PROGRAM :22:"ONE MOMENT PLEASE" (4);"BLOAD CHAIN, A520" 520"HYPERBOLA" X ROUTINE TO CALL UP CIRCLE PART OF PROGRACHOICE300,400,500,600,700/ :"TRY AGAIN!"M SCND2āI11000:I:130V 180 , ROUTINE TO CALL UP LINE PART OF PROGRAM 1:22:"ONE MOMENT PLEASE" 6(4);"BLOAD CHAIN, A520" @520"LINE"  ROUTINE TO CALL UP PARABOLA  :E OF THE GRAPH OF YOUR EQUATION?". x::255@ SCND2ė:21Q I11000:I "1 LINE 2 PARABOLA 3 HYPERBOLA" "4 CIRCLE 5 ELLIPSE" SCND2180 :"TYPE THE NUMBER OF YOUR CHOICE:" CHOICE$ CHOICE(CHOICE$) vSCND2130!START1700 :3::21Q" GRAPH CHECK"v" R.E. AND M.A. MALCOLM"(" SUMMER, 1980"21020<I13000:IF:START1::200:7P" WHICH OF THE FOLLOWING IS THE"! Z"SHAP     ;"PIONEER HIGH SCHOOL"@8);"REVISED BY CHRIS EDWARDS"QN11500.5XN^djq2140,0140,1591,90279,90I027910I,88I,92:I1,88I1,92I160ē137,I143,I:137,I1143,I1I278,88K(Z$)27586,L:(4);"RUN MENU":5N(6)eS"========================================"mX:]17);"MIDPOINT"b::g"========================================"lq20)"BY"v{14);"HOWARD JENSEN"|11):"TO CLASS AND SEND IN THE NEXT STUDENT":V:"(DON'T TURN ME OFF................."d?::::s@((37)4)D10)".....GOOD-BYE ";A$I23:"PRESS TO RUN PROGRAM AGAIN OR TO RETURN TO MENU =>";:16368,0JZ$:(Z$)13Ĭ:U2525:"SORRY ";A$;", THE X-COORDINATE IS 2"G V2540ZU2ĺ"AND ";"THE CORRECT Y-COORDINATE IS 2":"THE MIDPOINT OF AB IS (2,2)."&900::2+0"I'VE ENJOYED DOING THIS LESSON WITH YOU ";A$;". YOU SHOULD NOW RETURN"THE MIDPOINT."2:6);"A=(-1,4) AND B=(5,0)":O"THE X-COORDINATE IS ";jZ$:Z$""Ģ(37):49590:FLAG1Ģ(37):958:495U(Z$):"THE Y-COORDINATE IS ";Z$:Z$""Ģ(37):50090:FLAG1Ģ(37):958:500V(Z$) 5 BECAUSE:"-:10);"2+8=10, AND 10/2=5":Y6450O:X5ĺ"AND ";p"Y SHOULD EQUAL 6 BECAUSE:":10);"9+3=12, AND 12/2=6""THE CORRECT MIDPOINT IS (5,6)."900::2"HERE'S ANOTHER ";A$;", SEE":"IF YOU CAN FIND D (8,3).":("THE X-COORDINATE IS ";CZ$:Z$""Ģ(37):395e90:FLAG1Ģ(37):958:395sX(Z$):"THE Y-COORDINATE IS ";Z$:Z$""Ģ(37):40090:FLAG1Ģ(37):958:400Y(Z$):X5430 "SORRY, ";A$;" X =D(Z$)TYY"FOR THE POINTS (";A;",";B;") AND (";C;",";D;"),":"THE MIDPOINT IS:"c17)"(";(AC)2;",";(BD)2;")."m900::2w"NOW ";A$;", I'LL GIVE YOU":"TWO POINTS AND YOU TELL ME THE MIDPOINT." :"FIND THE MIDPOINT OF (2,9) AN141,0141,159!0,80279,800SX20:SY5BJ140270SX_$J,79J,81J1,81J1,79f.Jy8J1400(SX)BJ,79J,81J1,81J1,79LJVJ80150SY`139,J142,JjJtJ800(SY)~139,J142,JJ2 XX140XSX:WW80WSY: XX0XX279WW0WW159800M XX,WWXX1,WWT X\ 421 >"THE GRAPHS OF F, F', AND F''" R"ZEROS OF F'' ARE INFLECTION POINTS OF F"   ----PLOT AXES AND MARK UNITS  3 140,0140,1590ZG(X)$ :XX140XSX:ZZ80ZSYE DXX0XX279ZZ0ZZ159600X NXX,ZZXX1,ZZ_ XXe bm l21 v"THE GRAPHS OF F AND F'" 22 "THE ZEROS OF F' ARE THE EXTREMES OF F" PAUSE12500:PAUSE 2 XAB(2SX) WH(X)YOU WANT?"# "ENTER IT AS A,B.", A,B3 5E XAB(2SX)Q YF(X)l XX140XSX:YY80YSY XX0XX279YY0YY159500 XX,YYXX1,YY X  21 "THE GRAPH OF F" PAUSE11500:PAUSE !1 &XAB(2SX) LE SY MAY BE CHANGED FOR"G (" CONVENIENCE BY LISTING LINE 1040 AND"x *" RE-TYPING IT. CHOOSE MULTIPLES OF 5.": +"TYPE 'RUN 300'": ,F(X)X33X24X12 @G(X)3X26X4 JH(X)6X6 1000 21 "WHAT X-INTERVAL DO  " 300 DEF FN F(X) ="8 " 320 DEF FN G(X) = "T " 340 DEF FN H(X) ="Z ~ " INCLUDING THE APPROPRIATE" " RULES FOR EACH." " NOTE: G = F' AND H = F''"  $" THE HORIZONTAL SCALE SX AND THE " &" VERTICAL SCAd.n"THIS PROGRAM DRAWS A GRAPH OF A"Ux"FUNCTION F(X) AND GRAPHS OF THE""DERIVATIVES F' AND F'' ON THE SAME""AXES TO ILLUSTRATE HOW THEY ARE""YOU MUST DEFINE F, F', AND F'' AT""LINES 300, 320, AND 340 BY TYPING:"     C1(A(1,1)A(2,2)):C0A(1,1)A(2,2)A(1,2)A(2,1)D7000g8 -- COEFFS OF CP FOR SIZE 3 BC0A(1,1)A(2,2)A(3,3)A(1,2)A(2,3)A(3,1)A(1,3)A(3,2)A(2,1)A(1,3)A(3,1)A(2,2)A(1,2)A(2,1)A(3,3)A(2,3)A(3,2)A(1,1)HLC1A(1,1)A(2,RETURN AFTER EACH ENTRY."'zI1SIZE5J1SIZE<EIA(I,J)En -- SS = ORIGINAL A TO BE SAVED|SS(I,J)EJI 3,2,2,-4,2,3,2,-1,1,1,2,-1,2,2,2,-1SIZE46300SIZE36200-- COEFFS OF CP FOR SIZE 2C21I).001)7N)"*"I#1--SWITCH<J1NMH(J)A(K1,J)aA(K1,J)A(K2,J)rA(K2,J)H(J)yJHOLDB(K1)B(K1)B(K2)B(K2)HOLDp -- ENTER MATRIX As"ENTER MATRIX A BY ROWS, PRESSING"tu"0A(I,J))1004120,D(I,J)(A(I,J))3J:"I_,--MATRIX D IS ROUNDED FORM OF Am^7N)"*"xhI1MrJ1N|K7J6K)D(I,J);J(B(I))9N542557N)"* ";(100B(I).001)10042607N)"* ";(B( I1M IPR3240& DA(I,PC)1 T1NM E(I,T)E(I,T)E(PR,T)DT T` JPCN| A(I,J)A(I,J)A(PR,J)D J B(I)B(I)B(PR)D I --PRINT--ROUNDINGI1MJ1N(A(I,J))994100 D(I,J)(10CTR(LL,I,YY)X(I)0I#]K1N._X(K)05bK=gYYIlWW14XqCODE(WW)0`vWWu{KKKKNU(KK1)17288 --PIVOT DA(PR,PC) JPCN& A(PR,J)A(PR,J)D0 J2 T1N3 E(PR,T)E(PR,T)D4 T5 B(PR)B(PR)D RPRIPC1115X(I)0CODE(I)11790ICODE(I)11750SRR1`LI1NzS(I)S(I)A(R,L)X(L)LX(I)B(R)S(I)I400015I1N"X(";I;") = ";(100X(I))100!I#&I1N+VEY1Z3MM1=6"NOW TYPE THE SUBSCRIPT I AND THE VALUE"[@"X(I) OF AN ASSIGNMENT."gJI,X(I)uTCODE(I)1|^Y--SOLVINGT1NS(T)0TPCN1736LPC1NS(PC)S(PC)A(PR,L)X(L)LX(PC)B(PR)S(PC)ONS. LOOK AT THE ARRAY AND"I"DECIDE HOW MANY ARBITRARY ASSIGNMENTS"q""CAN BE MADE. ENTER THIS NUMBER."x'Z~(,NU(LL)Z-"THE NUMBER OF LINEARLY INDEPENDENT"."EIGENVECTORS IS ";Z;". LET'S COMPUTE ";Z;"."/0YY1Z1 4000 = "ENTER THE ROW AND COLUMN OF THE PIVOT."H PR,PCR 3000X b 4000k &350q  "WE PROCEED TO FIND SOLUTIONS."  --CHOOSE PARAMETERS 10 958  "THE SYSTEM HAS INFINITELY MANY""SOLUTI"IS THE AUGMENTED MATRIX IN"" cM h"REDUCED ROW ECHELON FORM? (Y OR N)";U rF$f |F$"Y"1200l  "IS A ROW INTERCHANGE NEEDED? (Y OR N)"; ANS$ ANS$"N"500  "WHICH ROWS DO YOU WANT TO INTERCHANGE?" K1,K2 50007N)"*" I "12G &"PRESS RETURN WHEN YOU ARE READY TO BEGIN"g )"THE SOLUTION PROCEDURE.";o *G$u , @"WE NOW PERFORM ELEMENTARY ROW" J"OPERATIONS ON THE AUGMENTED MATRIX." KPAUSE11000:PAUSE O Q4000 T W ^RATED" 7 "FROM THE COEFFICIENTS, PRESS RETURN"= E K$K ] NSIZE:MSIZEk 7N)"*"v I1M J1N JIA(I,J)SS(I,J)EV(LL):225 A(I,J)SS(I,J) K7J6 K)(100A(I,J))100; J 7N)"* ";B(I)  ! "SIZE # $' %6000- (M -"WE NOW SOLVE THE SYSTEM "S 2k 7" (A - TI)X = 0"q < A"WHERE T IS THE EIGENVALUE ";EV(LL);"." D "TO SEE THE AUGMENTED MATRIX OF THE"  "SYSTEM, WITH THE CONSTANTS SEPA; LL0KK1%I1107X(I)0:S(I)0>IK LL040u"THIS PROGRAM FINDS EIGENVALUES AND"{"AND CORRESPONDING EIGENVECTORS OF A ""MATRIX A OF YOUR CHOICE. ENTER THE ""NUMBER OF ROWS OF A."           Y(Y$):Y3ī790M :"NO ";A$;", 3 IS HALFWAY FROM":"Y=1 TO Y=5."V805z"GOOD ";A$;", Y=3 IS CORRECT."%230,60:229,60*900/X(1)150:Y(1)804X(2)230:Y(2)409X(1),Y(1)X(2),Y(2)C H"CAN YOU TELL WHICH POINT " 740K"THAT'S RIGHT! X = 5 IS HALFWAY FROM X = 1 TO X = 9.":_190,80:189,80h900n229,40:230,4024"WHAT NUMBER IS HALFWAY FROM Y=1 TO Y=5?";16368,0Y$:Y$""770(Y$)0Y$"0"769 278,92:137,159143,159>3:150,80:230,80:149,80:229,80F24~"WHAT POINT IS HALFWAY FROM X=1 TO X=9?";16368,0X$:X$""712(X$)0X$"0"711X(X$):X5730"NO! X = 5 IS HALFWAY FROM X=1 TO X= 9.&I #&")"#&#&J#&'#&MM-#&3#&9#'20:PAUSE"M&;"R&"HERE ARE THE RESULTS IN SUMMARY FORM:"A"\&G"a&M"f&"p&"EIGENVALUE"15)"REPRESENTATIVE EIGENVECTOR""&MM1MAX"&EV(MM);"&J1NU(MM)"&15"&"(";"&I1SIZE"&(100VECTR(MM,I,J))100;"&ISIZEĺ", ";#TER EACH EIGENVALUE AND PRESS RETURN";3!CI1MAX>!EEV(I)E!FIK!HQ!Jh!M"EIGENVALUES ARE"u!RI1MAX{!\!f" ";EV(I)!p!uI!xLLLL1!yLLMAX9800!z"PRESS RETURN TO FIND EIGENVECTORS"!WW$!5"H&PAUSE115017190 RIMID- (LEMID).00000172037 7130B LEMID^ (RIMID).0000017203h 7130 #(P(MID)).017210 %"NO EIGENVALUE IN THIS INTERVAL" '7120 *"ONE EIGENVALUE IS ";MID 4EV(I)MID >I ?ANS$"N"7240&!A"EN&"HOW MANY EIGENVALUES ARE THERE";/MAXQ"ARE THEY OBVIOUS (Y OR N)";[ANS$nANS$"N"7119x7233I1MAX"ENTER THE ENDPOINTS L,R OF AN INTERVAL"LE,RIMID(LERI)2P(MID)07210 (P(MID))(P(RI)) ";C3;", C4 = ";C4+_PAUSE12000:PAUSESbP(T)C0C1TC2T2C3T3C4T4Y"SOME VALUES OF THE CHAR POLY P(T):"T1010"T = ";T,"P(T) = ";(100P(T).01)100T"PRESS RETURN TO FIND EIGENVALUES";ROOT$3,1)A(4,2)f|D8A(1,4)A(2,3)A(3,2)A(4,1)A(1,4)A(3,1)A(4,3)A(2,2)A(1,4)A(2,1)A(4,2)A(3,3)C0D1D2D3D4D5D6D7D8X -- FIND ROOTS OF CPZ["THE COEFFICIENTS OF P(T) ARE:"]^"C0 = ";C0;", C1 ";C1;", C2 = ";C2;", C3 =A(1,3)A(2,1)A(3,2)A(4,4)A(1,3)A(3,4)A(4,1)A(2,2)A(1,3)A(2,4)A(4,2)A(3,1)hD6A(1,3)A(2,4)A(3,2)A(4,1)A(1,3)A(3,1)A(2,2)A(4,4)A(1,3)A(2,1)A(4,2)A(3,4) rD7A(1,4)A(2,1)A(3,2)A(4,3)A(1,4)A(4,1)A(2,2)A(3,3)A(1,4)A(2,3)A(2)A(3,3)A(1,1)A(2,3)A(3,2)A(4,4)A(1,1)A(3,4)A(4,3)A(2,2)JD3A(1,2)A(2,1)A(3,3)A(4,4)A(1,2)A(2,3)A(3,4)A(4,1)A(1,2)A(2,4)A(4,3)A(3,1)TD4A(1,2)A(2,4)A(4,1)A(3,3)A(1,2)A(2,3)A(3,1)A(4,4)A(1,2)A(2,1)A(3,4)A(4,3)S^D5(A(2,2)A(4,4))^R6A(1,4)A(4,1)(A(2,2)A(3,3))A(1,4)A(3,1)A(4,3)A(1,4)A(2,1)A(4,2)wC1R1R2R3R4R5R6,-- COMPUTE C06D1A(1,1)A(2,2)A(3,3)A(4,4)A(1,1)A(2,3)A(3,4)A(4,2)A(1,1)A(2,4)A(4,3)A(3,2)A@D2A(1,1)A(2,4)A(4,A(2,3)A(3,2)A(4,4)oR3A(3,4)A(4,3)A(2,2)A(1,1)A(2,4)A(4,2)A(1,1)A(2,3)A(3,2)A(1,1)A(3,4)A(4,3)R4A(1,2)A(2,1)(A(3,3)A(4,4))A(1,2)A(2,4)A(4,1)A(1,2)A(3,1)A(2,3)A(1,3)A(2,1)A(3,2)R5A(1,3)A(3,4)A(4,1)A(1,3)A(3,1)I1SIZE1<JI1SIZE>FSSA(I,I)A(J,J)A(I,J)A(J,I)EPJLZIUdC2Sh-- COMPUTE C1R1A(2,2)A(3,3)A(4,4)A(1,1)(A(2,2)A(3,3)A(3,3)A(4,4)A(4,4)A(2,2))R2A(2,3)A(3,4)A(4,2)A(2,4)A(4,3)A(3,2)A(2,4)A(4,2)A(3,3)2)A(2,2)A(3,3)A(3,3)A(1,1)A(1,2)A(2,1)A(2,3)A(3,2)A(3,1)A(1,3)dVC2A(1,1)A(2,2)A(3,3)n`C31r -- FIND ROOTS OF CPt7000 -- COEFFS OF CP FOR SIZE 4C41S0I1SIZESSA(I,I)IC3S(S0 224,271515,1727&27,2418=16)"MATH SERIES"NN03000:NTZ (Z1$)13ĺ:588&2412,2911B11,2029P29,1220^20,1112e7s18,131414,171317,1417,141590,393413,181919,221513,18221527,241313,1424 IS HALFWAY FROM (1,1) TO (9,5)?"3R190,80190,60FW230,60190,60Sa900::f"THE MIDPOINT OF (1,1) TO (9,1) IS (5,3)."k900z24:"PRESS TO GO ON - TO END";16368,0Z1$:(Z1$)13(Z1$)27902M$"YES"ī162?"THANK YOU FOR YOUR ATTENTION. "EdO77J1,81J#J1390(SX)@J,77J,81J1,81J1,77GJXJ79159SYi137,J141,JpJ J790(SY)"137,J141,J#J"DO YOU WANT TO ADD MORE TERMS OR""CHANGE THE SERIES? (YES OR NO)"M$ KX0X279ī620% NYSY(Z)799 PY0Y159ī620H XX,YX1,YO lIh PAUSE13000:PAUSEo 5u {   1950   3 139,0139,159 140,0140,159 0,79279,79 J139279SX J,77J,81 J1,PI, SYMMETRIC ABOUT 0; LINE 560 IS A SQUARE WAVE. 3H(X)43P24(X)(2X)49(3X)4P(X)2P(2X)4P3(3X) 46 5139SXA,79SY139,79SY 6139,79SY139SXB,79SY 85 :I0N ?XAIDLTA2 DZF(X) IXSXX13940 A,B WIDTHBA, N(WIDTH)SX= &DLTAWIDTHNG +1000U /P3.14159 0F(X)4P(X)4(3P)(3X)4(5P)(5X)4(7P)(7X)4(9P)(9X) 1G(X)4P(X)4(9P)(3X)02 2-LINE 561 REFERS TO A SAWTOOTH WAVE OF PERIOD 2 60 DEF FN F(X) =" F "FOLLOWED BY YOUR FUNCTION RULE IN BASIC"L { "THEN TYPE 'RUN 500' AND PRESS 'RETURN'."  A(X)0  "WHAT X-INTERVAL DO YOU WANT?"  "(ENTER A,B SEPARATED BY A COMMA.)"  SX40:SY+ "BE ADDED BY EDITING LINE 560 OR BY "1 Q "RE-TYPING IT COMPLETELY."j PAUSE11500:PAUSEp y 255 "THE CURRENT FUNCTION IS GIVEN BELOW:" 560 "IF YOU WANT A DIFFERENT FUNCTION, TYPE:"  " 5G 15029d"THIS PROGRAM PERMITS YOU TO GRAPH"?ikn"A FOURIER SERIES APPROXIMATION TO A "qsx"PERIODIC FUNCTION OF YOUR CHOICE."}"YOU MUST TYPE IN THE TERMS OF THE""SERIES AT LINE 560. MORE TERMS CAN"      0"YOUR EQUATION, Y=... , THEN PRESS RETURN" :"REMEMBER TO AVOID EQUATIONS THAT WILL CAUSE ERRORS SUCH AS SQUARE ROOT OF A NEGATIVE, LOG OF ZERO, ETC. THE PROGRAM")"HAS AN ERROR TRAP WHICH WILL TRY TO CORRECT ANY MISTAKES IN YOUR EQUEDY" L:;V"***************************************"F`32000LRi * INSTRUCTIONS *oz::2"THIS PROGRAM GRAPHS Y AS A FUNCTION ""OF X ON THE HIRES GRAPHIC SCREEN WHICH""HAS A RESOLUTION OF 280 X 160. INPUT",0::1740A%280ī430"X(8Y(X)(X)REQ$"Y=SIN(X)+COS(X)"X^dy * TITLE PAGE *:"***************************************"$:.12)"X - Y GRAPHER"8:18)"BY"B:12)"RONALD KENNW)(XOLDXNW)# @XOLDXNW:YOLDYNW< JX$(((X.0005)),4)Y T22:1:"X = ";X$;" "r ^Y$(((Y.0005)),4) h23:"Y = ";Y$;" " rSL$(((SL)),3) |24:"SLOPE = ";SL$;" "; (16384)155Ĺ16368,0:2310 (16384)141Ĺ16368RAPH ROUTINE *" XXLOXHIINCR> XXLOYYLOYYHISW1H (0)R Y2Xb Y(X)(X)x YYLOYYHIī290 B%(YHIY)(YHIYLO)159 XNWX:YNWY SW0ēA%,B% SW1ēA%,B%:SW0 "A%A%1 ,(XOLDXNW)0ī320 6SL(YOLDYNL USE &*&  *MAY NOT BE SOLD.COPY-*D  *RIGHT 1981 CUE,INC *b *********************** #(104)64Ĺ104,64:103,1:16384,0:(4);"RUN X-Y GRAPHER" d1040: ** BEGIN ** * THIS IS G * 333 MAIN STREET *6  * REDWOOD CITY *T  * CA 94063 *r  *(415)364-5600 EX 4401*  * *  * *  ***********************  *PROGRAM MAY BE COPIED*  *FOR EDUCATIONA *( * SAN MATEO COUNTY *F  * OFFICE OF EDUCATION *d  * & *  * COMPUTER-USING *  * EDUCATORS *  * *  * SOFTSWAP *  * *   X-Y GRAPHER 8/80' F PROGRAM LET'S USER PLOTa FUNCTIONS ON HI-RESy GRAPHICS SCREEN. APPLE II W/APPLESOFT  RONALD KENNEDY   *********************** *  " I0INēX,KX,YX1,YX1,K) I/ 7 21` N;" RECTANGLES GIVE THE VALUE ";SUMh 22 "(THE TRAPEZOID RULE GIVES ";AREA;")" d9 JZF(X), TTRAP(F(XL)F(XR))DLTAX2= ^RECTZDLTAXN hSUMSUMRECTa mAREAAREATRAP r ENLARGE SCALE AND PLOT GRAPH |XSXXH X0X279ī450 YSY(Z)K Y0Y159ī450 1 X,YX1,Y  DRAW LINES X = A AND X = B)N SUM0 AREA0) SET SCALES3 SX20C J0279SXT J,K2J,K2[ Je SY20u J0159SY H2,JH3,J J " ADD AREAS OF RECTANGLES ,F(X)(X) 1I0N 6XAIDLTAX ;XLX:XRXDLTAX @ ENTER FUNCTIONS NOW" 300< "TO CHANGE F(X), RE-TYPE LINE 300 NOW."B V "THEN RUN 50."\ b  2"ENTER N,A,B SEPARATED BY COMMAS." 7N,A,B n xH140 K80 2 DRAW AXES H,0H,159H1,159H1,0 0,K279,K DLTAX(BA :"THIS PROGRAM INTEGRATES THE FUNCTION "@l "F(X) OVER THE INTERVAL (A,B) USING N"r  "RECTANGLES ERECTED AT THE LEFT ENDPOINTS" "OF THE SUBINTERVALS. A SECOND VALUE IS" "OBTAINED USING TRAPEZOIDS. F(X) I    N THE *&* PROGRAM. *,B(4);"OPEN TEMP"Z"(4);"DELETE TEMP"p,(4);"OPEN TEMP"6(4);"WRITE TEMP"@W$"F"ĺ"220":"212":"260":"1370":"1600":"DEL 300,380"J"230 ";EQ$T"500 ";EQ$^"510 EQ$=";(34);EQ RETURNS TO THE SCREEN THE GRAPH IS COMPLETE.":"THEN PRESS THE KEY TO CONTINUE.":P"EQUATION --> Y = ";:EQ$:EQ$""Ģ(37):1360UEQ$"Y="EQ$Z2700* CREATE AN EXEC FILE ** IN ORDER TO INSERT * * EQUATION IATION IF POSSIBLE. AT ANY TIME DURING "S"THE X-Y GRAPHING YOU MAY PRESS THE"(" KEY IN ORDER TO RESET THE UPPER":(37)2"AND LOWER X-Y VALUES FOR THE AXES."<"PRESS TO ABORT GRAPH ROUTINE."\F:"WHEN THE FLASHING CURSOR300N1103"X = ";10N,"F(X) = ";F(10N):N@F Z (F(XL)L)E(F(XR)L)E1110.PBEEP158R(7)BTBEEPMVI15S`vj"(Y TO CONTINUE, N TO STOP)";~tA$~A$"N"1200NN11000X09992200N110"X = ";10N,"F(X) = ";F(10N)N2""X"10)"F(X)"26)"ERROR"($.&F.XLX0ND:XRX0NDX0V(F(XL)L)c2VVV1p4V$(VV)6P$(V$,(V$)1)8XL10)F(XL)25)P$:W(F(XR)L)<WWW1>W$(WW)@Q$(W$,(W$)1)BLXR10)F(XR)25)Q$ MPE 'Y' TO CONTINUE,"?"'N' TO STOP. WHEN F(X) - L EXCEEDS"m"THE TOLERANCE EPSILON, YOU WILL HEAR A""SIGNAL. NOW ENTER DELTA."D$D(D$)N1"DELTA = ";D$,"EPSILON = ";E$"X0 = ";X0,"L = ";LM L BY"0R"MORE THAN EPSILON, CHOOSE A SMALL"[\"VALUE OF DELTA AND WE WILL EVALUATE"f"F(X) IN STEPS OF DELTA AWAY FROM X0.";pz"WE WILL EVALUATE F(X) AT X0-ND AND""X0+ND, WHERE D = DELTA AND N = 1,2,...""AFTER EACH PAIR, TYAND L YOU WILL ALLOW."B "ENTER A SMALL VALUE OF THE TOLERANCE"k"EPSILON (.1 OR .01, FOR EXAMPLE)";s E$%E(E$)*4"LET DELTA BE THE DIVERGENCE FROM X0.">"TO SEE HOW BIG DELTA CAN BE WITHOUT"H"PERMITTING F(X) TO DIFFER FROPPROACHES X0? (Y OR N)"; vA$1 A$"N"12007 Z "ENTER THE APPARENT LIMIT L";a Lg  "TO MAKE F(X) CLOSE TO L, X SHOULD BE" "CLOSE TO X0. HOW CLOSE SHOULD IT BE?" "WELL, THAT DEPENDS ON WHAT TOLERANCE""BETWEEN F(X) E" ZA$ ! "X","F(X)"' : X0A,F(X0A)@ S X0A,F(X0A)Y c AA2n I15t !{ "I #"(Y TO CONTINUE, N TO STOP)"; 7A$ :A$"N"600 D400 X b"DOES THERE SEEM TO BE A LIMIT " l"TO F(X) AS X A99İ2000 ^"ENTER A." hA% mU r"AFTER EACH TWO EVALUATIONS, THE DISTANCE" w"BETWEEN X AND X0 IS HALVED. TO EVALUATE" y |"F AT X0-A/2*N AND X0 + A/2*N TYPE 'Y'."  "TO STOP EVALUATING, TYPE 'N'." :"TYPE 'GO' TO CONTINUOOSE A NUMBER X0 AND A NUMBER A SO") ;Y @"THAT F IS DEFINED ON (X0-A,X0+A), THOUGH" J"NOT NECESSARILY AT X0 ITSELF. ENTER X0." N O"IF X0 IS INFINITE, ENTER -999 FOR MINUS" P Q"INFINITY, 999 FOR PLUS INFINITY." TX0 Y(X0)9T FUNCTION IS GIVEN BY:"! 300L "ENTER YOUR FUNCTION RULE BY TYPING:"R l "300 DEF FN F(X) = "r "FOLLOWED BY YOUR FUNCTION RULE." "THEN TYPE 'RUN 300' AND PRESS RETURN." ,F(X)(1X2)(1X) 1# 6"CHH d4n"THIS PROGRAM EVALUATES A FUNCTION OF "cx"YOUR CHOICE NEAR A POINT OF YOUR CHOICE""TO SEE WHETHER THE FUNCTION VALUES""APPROACH A LIMIT AS X APPROACHES YOUR""CHOSEN NUMBER X0 (OR GOES TO INFINITY)." "THE CURREN      WILL DO IT FASTER THAN POSSIBLE WITH THE SLOWVERSION. ONCE CHOOSEN, YOU WILL NOT HAVETHE OPTION OF USING THE SLOW VERSION." 30000::4 "DO YOU WANT THE FAST OR SLOW VERSION?":"PLEASE ANSWER F OR S =>"; 16368,0 W$:W$""2780 W$ SPEED AT WHICH YOUR EQUATIONS IS GRAPHED BY USING PADDLE ZERO. IT WILL ALSO DISPLAY THE VALUES OF THE X AND Y COORDINATES AND THE SLOPE." ::14::"FAST VERSION"::| "THE FAST VERSION WILL ONLY DISLPAY THE GRAPH OF THE EQUATION. HOWEVER, ITECT THE ERROR "@2 "THAT YOUR EQUATION IS GENERATING. SORRY"N< ::2320 :2:"YOU NOW HAVE THE OPTION OF CONTROLLING THE SPEED AT WHICH I GRAPH THE EQUATION.": 14::"SLOW VERSION":: "THE SLOW VERSION WILL GIVE YOU CONTROL OF THE(4);"RUN MENU"  2 * ERROR TRAP *8 B WW1 21:1:" ERROR HAS OCCURRED. PLEASE WAIT WHILE I TRY TO CORRECT." K11000:K W1X11030::2: W2X2::2: W3X2::2:( ::"I CANNOT SEEM TO CORRKE ? " :5$ " 1. RERUN THE EQUATION -- ";EQ$W. :" 2. ENTER A NEW EQUATION"h8 :" 3. END"B ::"CHOOSE 1-3 ?";L Q$:Q$""2380V Q(Q$):Q1Q3ī2310` Q2410,2420,2430j 1740t 1240~ ::104,8:103,1:2048,0 :%0A%279ī2240!A%,0A%,159/A%0:B%0FINCR(XHIXLO)280WXLOXLOINCR200: THE GRAPH ROUTINE IS AT THE BEGINNING OF PROGRAM FOR INCREASED SPEED 16368,024:18A$:(A$)132300 : "WHAT WOULD YOU LIHI4>,H * DRAW AXES AND LABEL *5R:3?\:W3Pf21:13:EQ$rp23:20:"X= ";XLO;" TO ";XHIz24:20:"Y= ";YLO;" TO ";YHI;B%(YHI159)(YHIYLO)B%0B%159ī22100,B%279,B%A%279((XHI279)(XHIXLO))A0:XXLO:5005W0ė:2:20:"** ERROR **":1950J13:20:"Y= ";Yg14:"X-HI: FOR X= ";XHIzW0:XXHI:500W0ė:2:20:"** ERROR **":199014:20:"Y= ";Y:"LOW VALUE OF Y-AXIS ";YLO"HIGH VALUE OF Y-AXIS ";YX-AXIS ";XHI&09:1K:"THE FOLLOWING VALUES MAY BE OF HELP IN"uD"SELECTING A RANGE FOR THE Y-AXIS :"N12:"ZERO: FOR X= 0"XW0:X0:500bW0ė:2:20:"** ERROR **":1910l12:20:"Y= ";Yv13:"X-LO: FOR X= ";XLO W$;(34)h"RUN 1740".r(4);"CLOSE TEMP"D|(4);"EXEC TEMP"JPVs * SELECT AXIS VALUES *y:2540XOLD1:YOLD1:X2500:2:3:EQ$:"LOW VALUE OF X-AXIS ";XLO "HIGH VALUE OF 2:Y(Y0Y)2 340 G "TO USE A DIFFERENT PATH TO (X0,Y0),"l "TYPE 'Y'. OTHERWISE TYPE 'N'."t A$ A$"Y"270  "DO YOU WANT ANOTHER FUNCTION? (Y OR N)" A$ A$"Y"10 2E;X0;",";Y0;")" @C B"REMEMBER: TYPE 1 TO CONTINUE, 0 TO STOP"I Dh J1)"X"13)"Y"26)"F(X,Y)"n T ^Z(XY)(XY) `X1(100000X)100000:Y1(100000Y)100000:Z1(100000Z)100000 cX113)Y126)Z1 hN$ rN$"0"400 |X(X0X) :"EACH EVALUATION." H "TYPE '1' AFTER EACH EVALUATION TO"N { "EVALUATE AT A CLOSER POINT. TYPE '0'" "TO STOP EVALUATION ALONG THAT PATH." : "ENTER X1,Y1, THE STARTING POINT." X,Y , 6" (X0,Y0) = ("IS CURRENTLY AS GIVEN BELOW:"& ^350, _2 db x"ENTER X0,Y0 (THE POINT TO BE APPROACHED)"m X0,Y0u : "WE WILL EVALUATE F(X,Y) ALONG" "THE SEGMENT FROM (X1,Y1) TO (X0,Y0)," "HALVING THE DISTANCE TO (X0,Y0) AFTER" 5"THIS PROGRAM INVESTIGATES THE BEHAVIOR";e("OF F(X,Y) NEAR (X0,Y0). ENTER THE"k2<"RULE FOR F(X,Y) BY TYPING "FP" 350 Z = (YOUR NEW RULE)"UZ"THEN TYPE 'RUN 100' AND PRESS RETURN."[ \" LINE 350     /80 G:103,1:2048,0& Fu:(4);"RUN MENU"B y * CENTER PRINT * n "yWIDTH20((TT$)2):WIDTH:TT$(13): }18:TT$"ALLOWS YOU TO PLOT FUNCTIONS ON THE":31000:19:TT$"HIGH RESOLUTION GRAPHICS SCREEN.":31000:30000:! } ADDED TO LIBRARY 8 33611 +************************2"VXQ0u * ESCAPE ROUTINE * _5u16368,0:u23:9:"PRESS TO CONTINUE":24:12:"PRESS TO END =>";:QQ$:QQ$(27)QQ$(13)Č868:30010;u(QQ$)13ė: DuQQ$(27)ĉ::104,8"F"W$"S"2770 :1500#p@z PROGRAM MAY BE SPEEDED] UP BY DELETING STATE- r MENTS 50 - 90.x*********************** PROPERTY OF:  RONALD KENNEDY 4621 BAY COURT  TAMPA FL520 -- PLOT AXES#*3=140,0140,159P 141,0141,159a0,80279,80pI02755I,79I,81I1,81I1,79$I.I015543139,I142,I8IBG990  !21# #"ENTER X,Y", &X,Y3 05V :1405X,804Y1415X,804Yn DUAXBY:VCXDYu N1 X1405U,804V1415U,804V b l21 v"THE IMAGE OF (";X;",";Y;") IS (";U;",";V;")" "RETURN FOR MORE, Q TO QUIT";K2K11,K2H11,H2H1,H2K1,K2$ , 21Y "HERE'S THE IMAGE. EQUATIONS OF T ARE" "X' = ";A;"X + ";B;"Y, Y' = ";C;"X + ";D;"Y" "TO FIND THE IMAGE OF A NEW POINT (X,Y)," "JUST PRESS RETURN. TO QUIT, TYPE Q."; ANS$ ANS$"Q"AXSBYS:YKCXSDYS1 TH11405XH:H2804YHL ^I11405XI:I2804YIg hJ11405XJ:J2804YJ rK11405XK:K2804YK |H1,H2H11,H2I11,I2I1,I2H1,H2 I1,I2I11,I2J11,J2J1,J2I1,I2 J1,J2J11,J2K11,K2K1,K2J1,J2 K1,GLE. PRESS RETURN TO "G "SEE ITS IMAGE UNDER THE TRANSFORMATION.";O W$V 1d XP2:YP2r XQ6:YQ2 XR10:YR10 XR6:YR4 XS2:YS4 ,XHAXPBYP:YHCXPDYP 6XIAXQBYQ:YICXQDYQ @XJAXRBYR:YJCXRDYR JXKX + DY" = "YOU MAY CHOOSE VALUES OF A, B, C, AND D."U "ENTER THESE NOW."[ h A,B,C,Dr 1000y 5 150,70170,70 170,70170,60171,60171,70 170,60150,60 150,60150,70151,70151,60 21 "HERE IS A RECTAN 5d"THIS PROGRAM ILLUSTRATES LINEAR ";ijn"TRANSFORMATIONS OF THE PLANE BY SHOWING"psx"A CERTAIN SQUARE AND ITS IMAGE UNDER THE""TRANSFORMATION T. EQUATIONS FOR T ARE:"" X' = AX + BY" " Y' = C     ! ! !!!!!!!!!""""""""  = ";X(I)I6" NOTE: THE DETERMINANT IS ";DT<8BXgb"INVERSE OF COEFFICIENT MATRIX"mlsv~I1NJN12NMJNK8M7K)(1000B(I,J))1000;JI dS172 06000?4"TO USE DIFFERENT B'S, TYPE 'Y' ELSE 'N'";D$P8D$"Y"5000VP\pu"COEFFICIENT MATRIX"30)"CONSTANTS"vzI1NJ1NK7J6K)A(I,J);J33)H(I)II1N"X(";I;") E SOLUTIONS ARE:""I1N-X(I)04I?I1NJ J1NdX(I)X(I)C(I,J)H(J)kJ("X(";I;") = ";X(I))*I+"TO SEE THE ORIGINAL COEFFICIENT MATRIX","AND THE SOLUTIONS, TYPE 'Y' ELSE 'N'"-Y$.Y$"N"5 I& I1N: J12N3< N4K5J4:3140J> N5K4J3:3140V? K7J6fD K)D(I,J);mN Jsz y{  I --SOLVE AX = B--ENTER B"ENTER THE ";N;" CONSTANTS B1,...B";N;I1NH(I)I"THC(S,T)B(S,TN)TSA--PIVOT COMPLETED; NOW PRINTGe --PRINT AUGMENTED MATRIXk { --ROUNDING I1N J12N N3D(I,J)(10B(I,J))10:3060 N4D(I,J)(B(I,J)):3060 D(I,J)(100B(I,J))100 J --PIVOT ON B(ROW,ROW) 3DENB(ROW,ROW)ADTDTDENNJ12NhB(ROW,J)B(ROW,J)DENoJzL1N LROW2110MULTB(L,ROW) J12N*B(L,J)B(L,J)MULTB(ROW,J)4J>L--UPDATE CS1NT1N21+"THE MATRIX HAS NO INVERSE..."1_"DO YOU HAVE ANOTHER MATRIX (Y OR N)";G$nG$"Y"10t--SWITCH ROWS IF A(I,I) = 0M12NH(M)B(ROW,M)B(ROW,M)B(K,M)B(K,M)H(M)M$--PRINT NEW MATRIXB "FOR MORE ACCURACY, TYPE 'Y' ELSE 'N'"0rANS$BsANS$"N"885Lt7000xu"TYPE 'GO' WHEN YOU HAVE SEEN ENOUGH."zZ${|"DO YOU WANT TO SOLVE A SYSTEM AX = B"}"FOR THE CURRENT MATRIX A? (Y OR N)"~Y$Y$"Y"İ5000920"WE SWITCH ROWS ";ROW;" AND ";K;" AND THEN PIVOT.":840g >"NOW WE PIVOT ON ROW ";ROW;", COLUMN ";ROW HPAUSE11500:PAUSE R2000 \ROW ^3000 c d e f"WE ARE DONE. THE INVERSE OF A IS IN" p"THE LAST ";N;" COLUMNS."&q 2 "ZERO, LOOK BELOW IT AND TYPE THE ROW"8 f "NUMBER OF THE FIRST NON-ZERO ENTRY YOU"l  "FIND. (IF YOU CAN'T FIND ONE, TYPE 0.)"; K K99800 K0İ1000 K0900 --MESSAGE ON PIVOTING 4227 7K0K99ĺ 8 "COLUMNS AND THE INVERSE IN THE LAST ";N;"."> b "PRESS RETURN TO CONTINUE";GO$x X--CHECK A(I,I)=0 bROW1N l3000 v11 "LOOK AT THE ROW ";ROW;", COLUMN ";ROW;" ENTRY."  "IF IT IS NON-ZERO, TYPE 99. IF IT IS"USER 11< "THE COEFFICIENT MATRIX IS AUGMENTED WITH"j "THE IDENTITY MATRIX I. WE WILL INVERT"p  "THE MATRIX BY PERFORMING ROW OPERATIONS"  "ON THE AUGMENTED MATRIX TO PRODUCE THE"  "IDENTITY MATRIX IN THE FIRST ";N--READ A, COPY IN B; C = 0( I1N3 J1N? A(I,J)Q B(I,J)A(I,J)^ C(I,J)0e Jl I --AUGMENT WITH IDENTITY I1N JN12N JNI270 B(I,J)0 280 B(I,J)1 J "I ,3000 --MESSAGE TO   DT1*( 3,1,1,1,2,2,2,3,4,52 5,1,1,1,1,1,2,2,1,2, 2 , 3 ,7,3,5,2,5,6,8,4, 3,2,4,4,1,2d 3,2,4,0,0,2,1,3,0,2i 4,1,-2,3,1,4,3,-6,8,2,0,5,-4,-1,2,5,8nN      G$"Y"COUNTCOUNT1::21:"TYPE T, ROT, REF, G, OR D";:80MG$"N"ĉ:x"THANK YOU. I HOPE THIS HAS BEEN A ":"M-O-V-I-N-G EXPERIENCE FOR YOU TOO."L--COMPUTE IMAGE (T OR ROT)******VRP(I)AR(I)BS(I)C`SP(I)BR(I)AʓP(1),Q(1)P(2),Q(2)P(3),Q(3)P(3)1,Q(3)P(2)1,Q(2)P(1)1,Q(1)~TYPE$"T"ē140,801405C,805D1415C,805D141,80:21"A FIGURE AND ITS IMAGE...""TO FOLLOW THIS TRANSFORMATION WITH""ANOTHER, TYPE Y ELSE N.";G$="Y"949;A1X(1):A2Y(1):B1X(2):B2Y(2):C1X(3):C2Y(3)E2000XBETA(COUNT1)A1XP(1):A2YP(1):B1XP(2):B2YP(2):C1XP(3):C2YP(3)2000TYPE$"REF"ēP(1),Q(1)P(2),Q(2)P(3),Q(3)P(3)1,Q(3)P(2)1,Q(2)P(1)1,Q(1)BTYPE$"G"),YP(I)XP(I)1,YP(I)-Q(I)(Y(I)YP(I))2EP(I)(X(I)XP(I))2O:23jRP(I)(100RP(I))100SP(I)(100SP(I))100"THE IMAGE OF (";R(I);",";S(I);") IS (";RP(I);",";SP(I);")"PAUSE11500:PAUSEIBETA(COUNT)G$(I)#pTYPE$"T"TYPE$"ROT"11007rTYPE$"D"1155Au1200WzZ1XP(I):Z2YP(I)x{Z10Z1280Z20Z2160894|G$"Y"Ģ23:"OFF SCREEN...TYPE 'RUN' TO START OVER.":}23:"OFF SCREEN...TRY ANOTHER POINT":840~BETA(COUNT1)XP(I00A1:B0:CH:D2JN@ --ENTER THREE POINTS***********K*I13\,BETA(COUNT)l/G$"Y"842v4:21>"ENTER X";I;",Y";I;HR(I),S(I)I850JR(I)RP(I):S(I)SP(I)RX(I)140R(I)5\Y(I)805S(I)fX(I),Y(I)X(I)1,YMH685<"VECTOR NOT PARALLEL TO AXIS...TRY AGAIN.":670Z--NORMALIZE COEFFICIENTSkW(M2N2)MMW:NNW:JJWM0760AN2M2:B2MN:C2MJH:D2NJKG$"Y"800--PLOT AXES1500--PLOT POINTS8* bg21=l"ENTER THE COEFFICIENTS A,B,C OF THE"iv"EQUATION AX + BY + C = 0 OF THE AXIS""OF THE REFLECTION PART"M,N,J"ENTER THE COMPONENTS H,K OF THE VECTOR""FOR THE TRANSLATION PART"H,KKNM05103AN2M2:B2MN:C2MJ:D2NJCG$"Y"800T--PLOT AXES^1500q--PLOT POINTSz800A1:B0:C0:D2JNG$"Y"800--PLOT AXES1500--PLOT POINTS800X--GLIDE-REFLECTION**************800/ --REFLECTION********************* 5 = 21h "ENTER THE COEFFICIENTS A,B,C IN THE" "EQUATION AX + BY + C = 0 OF THE" "AXIS OF THE REFLECTION" M,N,J --NORMALIZE COEFFICIENTS W(M2N2) MMW:NNW:JJW H,K O6 T"ENTER THE DEGREE MEASURE OF THE ANGLE"A ^THETA^ cTHETATHETA3.141593180x hA(THETA):B(THETA) |CH(1A)KB DK(1A)HB G$"Y"396 --PLOT AXES 1500 BETA(COUNT) 1405H,805K1415H,805K  :21. "ENTER THE COMPONENTS OF THE "O "TRANSLATION VECTOR AS C,D"X C,Dd A1:B0t G$"Y"800 --PLOT AXES 1500 800 ,--ROTATION*********************** 6:21 @"ENTER THE COORDINATES OF THE CENTER H,K" JTION," J) K" OR D FOR DILATION.";4 PTYPE$G ZTYPE$"T"200\ dTYPE$"ROT"300q nTYPE$"REF"400 xTYPE$"G"600 zTYPE$"D"1700 } " TYPING ERROR...TRY AGAIN" 80 --TRANSLATION*********** UR CHOICE OR" ; #"UNDER A DILATION OF YOUR CHOICE."A %d ("WHAT KIND OF TRANSFORMATION"j ) *"DO YOU WANT?"; .:: 2" TYPE T FOR TRANSLATION, ROT FOR" 7 <" ROTATION, REF FOR REFLECTION," A F" G FOR GLIDE-REFLEC COUNT1 3M"I WILL PLOT 3 POINTS AND THEIR IMAGES"BETA(1)1:BETA(2)2:BETA(3)5:BETA(4)6:BETA(5)3BETA(5)3 -- BETA IS COLOR CODE....1 GREEN, 2 PURPLE, 3 WHITE, 5 PINK, 6 BLUE "UNDER AN ISOMETRY OF YO          !!! ! ! HE SECOND POINT."'40::2`1"NOW ";A$;", YOU GIVE":"ME POINTS AS THE COMPUTER DIRECTS."6"PRESS THE KEY AFTER EACH POINT.":;"X(1)=";:Z$:Z$""Ģ(37):315<45=FLAG1Ģ(37):958:315>A(Z$)@"Y(1)=";:Z$:Z$====" #16);"Y(2) - Y(1)";16);"-----------"S16);"X(2) - X(1)"Y _"========================================""WHERE X(1) AND Y(1) ARE THE COORDINATES OF THE FIRST POINT AND X(2) AND Y(2) ARETHE COORDINATES OF TE FIRST X-COORDINATE FROM THE SECOND.",B10);"9 - 5 = 4"J:v"THIS TELLS US THAT THE SLOPE IS 5/4."40::2"FROM THIS ";A$;", WE CAN SEE":"THAT THE FORMULA FOR SLOPE IS:""====================================IGHT."40::3["LET'S SAY THAT YOU WANTED TO FIND THE SLOPE BETWEEN THE POINTS"a|8);"(5,2) AND (9,7)""FIRST WE SUBTRACT THE FIRST Y-COORDINATEFROM THE SECOND."10);"7 - 2 = 5":&"NEXT WE SUBTRACT THSTEEP A LINE IS."inn"IT REFLECTS THE CHANGE IN Y-COORDINATES DIVIDED BY THE CHANGE IN X-COORDINATES."tsx"IF THE SLOPE IS POSITIVE, THE LINE RISES AS IT GOES TO THE RIGHT."}"IF THE SLOPE IS NEGATIVE, THE LINE FALLS AS IT GOES TO THE R FA$(20),Z$(20),Z1$(20)" H:5< P"WHAT IS YOUR NAME";V QA$:A$""Ģ(37):80g R(A$)1172p U:2 Z"HELLO ";A$",":"TODAY I'M GOING TO SHOW YOU HOW TO FIND THE SLOPE BETWEEN 2 POINTS." _d"SLOPE IS A NUMBER WHICH TELLS US HOW (Z1$)2742" +(Z1$)27ī908( ,? -FLAG0:(Z$)148t .Z1(Z$):Z1$(Z$,Z,1):(Z1$)48(Z1$)5750} /Z: 0(Z$)0Z$"0"FLAG1: 1 2Z1Z1$"-"Z1$"+"ĂZ 3Z1$"."ĂZ 4FLAG1: A:7000::990 BN13000:NTIONAL USE &*+ *MAY NOT BE SOLD.COPY-*I ! *RIGHT 1981 CUE,INC *g " *********************** #(104)64Ĺ104,64:103,1:16384,0:(4);"RUN SLOPES" '65 (24:"PRESS TO GO ON - TO END"; )16368,0 *Z1$:(Z1$)13  * 333 MAIN STREET *;  * REDWOOD CITY *Y  * CA 94063 *w  *(415)364-5600 EX 4401*  * *  * *  ***********************  *PROGRAM MAY BE COPIED*  *FOR EDUCA *-  * SAN MATEO COUNTY *K  * OFFICE OF EDUCATION *i  * & *  * COMPUTER-USING *  * EDUCATORS *  * *  * SOFTSWAP *  * *" SLOPES 7/81% k REENFORCES CALCULATIONS OF THE SLOPE OF A LINE SEGMENTv   APPLE II W/APPLESOFT  HOWARD JENSEN   *********************** * T(C1B1)MM,B2T(C2B2)MM$ T2*T1NN5y4C1T(A1C1)NN,C2T(A2C2)NN1C1T(A1C1)NN,C2T(A2C2)NN>Td(OT POINTS8000NN((C1A1)2(C2A2)2)NMM((B1C1)2(B2C2)2)lLL((A1B1)2(A2B2)2)zT1LL5A1T(B1A1)LL,A2T(B2A2)LL1A1T(B1A1)LL,A2T(B2A2)LLT T1MM5B1T(C1B1)MM,B2T(C2B2)MM1B1T$--DILATION******************221a"ENTER THE COORDINATES OF THE CENTER H,K"grHD,KDx"ENTER THE SCALE FACTOR"RT--PLOT AXESG$"Y"8001500 1405HD,805KD1415HD,805KD --PLS(I)C SP(I)BR(I)AS(I)D6XP(I)1405RP(I)KYP(I)805SP(I)T890r --PLOT AXES************x30,80279,80140,0140,159141,159141,0I52755"I,79I,81,I6I51555@139,I142,IJIS(I)DjXP(I)1405RP(I)1tYP(I)805SP(I):~890^ --COMPUTE IMAGE (D)**********xRP(I)RT(R(I)HD)HDSP(I)RT(S(I)KD)KDXP(I)1405RP(I)YP(I)805SP(I)890--COMPUTE IMAGE(REF OR G)*******RP(I)AR(I)B5Z$:Z$""555%6(Z$)8959087(Z$)78555>:?::"SORRY ";A$;", THEY":"BOTH HAVE A SLOPE OF -7/10 AND ARE PARALLEL."D::"TRY THESE."I::605N:::"GOOD ";A$;", THEY":"BOTH HAVE A SLOPE OF -7/10 AND ARE PAT THEY HAVE THE SAME SLOPE."%400::2&"LINE 1 CONTAINS THE POINTS (6,3) AND (-4,10), AND LINE 2 CONTAINS THE POINTS (-8,6) AND (2,-1)."(:::+((37)1):"ARE THESE LINES PARALLEL?"0"ANSWER EITHER Y OR N =>";416368,0AIN, YOU HAD BETTER RETURN TO CLASS."D104,8:103,1:2048,0[(4);"RUN MENU"::"VERY GOOD ";A$;", NOW":"YOU ARE READY TO CONTINUE WITH SOME PROPERTIES OF SLOPE."40::2910:24 "ONE PROPERTY OF PARALLEL LINES IS THAZ1Z$"/"ĂZ((Z$)48(Z$)574404Z:445CZ$"-"ĂZY(37):958:436lF$"-4/8"490F$"4/-8"490A1480:"SORRY ";A$;", THAT'S WRONG.":"I'M GOING TO GIVE YOU ANOTHER CHANCE."A1:436*:"YOU ARE WRONG AG":A14208"VERY GOOD ";A$;", 4/5 IS CORRECT!":E40::3u"FIND THE SLOPE BETWEEN (5,2) AND (-3,6)."{"ENTER YOUR ANSWER AS A FRACTION BUT DO NOT REDUCE IT.":"SLOPE =";:F$:F$""Ģ(37):436 Z1(F$):Z$(F$,Z,1):"SLOPE =";:E$:E$""Ģ(37):391PZ1(E$):Z$(E$,Z,1):Z1Z$"/"ĂZk(Z$)48(Z$)57395wZ:398Z$"-"ĂZ(37):958:391((37)2)E$"4/5"415"SORRY ";A$;", THATS NOT RIGHT!":"THE CORRECT ANSWER IS 4/5.B;"=";DB;" AND ";C;"-";A;"=";CA)Y:M^"SO THE SLOPE IS ";DB;"/";CASc`h40::2r"NOW ";A$;", LET ME GIVE":"YOU 2 POINTS."w:|"FIND THE SLOPE BETWEEN (3,1) AND(8,5).":A0"ENTER YOUR ANSWER AS A FRACTION."%""Ģ(37):320A454BFLAG1Ģ(37):958:320@CB(Z$)eE"X(2)=";:Z$:Z$""Ģ(37):325mF45GFLAG1Ģ(37):958:325HC(Z$)J"Y(2)=";:Z$:Z$""Ģ(37):330K45LFLAG1Ģ(37):958:330MD(Z$)O!TD;"-";157O62,157!VI120279142`I,99I1,999jIJtI100014[~122,I123,IbIy---AXES COMPLETED2B  1, ---PLOT AXES AND MARK UNITSA 120,100279,100T 120,0120,100g 121,0121,100{ 120,10061,159 111,107 112,107 $101,117 )102,117 .91,127 392,127 881,137 =82,137 B71,147 G72,147L61,OUNTCOUNT1 XU12014Y10X/ ]W10010X6 `5E bU,WU1,WL g6Z jWWW14Zk lU,WWU1,WWr Yy X  7 21 "WITH ";COUNT;" SUBDIVISIONS, THE INTEGRAL IS" (100V)100;". DECREASE DX FOR MORE ACCURACY." DYDX  1000* XADX2BDX9 YTPG2(X)I YBOTG1(X)[ YTPYBOT675m YTPYBOT580z HOLDYTP &YTPYBOT 0YBOTHOLD DYYBOTDY2YTPDY IYYTPDY2590 KYYTP NZ7(X2Y2)2 PDVZDXDY RVVDV TCPE THEM." _+ `"THEN TYPE 'RUN 100'."1 b9 d:A iV0M lCOUNT0o n"WHAT IS THE LOWER VALUE A";v pA| q r"WHAT IS THE UPPER VALUE B"; sB t u"WHAT VALUE OF DX (= DY) DO YOU WANT"; wDX xG1(X)0 G2(X)3X  >3 A"Z = F(X,Y) ARE PLOTTED POINT BY POINT."9 Dg F"FOR VISUAL CLARITY, THE PRISMS ARE NOT"m K P"SHOWN. TO CONTINUE, PRESS RETURN." UH$ W Y" THE CURRENT FUNCTIONS ARE:" \120:130:590 ^"TO CHANGE ANY OF THESE, RE-TY  ;"THIS PROGRAM APPROXIMATES THE INTEGRAL"Am"OF F(X,Y) OVER A REGION R DEFINED BY"s#("THE VERTICAL LINES X = A AND X = B"-2"AND BY THE CURVES Y = G1(X) AND"7<"Y = G2(X). THE REGION R AND THE 'ROOF'""" " " " " "