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|00000540| 4f 44 45 0d 43 41 4e 20 | 42 45 20 41 4e 41 4c 41 |ODE.CAN |BE ANALA|
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|00000ce0| 4f 20 53 55 43 43 45 53 | 53 49 56 45 20 54 45 52 |O SUCCES|SIVE TER|
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|00000d60| 58 41 4d 50 4c 45 2c 20 | 54 48 45 0d 46 4f 55 52 |XAMPLE, |THE.FOUR|
|00000d70| 54 48 20 4e 55 4d 42 45 | 52 20 49 53 20 33 2a 34 |TH NUMBE|R IS 3*4|
|00000d80| 2b 31 20 4f 52 20 31 33 | 2e 20 20 d4 48 55 53 20 |+1 OR 13|.  .HUS |
|00000d90| 48 45 0d 57 4f 55 4c 44 | 20 57 52 49 54 45 3a 0d |HE.WOULD| WRITE:.|
|00000da0| 0d c6 cf d2 c9 3d 31 d4 | 30 39 3a c1 3d 33 2a c9 |.....=1.|09:.=3*.|
|00000db0| 2b 31 3a c7 cf d3 d5 c2 | 38 30 30 3a ce c5 d8 d4 |+1:.....|800:....|
|00000dc0| 2e 0d 0d 20 20 20 20 d4 | 48 45 20 53 45 43 4f 4e |...    .|HE SECON|
|00000dd0| 44 20 53 49 54 55 41 54 | 49 4f 4e 20 41 52 49 53 |D SITUAT|ION ARIS|
|00000de0| 45 53 20 57 48 45 4e 0d | 54 48 45 52 45 20 49 53 |ES WHEN.|THERE IS|
|00000df0| 20 41 20 4e 45 45 44 20 | 54 4f 20 42 52 41 4e 43 | A NEED |TO BRANC|
|00000e00| 48 20 57 48 45 4e 20 41 | 0d 56 41 52 49 41 42 4c |H WHEN A|.VARIABL|
|00000e10| 45 20 54 41 4b 45 53 20 | 4f 4e 20 41 20 53 45 54 |E TAKES |ON A SET|
|00000e20| 20 4f 46 20 56 41 4c 55 | 45 53 2e 0d cc 45 54 20 | OF VALU|ES...ET |
|00000e30| 55 53 20 55 53 45 20 54 | 48 45 20 53 41 4d 45 20 |US USE T|HE SAME |
|00000e40| 53 45 54 20 4f 46 20 4e | 55 4d 42 45 52 53 20 41 |SET OF N|UMBERS A|
|00000e50| 53 0d 49 4e 20 54 48 45 | 20 46 49 52 53 54 20 45 |S.IN THE| FIRST E|
|00000e60| 58 41 4d 50 4c 45 2e 20 | 20 d4 48 45 20 4e 4f 4e |XAMPLE. | .HE NON|
|00000e70| 2d 0d 4d 41 54 48 45 4d | 41 54 49 43 41 4c 20 50 |-.MATHEM|ATICAL P|
|00000e80| 45 52 53 4f 4e 20 57 49 | 4c 4c 20 4d 4f 53 54 20 |ERSON WI|LL MOST |
|00000e90| 4c 49 4b 45 4c 59 0d 57 | 52 49 54 45 20 41 20 53 |LIKELY.W|RITE A S|
|00000ea0| 45 52 49 45 53 20 4f 46 | 20 c9 c6 2d d4 c8 c5 ce |ERIES OF| ..-....|
|00000eb0| 20 53 54 41 54 45 4d 45 | 4e 54 53 2c 0d 42 55 54 | STATEME|NTS,.BUT|
|00000ec0| 20 54 48 45 20 4d 41 54 | 48 45 4d 41 54 49 43 41 | THE MAT|HEMATICA|
|00000ed0| 4c 4c 59 20 54 52 41 49 | 4e 45 44 20 50 45 52 53 |LLY TRAI|NED PERS|
|00000ee0| 4f 4e 0d 57 49 4c 4c 20 | 4c 49 4b 45 4c 59 20 55 |ON.WILL |LIKELY U|
|00000ef0| 53 45 20 41 4e 20 cf ce | 2d c7 cf d4 cf 20 53 54 |SE AN ..|-.... ST|
|00000f00| 41 54 45 4d 45 4e 54 2e | 0d c8 45 20 57 49 4c 4c |ATEMENT.|..E WILL|
|00000f10| 20 52 45 43 4f 47 4e 49 | 5a 45 20 54 48 41 54 20 | RECOGNI|ZE THAT |
|00000f20| 48 45 20 49 53 20 44 45 | 41 4c 49 4e 47 0d 57 49 |HE IS DE|ALING.WI|
|00000f30| 54 48 20 41 20 4c 49 4e | 45 41 52 20 46 55 4e 43 |TH A LIN|EAR FUNC|
|00000f40| 54 49 4f 4e 20 57 48 49 | 43 48 20 49 4e 43 4c 55 |TION WHI|CH INCLU|
|00000f50| 44 45 53 0d 54 48 45 20 | 50 41 49 52 53 20 28 34 |DES.THE |PAIRS (4|
|00000f60| 2c 31 29 2c 20 28 37 2c | 32 29 2c 20 28 31 30 2c |,1), (7,|2), (10,|
|00000f70| 33 29 2c 20 45 54 43 2e | 0d c9 54 20 49 53 20 41 |3), ETC.|..T IS A|
|00000f80| 4e 20 45 41 53 59 20 4d | 41 54 54 45 52 20 54 4f |N EASY M|ATTER TO|
|00000f90| 20 57 52 49 54 45 20 54 | 48 45 0d 52 55 4c 45 20 | WRITE T|HE.RULE |
|00000fa0| 59 2d 59 31 3d 4d 2a 28 | 58 2d 58 31 29 20 57 48 |Y-Y1=M*(|X-X1) WH|
|00000fb0| 45 52 45 20 4d 20 49 53 | 0d 28 59 32 2d 59 31 29 |ERE M IS|.(Y2-Y1)|
|00000fc0| 2f 28 58 32 2d 58 31 29 | 20 41 4e 44 20 59 31 20 |/(X2-X1)| AND Y1 |
|00000fd0| 49 53 20 54 48 45 20 53 | 45 43 4f 4e 44 0d 45 4c |IS THE S|ECOND.EL|
|00000fe0| 45 4d 45 4e 54 20 49 4e | 20 41 4e 59 20 4f 46 20 |EMENT IN| ANY OF |
|00000ff0| 54 48 45 20 50 41 49 52 | 53 2c 20 58 31 20 49 53 |THE PAIR|S, X1 IS|
|00001000| 20 54 48 45 0d 46 49 52 | 53 54 20 45 4c 45 4d 45 | THE.FIR|ST ELEME|
|00001010| 4e 54 20 49 4e 20 54 48 | 45 20 53 41 4d 45 20 50 |NT IN TH|E SAME P|
|00001020| 41 49 52 2c 20 41 4e 44 | 20 58 32 0d 41 4e 44 20 |AIR, AND| X2.AND |
|00001030| 59 32 20 41 52 45 20 54 | 48 45 20 43 4f 52 52 45 |Y2 ARE T|HE CORRE|
|00001040| 53 50 4f 4e 44 49 4e 47 | 20 45 4c 45 4d 45 4e 54 |SPONDING| ELEMENT|
|00001050| 53 0d 4f 46 20 41 4e 59 | 20 4f 54 48 45 52 20 50 |S.OF ANY| OTHER P|
|00001060| 41 49 52 2e 0d 0d 20 20 | 20 20 c3 48 4f 4f 53 49 |AIR...  |  .HOOSI|
|00001070| 4e 47 20 54 48 45 20 50 | 41 49 52 53 20 28 37 2c |NG THE P|AIRS (7,|
|00001080| 32 29 20 41 4e 44 0d 28 | 31 30 2c 33 29 20 57 45 |2) AND.(|10,3) WE|
|00001090| 20 48 41 56 45 20 4d 3d | 28 33 2d 32 29 2f 28 31 | HAVE M=|(3-2)/(1|
|000010a0| 30 2d 37 29 20 4f 52 0d | 4d 20 3d 20 31 2f 33 2e |0-7) OR.|M = 1/3.|
|000010b0| 20 20 d4 48 55 53 0d 0d | 20 59 2d 32 3d 31 2f 33 |  .HUS..| Y-2=1/3|
|000010c0| 2a 28 58 2d 37 29 20 20 | 20 4f 52 0d 20 59 2d 32 |*(X-7)  | OR. Y-2|
|000010d0| 3d 31 2f 33 2a 58 2d 37 | 2f 33 20 20 20 4f 52 0d |=1/3*X-7|/3   OR.|
|000010e0| 20 59 3d 31 2f 33 2a 58 | 2d 37 2f 33 2b 36 2f 33 | Y=1/3*X|-7/3+6/3|
|000010f0| 20 4f 52 0d 20 59 3d 31 | 2f 33 2a 58 2d 31 2f 33 | OR. Y=1|/3*X-1/3|
|00001100| 2e 0d 0d d4 48 55 53 2c | 20 57 48 45 4e 20 58 20 |....HUS,| WHEN X |
|00001110| 48 41 53 20 54 48 45 20 | 56 41 4c 55 45 53 20 34 |HAS THE |VALUES 4|
|00001120| 2c 37 2c 31 30 2c 0d 31 | 33 2c 31 36 2c 31 39 2c |,7,10,.1|3,16,19,|
|00001130| 32 32 2c 32 35 2c 41 4e | 44 20 32 38 2c 20 59 20 |22,25,AN|D 28, Y |
|00001140| 48 41 53 20 54 48 45 0d | 56 41 4c 55 45 53 20 31 |HAS THE.|VALUES 1|
|00001150| 2c 32 2c 33 2c 34 2c 35 | 2c 36 2c 37 2c 38 2c 41 |,2,3,4,5|,6,7,8,A|
|00001160| 4e 44 20 39 2e 20 20 d3 | 49 4e 43 45 0d 28 58 2d |ND 9.  .|INCE.(X-|
|00001170| 31 29 2f 33 20 49 53 20 | 45 51 55 49 56 41 4c 45 |1)/3 IS |EQUIVALE|
|00001180| 4e 54 20 54 4f 20 31 2f | 33 2a 58 2d 31 2f 33 0d |NT TO 1/|3*X-1/3.|
|00001190| 41 4e 44 20 4f 4e 4c 59 | 20 52 45 51 55 49 52 45 |AND ONLY| REQUIRE|
|000011a0| 53 20 4f 4e 45 20 44 49 | 56 49 53 49 4f 4e 2c 20 |S ONE DI|VISION, |
|000011b0| 57 45 0d 57 4f 55 4c 44 | 20 57 52 49 54 45 3a 0d |WE.WOULD| WRITE:.|
|000011c0| 0d 20 20 cf ce 20 28 58 | 2d 31 29 2f 33 20 c7 cf |.  .. (X|-1)/3 ..|
|000011d0| d4 cf 20 2e 2e 2e 20 20 | cf 4e 45 20 4c 49 4e 45 |.. ...  |.NE LINE|
|000011e0| 0d 49 4e 53 54 45 41 44 | 20 4f 46 20 4e 49 4e 45 |.INSTEAD| OF NINE|
|000011f0| 20 c9 c6 2d d4 c8 c5 ce | 20 53 54 41 54 45 4d 45 | ..-....| STATEME|
|00001200| 4e 54 53 2e 0d 0d 20 20 | 20 20 c9 4e 20 52 45 46 |NTS...  |  .N REF|
|00001210| 45 52 45 4e 43 45 20 54 | 4f 20 54 48 45 20 46 49 |ERENCE T|O THE FI|
|00001220| 52 53 54 20 43 41 53 45 | 2c 20 c9 0d 43 4f 4d 4d |RST CASE|, ..COMM|
|00001230| 45 4e 54 45 44 20 54 48 | 41 54 20 54 48 45 20 4d |ENTED TH|AT THE M|
|00001240| 41 54 48 45 4d 41 54 49 | 43 41 4c 4c 59 0d 54 52 |ATHEMATI|CALLY.TR|
|00001250| 41 49 4e 45 44 20 cd c9 | c7 c8 d4 20 4b 4e 4f 57 |AINED ..|... KNOW|
|00001260| 20 54 48 45 20 46 4f 52 | 4d 55 4c 41 20 46 4f 52 | THE FOR|MULA FOR|
|00001270| 20 54 48 45 0d 4e 54 48 | 20 54 45 52 4d 20 4f 46 | THE.NTH| TERM OF|
|00001280| 20 41 4e 20 41 52 49 54 | 48 4d 45 54 49 43 20 53 | AN ARIT|HMETIC S|
|00001290| 45 51 55 45 4e 43 45 2e | 0d cd 41 4e 59 20 50 45 |EQUENCE.|..ANY PE|
|000012a0| 4f 50 4c 45 20 56 49 45 | 57 20 4d 41 54 48 45 4d |OPLE VIE|W MATHEM|
|000012b0| 41 54 49 43 53 20 41 53 | 20 41 0d 43 4f 4c 4c 45 |ATICS AS| A.COLLE|
|000012c0| 43 54 49 4f 4e 20 4f 46 | 20 46 41 43 54 53 2c 20 |CTION OF| FACTS, |
|000012d0| 57 48 45 52 45 41 53 20 | 54 48 45 0d 4d 41 54 48 |WHEREAS |THE.MATH|
|000012e0| 45 4d 41 54 49 43 49 41 | 4e 20 56 49 45 57 53 20 |EMATICIA|N VIEWS |
|000012f0| 46 4f 52 4d 55 4c 41 53 | 20 41 53 20 41 0d 4e 41 |FORMULAS| AS A.NA|
|00001300| 54 55 52 41 4c 20 43 4f | 4e 53 45 51 55 45 4e 43 |TURAL CO|NSEQUENC|
|00001310| 45 20 4f 46 20 55 4e 44 | 45 52 53 54 41 4e 44 49 |E OF UND|ERSTANDI|
|00001320| 4e 47 0d 41 4e 20 41 52 | 45 41 20 4f 46 20 49 4e |NG.AN AR|EA OF IN|
|00001330| 51 55 49 52 59 2e 20 20 | c9 46 20 48 45 20 44 4f |QUIRY.  |.F HE DO|
|00001340| 45 53 4e 27 54 0d 52 45 | 4d 45 4d 42 45 52 20 54 |ESN'T.RE|MEMBER T|
|00001350| 48 45 20 46 4f 52 4d 55 | 4c 41 2c 20 48 45 20 44 |HE FORMU|LA, HE D|
|00001360| 45 52 49 56 45 53 20 49 | 54 2e 0d d4 48 49 53 20 |ERIVES I|T...HIS |
|00001370| 49 53 20 45 58 41 43 54 | 4c 59 20 54 48 45 20 41 |IS EXACT|LY THE A|
|00001380| 54 54 49 54 55 44 45 20 | 48 45 20 42 52 49 4e 47 |TTITUDE |HE BRING|
|00001390| 53 0d 54 4f 20 50 52 4f | 47 52 41 4d 4d 49 4e 47 |S.TO PRO|GRAMMING|
|000013a0| 2e 20 20 c8 45 20 55 53 | 45 53 20 52 4f 55 54 49 |.  .E US|ES ROUTI|
|000013b0| 4e 45 53 20 46 52 4f 4d | 0d 41 4c 4c 20 54 48 45 |NES FROM|.ALL THE|
|000013c0| 20 53 4f 55 52 43 45 53 | 20 41 54 20 48 49 53 20 | SOURCES| AT HIS |
|000013d0| 44 49 53 50 4f 53 41 4c | 2c 20 42 55 54 0d 49 46 |DISPOSAL|, BUT.IF|
|000013e0| 20 48 45 20 48 41 53 20 | 4e 4f 20 52 4f 55 54 49 | HE HAS |NO ROUTI|
|000013f0| 4e 45 20 46 4f 52 20 54 | 48 45 20 54 41 53 4b 20 |NE FOR T|HE TASK |
|00001400| 41 54 0d 48 41 4e 44 2c | 20 48 45 20 44 45 56 45 |AT.HAND,| HE DEVE|
|00001410| 4c 4f 50 53 20 54 48 45 | 20 52 4f 55 54 49 4e 45 |LOPS THE| ROUTINE|
|00001420| 20 48 45 20 4e 45 45 44 | 53 0d 49 4e 53 54 45 41 | HE NEED|S.INSTEA|
|00001430| 44 20 4f 46 20 53 45 41 | 52 43 48 49 4e 47 20 54 |D OF SEA|RCHING T|
|00001440| 48 52 4f 55 47 48 20 42 | 41 43 4b 0d 49 53 53 55 |HROUGH B|ACK.ISSU|
|00001450| 45 53 20 4f 46 20 cc cf | c1 c4 d3 d4 c1 d2 e0 4f |ES OF ..|.......O|
|00001460| 52 20 d2 d5 ce 2e 0d 0d | cd ca 0d 0d c6 c5 ce c4 |R ......|........|
|00001470| c5 d2 27 d3 20 c3 cf cd | cd c5 ce d4 d3 3a 20 c1 |..'. ...|.....: .|
|00001480| 4e 44 20 57 48 41 54 27 | 53 20 57 52 4f 4e 47 0d |ND WHAT'|S WRONG.|
|00001490| 57 49 54 48 20 53 45 41 | 52 43 48 49 4e 47 20 54 |WITH SEA|RCHING T|
|000014a0| 48 52 4f 55 47 48 20 42 | 41 43 4b 20 49 53 53 55 |HROUGH B|ACK ISSU|
|000014b0| 45 53 20 4f 46 0d cc cf | c1 c4 d3 d4 c1 d2 3f 20 |ES OF...|......? |
|000014c0| 20 d3 45 52 49 4f 55 53 | 4c 59 2c 20 cd 41 55 52 | .ERIOUS|LY, .AUR|
|000014d0| 49 43 45 2c 20 59 4f 55 | 52 0d 50 4f 49 4e 54 20 |ICE, YOU|R.POINT |
|000014e0| 49 53 20 57 45 4c 4c 2d | 54 41 4b 45 4e 2e 20 20 |IS WELL-|TAKEN.  |
|000014f0| c4 55 52 49 4e 47 20 4d | 59 20 22 4c 4f 53 54 0d |.URING M|Y "LOST.|
|00001500| 59 45 41 52 53 22 20 41 | 53 20 41 20 43 4f 4c 4c |YEARS" A|S A COLL|
|00001510| 45 47 45 20 45 4e 47 49 | 4e 45 45 52 49 4e 47 0d |EGE ENGI|NEERING.|
|00001520| 53 54 55 44 45 4e 54 20 | c9 20 48 41 44 20 41 20 |STUDENT |. HAD A |
|00001530| 4c 4f 54 20 4f 46 20 4d | 41 54 48 20 57 48 49 43 |LOT OF M|ATH WHIC|
|00001540| 48 20 4e 4f 57 0d 45 53 | 43 41 50 45 53 20 4d 45 |H NOW.ES|CAPES ME|
|00001550| 2c 20 42 55 54 20 54 48 | 45 20 49 44 45 41 20 4f |, BUT TH|E IDEA O|
|00001560| 46 20 22 4c 4f 4f 4b 49 | 4e 47 0d 46 4f 52 20 41 |F "LOOKI|NG.FOR A|
|00001570| 20 50 41 54 54 45 52 4e | 22 20 53 54 41 59 45 44 | PATTERN|" STAYED|
|00001580| 20 57 49 54 48 20 4d 45 | 20 41 4e 44 20 c9 0d 48 | WITH ME| AND ..H|
|00001590| 41 56 45 20 55 53 45 44 | 20 49 54 20 49 4e 20 45 |AVE USED| IT IN E|
|000015a0| 56 45 52 59 20 50 52 4f | 47 52 41 4d 20 c9 27 56 |VERY PRO|GRAM .'V|
|000015b0| 45 0d 45 56 45 52 20 57 | 52 49 54 54 45 4e 2e 0d |E.EVER W|RITTEN..|
|000015c0| 0d c1 4e 44 20 57 48 49 | 4c 45 20 4d 59 20 56 4f |..ND WHI|LE MY VO|
|000015d0| 49 43 45 20 4d 41 59 20 | 4e 4f 54 20 48 41 56 45 |ICE MAY |NOT HAVE|
|000015e0| 20 54 48 45 0d 49 4d 50 | 41 43 54 20 4f 46 20 41 | THE.IMP|ACT OF A|
|000015f0| 20 c3 48 41 52 4c 45 53 | 20 c2 41 52 4b 4c 45 59 | .HARLES| .ARKLEY|
|00001600| 20 4f 52 20 41 0d cd 49 | 43 48 41 45 4c 20 ca 4f | OR A..I|CHAEL .O|
|00001610| 52 44 41 4e 2c 20 c9 27 | 44 20 4c 49 4b 45 20 54 |RDAN, .'|D LIKE T|
|00001620| 4f 20 4a 4f 49 4e 20 54 | 48 45 4d 0d 49 4e 20 53 |O JOIN T|HEM.IN S|
|00001630| 41 59 49 4e 47 2c 20 22 | c9 54 27 53 20 43 4f 4f |AYING, "|.T'S COO|
|00001640| 4c 20 54 4f 20 53 54 41 | 59 20 49 4e 0d 53 43 48 |L TO STA|Y IN.SCH|
|00001650| 4f 4f 4c 2e 22 0d 0d 20 | 20 20 20 20 20 20 20 20 |OOL.".. |        |
|00001660| 2a 2a 2a 2a 20 c5 4e 44 | 20 4f 46 20 d4 45 58 54 |**** .ND| OF .EXT|
|00001670| 20 2a 2a 2a 2a 0d       |                         | ****.  |        |
+--------+-------------------------+-------------------------+--------+--------+