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MacOS 8.1

Win98

DOS

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+--------+-------------------------+-------------------------+--------+--------+
|00000000| 4d 5a 9d 00 03 00 00 00 | 20 00 00 00 ff ff 07 00 |MZ......| .......|
|00000010| 00 01 65 40 00 00 00 00 | 40 00 00 00 01 00 00 00 |..e@....|@.......|
|00000020| 00 00 00 00 00 00 00 00 | 00 00 00 00 00 00 00 00 |........|........|
|00000030| 00 00 00 00 00 00 00 00 | 00 00 00 00 00 04 00 00 |........|........|
|00000040| 00 00 00 00 00 00 00 00 | 00 00 00 00 00 00 00 00 |........|........|
|00000050| 00 00 00 00 00 00 00 00 | 00 00 00 00 00 00 00 00 |........|........|
|00000060| 00 00 00 00 00 00 00 00 | 00 00 00 00 00 00 00 00 |........|........|
|00000070| 00 00 00 00 00 00 00 00 | 00 00 00 00 00 00 00 00 |........|........|
|00000080| 00 00 00 00 00 00 00 00 | 00 00 00 00 00 00 00 00 |........|........|
|00000090| 00 00 00 00 00 00 00 00 | 00 00 00 00 00 00 00 00 |........|........|
|000000a0| 00 00 00 00 00 00 00 00 | 00 00 00 00 00 00 00 00 |........|........|
|000000b0| 00 00 00 00 00 00 00 00 | 00 00 00 00 00 00 00 00 |........|........|
|000000c0| 00 00 00 00 00 00 00 00 | 00 00 00 00 00 00 00 00 |........|........|
|000000d0| 00 00 00 00 00 00 00 00 | 00 00 00 00 00 00 00 00 |........|........|
|000000e0| 00 00 00 00 00 00 00 00 | 00 00 00 00 00 00 00 00 |........|........|
|000000f0| 00 00 00 00 00 00 00 00 | 00 00 00 00 00 00 00 00 |........|........|
|00000100| 00 00 00 00 00 00 00 00 | 00 00 00 00 00 00 00 00 |........|........|
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|00000140| 00 00 00 00 00 00 00 00 | 00 00 00 00 00 00 00 00 |........|........|
|00000150| 00 00 00 00 00 00 00 00 | 00 00 00 00 00 00 00 00 |........|........|
|00000160| 00 00 00 00 00 00 00 00 | 00 00 00 00 00 00 00 00 |........|........|
|00000170| 00 00 00 00 00 00 00 00 | 00 00 00 00 00 00 00 00 |........|........|
|00000180| 00 00 00 00 00 00 00 00 | 00 00 00 00 00 00 00 00 |........|........|
|00000190| 00 00 00 00 00 00 00 00 | 00 00 00 00 00 00 00 00 |........|........|
|000001a0| 00 00 00 00 00 00 00 00 | 00 00 00 00 00 00 00 00 |........|........|
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|000001f0| 00 00 00 00 00 00 00 00 | 00 00 00 00 00 00 00 00 |........|........|
|00000200| e8 53 00 54 68 69 73 20 | 70 72 6f 67 72 61 6d 20 |.S.This |program |
|00000210| 72 65 71 75 69 72 65 73 | 20 4d 69 63 72 6f 73 6f |requires| Microso|
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|00000260| cd 21 00 00 00 00 00 00 | 00 00 00 00 00 00 00 00 |.!......|........|
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|00000290| 00 00 00 00 00 00 00 00 | 00 00 00 00 00 00 00 00 |........|........|
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|00000300| 00 00 00 00 00 00 00 00 | 00 00 00 00 00 00 00 00 |........|........|
|00000310| 00 00 00 00 00 00 00 00 | 00 00 00 00 00 00 00 00 |........|........|
|00000320| 00 00 00 00 00 00 00 00 | 00 00 00 00 00 00 00 00 |........|........|
|00000330| 00 00 00 00 00 00 00 00 | 00 00 00 00 00 00 00 00 |........|........|
|00000340| 00 00 00 00 00 00 00 00 | 00 00 00 00 00 00 00 00 |........|........|
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|00000740| 00 00 ee 09 19 00 30 0c | 9c 80 00 00 00 00 07 0a |......0.|........|
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|00000770| 00 00 54 0a 22 00 30 0c | a9 80 00 00 00 00 76 0a |..T.".0.|......v.|
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|00000d40| 00 00 26 12 03 00 30 0c | 66 88 00 00 00 00 29 12 |..&...0.|f.....).|
|00000d50| 03 00 30 0c 67 88 00 00 | 00 00 2c 12 03 00 30 0c |..0.g...|..,...0.|
|00000d60| 68 88 00 00 00 00 2f 12 | 03 00 30 0c 40 88 00 00 |h...../.|..0.@...|
|00000d70| 00 00 32 12 03 00 30 0c | 6e 88 00 00 00 00 35 12 |..2...0.|n.....5.|
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|00000d90| 6b 88 00 00 00 00 3b 12 | 03 00 30 0c 19 88 00 00 |k.....;.|..0.....|
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|00000db0| 03 00 30 0c 6d 88 00 00 | 00 00 44 12 03 00 30 0c |..0.m...|..D...0.|
|00000dc0| 2a 88 00 00 00 00 47 12 | 03 00 30 0c 78 88 00 00 |*.....G.|..0.x...|
|00000dd0| 00 00 4a 12 03 00 30 0c | 79 88 00 00 00 00 4d 12 |..J...0.|y.....M.|
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|00000df0| 24 88 00 00 00 00 53 12 | 03 00 30 0c 27 88 00 00 |$.....S.|..0.'...|
|00000e00| 00 00 56 12 03 00 30 0c | 26 88 00 00 00 00 59 12 |..V...0.|&.....Y.|
|00000e10| 03 00 30 0c 25 88 00 00 | 00 00 5c 12 03 00 30 0c |..0.%...|..\...0.|
|00000e20| c7 89 00 00 00 00 5f 12 | 03 00 30 0c 14 88 00 00 |......_.|..0.....|
|00000e30| 00 00 62 12 03 00 30 0c | 15 88 00 00 00 00 65 12 |..b...0.|......e.|
|00000e40| 03 00 30 0c 1d 88 00 00 | 00 00 68 12 03 00 30 0c |..0.....|..h...0.|
|00000e50| 1e 88 00 00 00 00 6b 12 | 03 00 30 0c 22 88 00 00 |......k.|..0."...|
|00000e60| 00 00 6e 12 03 00 30 0c | 21 88 00 00 00 00 71 12 |..n...0.|!.....q.|
|00000e70| 03 00 30 0c 1a 88 00 00 | 00 00 74 12 03 00 30 0c |..0.....|..t...0.|
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|00002660| 57 6f 72 6b 69 6e 67 20 | 77 69 74 68 20 49 6e 65 |Working |with Ine|
|00002670| 71 75 61 6c 69 74 69 65 | 73 0d 20 20 20 20 20 20 |qualitie|s.      |
|00002680| 0d 20 20 20 20 20 20 54 | 68 69 6e 6b 20 6f 66 20 |.      T|hink of |
|00002690| 74 68 65 20 6e 75 6d 62 | 65 72 20 6c 69 6e 65 3a |the numb|er line:|
|000026a0| 0d 5f 5f 5f 5f 5f 5f 5f | 5f 5f 5f 5f 5f 5f 5f 5f |._______|________|
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|000026e0| 20 20 36 20 20 20 37 20 | 2e 2e 2e 0d 0d 45 78 61 |  6   7 |.....Exa|
|000026f0| 6d 70 6c 65 20 31 3a 20 | 20 32 20 3c 20 34 20 20 |mple 1: | 2 < 4  |
|00002700| 0d 20 20 20 20 20 32 20 | 69 73 20 6c 65 73 73 20 |.     2 |is less |
|00002710| 74 68 61 6e 20 34 20 0d | 20 20 20 20 20 62 65 63 |than 4 .|     bec|
|00002720| 61 75 73 65 20 32 20 6c | 69 65 73 20 74 6f 20 74 |ause 2 l|ies to t|
|00002730| 68 65 20 4c 45 46 54 20 | 6f 66 20 34 0d 20 20 20 |he LEFT |of 4.   |
|00002740| 20 20 6f 6e 20 74 68 65 | 20 6e 75 6d 62 65 72 20 |  on the| number |
|00002750| 6c 69 6e 65 2e 0d 20 20 | 20 20 20 20 20 20 0d 45 |line..  |      .E|
|00002760| 78 61 6d 70 6c 65 20 32 | 3a 20 20 31 2e 30 30 30 |xample 2|:  1.000|
|00002770| 30 31 20 3e 20 31 0d 20 | 20 20 20 20 31 2e 30 30 |01 > 1. |    1.00|
|00002780| 30 30 31 20 69 73 20 67 | 72 65 61 74 65 72 20 74 |001 is g|reater t|
|00002790| 68 61 6e 20 31 0d 20 20 | 20 20 20 62 65 63 61 75 |han 1.  |   becau|
|000027a0| 73 65 20 31 2e 30 30 30 | 30 31 20 69 73 20 74 6f |se 1.000|01 is to|
|000027b0| 20 74 68 65 20 52 49 47 | 48 54 20 6f 66 20 31 2e | the RIG|HT of 1.|
|000027c0| 0d 5f 5f 5f 5f 5f 5f 5f | 5f 5f 5f 5f 5f 5f 5f 5f |._______|________|
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|000027e0| 5f 5f 5f 5f 5f 5f 5f 5f | 0d 45 78 61 6d 70 6c 65 |________|.Example|
|000027f0| 20 33 3a 20 53 6f 6c 76 | 65 20 38 20 2d 20 33 78 | 3: Solv|e 8 - 3x|
|00002800| 20 f7 20 35 0d 0d 53 74 | 65 70 20 31 3a 20 41 73 | . 5..St|ep 1: As|
|00002810| 20 77 69 74 68 20 65 71 | 75 61 74 69 6f 6e 73 2c | with eq|uations,|
|00002820| 20 69 73 6f 6c 61 74 65 | 20 78 2e 20 46 69 72 73 | isolate| x. Firs|
|00002830| 74 2c 20 73 75 62 74 72 | 61 63 74 20 38 20 66 72 |t, subtr|act 8 fr|
|00002840| 6f 6d 20 65 61 63 68 20 | 73 69 64 65 3a 0d 20 20 |om each |side:.  |
|00002850| 20 20 20 20 20 20 20 20 | 38 20 2d 20 38 20 2d 20 |        |8 - 8 - |
|00002860| 33 78 20 f7 20 35 20 2d | 20 38 0d 20 20 20 20 20 |3x . 5 -| 8.     |
|00002870| 20 20 20 20 20 20 20 20 | 20 20 20 20 2d 33 78 20 |        |    -3x |
|00002880| f7 20 2d 33 0d 0d 53 74 | 65 70 20 32 3a 20 4d 75 |. -3..St|ep 2: Mu|
|00002890| 6c 74 69 70 6c 79 20 62 | 79 20 2d 31 2f 33 2e 20 |ltiply b|y -1/3. |
|000028a0| 28 43 61 72 65 66 75 6c | 21 20 59 6f 75 20 6d 75 |(Careful|! You mu|
|000028b0| 73 74 20 63 68 61 6e 67 | 65 20 74 68 65 20 69 6e |st chang|e the in|
|000028c0| 65 71 75 61 6c 69 74 79 | 27 73 20 64 69 72 65 63 |equality|'s direc|
|000028d0| 74 69 6f 6e 20 77 68 65 | 6e 20 79 6f 75 20 6d 75 |tion whe|n you mu|
|000028e0| 6c 74 69 70 6c 79 20 62 | 79 20 61 20 6e 65 67 61 |ltiply b|y a nega|
|000028f0| 74 69 76 65 20 6e 75 6d | 62 65 72 2e 29 3a 0d 20 |tive num|ber.):. |
|00002900| 20 20 20 2d 33 78 28 2d | 31 2f 33 29 20 f6 20 2d |   -3x(-|1/3) . -|
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|00002920| 0d 0d 0d 0d 0d 0d 0d 0d | 0d 00 00 00 00 00 00 00 |........|........|
|00002930| 53 6f 6c 76 69 6e 67 20 | 41 6c 67 65 62 72 61 69 |Solving |Algebrai|
|00002940| 63 20 45 71 75 61 74 69 | 6f 6e 73 2a 0d 0d 42 65 |c Equati|ons*..Be|
|00002950| 6c 6f 77 20 61 72 65 20 | 74 77 6f 20 65 78 61 6d |low are |two exam|
|00002960| 70 6c 65 73 20 6f 66 20 | 73 6f 6c 76 69 6e 67 20 |ples of |solving |
|00002970| 66 6f 72 20 74 68 65 20 | 76 61 72 69 61 62 6c 65 |for the |variable|
|00002980| 20 78 2e 20 20 0d 0d 45 | 78 61 6d 70 6c 65 20 31 | x.  ..E|xample 1|
|00002990| 3a 20 20 53 6f 6c 76 65 | 20 66 6f 72 20 78 3a 20 |:  Solve| for x: |
|000029a0| 32 28 78 2b 33 29 20 3d | 20 33 78 2d 37 0d 0d 53 |2(x+3) =| 3x-7..S|
|000029b0| 74 65 70 20 31 3a 20 45 | 6c 69 6d 69 6e 61 74 65 |tep 1: E|liminate|
|000029c0| 20 74 68 65 20 67 72 6f | 75 70 69 6e 67 20 73 79 | the gro|uping sy|
|000029d0| 6d 62 6f 6c 73 2e 0d 20 | 20 20 20 20 20 20 20 20 |mbols.. |        |
|000029e0| 20 20 20 20 20 32 78 2b | 36 20 3d 20 33 78 2d 37 |     2x+|6 = 3x-7|
|000029f0| 0d 20 0d 53 74 65 70 20 | 32 3a 20 43 6f 6d 62 69 |. .Step |2: Combi|
|00002a00| 6e 65 20 74 65 72 6d 73 | 2e 0d 20 20 20 20 20 20 |ne terms|..      |
|00002a10| 20 20 20 20 20 20 20 20 | 32 78 2d 33 78 20 3d 20 |        |2x-3x = |
|00002a20| 2d 37 2d 36 0d 20 20 20 | 20 20 20 20 20 20 20 20 |-7-6.   |        |
|00002a30| 20 20 20 20 20 20 2d 78 | 20 3d 20 2d 31 33 0d 20 |      -x| = -13. |
|00002a40| 0d 53 74 65 70 20 33 3a | 20 57 72 69 74 65 20 69 |.Step 3:| Write i|
|00002a50| 6e 20 73 74 61 6e 64 61 | 72 64 20 66 6f 72 6d 2e |n standa|rd form.|
|00002a60| 0d 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |.       |        |
|00002a70| 20 20 20 78 20 3d 20 31 | 33 0d 5f 5f 5f 5f 5f 5f |   x = 1|3.______|
|00002a80| 5f 5f 5f 5f 5f 5f 5f 5f | 5f 5f 5f 5f 5f 5f 5f 5f |________|________|
|00002a90| 5f 5f 5f 5f 5f 5f 5f 5f | 5f 5f 5f 5f 5f 5f 5f 5f |________|________|
|00002aa0| 0d 45 78 61 6d 70 6c 65 | 20 32 3a 20 53 6f 6c 76 |.Example| 2: Solv|
|00002ab0| 65 20 66 6f 72 20 78 3a | 20 34 20 2b 20 32 37 2f |e for x:| 4 + 27/|
|00002ac0| 78 20 3d 20 2d 35 0d 0d | 20 20 20 20 20 20 20 20 |x = -5..|        |
|00002ad0| 20 20 20 20 20 20 34 78 | 20 2b 20 32 37 20 3d 20 |      4x| + 27 = |
|00002ae0| 2d 35 78 0d 20 20 20 20 | 20 20 20 20 20 20 20 20 |-5x.    |        |
|00002af0| 20 20 39 78 20 2b 20 32 | 37 20 3d 20 30 0d 20 20 |  9x + 2|7 = 0.  |
|00002b00| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |        |        |
|00002b10| 20 39 78 20 3d 20 2d 32 | 37 0d 20 20 20 20 20 20 | 9x = -2|7.      |
|00002b20| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 78 20 |        |      x |
|00002b30| 3d 20 2d 33 20 20 20 20 | 20 20 20 20 20 20 20 20 |= -3    |        |
|00002b40| 20 20 20 0d 0d 53 65 65 | 20 74 68 65 20 52 65 66 |   ..See| the Ref|
|00002b50| 65 72 65 6e 63 65 20 66 | 6f 72 20 6d 6f 72 65 20 |erence f|or more |
|00002b60| 72 75 6c 65 73 20 61 6e | 64 20 6d 65 74 68 6f 64 |rules an|d method|
|00002b70| 73 20 66 6f 72 20 73 6f | 6c 76 69 6e 67 20 65 71 |s for so|lving eq|
|00002b80| 75 61 74 69 6f 6e 73 2e | 00 00 00 00 00 00 00 00 |uations.|........|
|00002b90| 55 6e 64 65 72 73 74 61 | 6e 64 69 6e 67 20 56 61 |Understa|nding Va|
|00002ba0| 72 69 61 62 6c 65 73 0d | 0d 45 78 61 6d 70 6c 65 |riables.|.Example|
|00002bb0| 20 31 3a 20 20 49 66 20 | 6e 20 3d 20 35 2c 20 74 | 1:  If |n = 5, t|
|00002bc0| 68 65 6e 20 20 6e 20 2b | 20 33 20 3d 20 3f 0d 20 |hen  n +| 3 = ?. |
|00002bd0| 0d 53 74 65 70 20 31 3a | 20 53 75 62 73 74 69 74 |.Step 1:| Substit|
|00002be0| 75 74 65 20 6e 27 73 20 | 63 75 72 72 65 6e 74 20 |ute n's |current |
|00002bf0| 76 61 6c 75 65 20 69 6e | 74 6f 20 74 68 65 20 65 |value in|to the e|
|00002c00| 71 75 61 74 69 6f 6e 2e | 20 28 54 68 65 20 6c 65 |quation.| (The le|
|00002c10| 74 74 65 72 20 6e 20 72 | 65 70 72 65 73 65 6e 74 |tter n r|epresent|
|00002c20| 73 20 35 29 3a 0d 20 20 | 20 20 20 20 20 20 20 20 |s 5):.  |        |
|00002c30| 20 20 6e 20 2b 20 33 20 | 3d 20 3f 0d 20 20 20 20 |  n + 3 |= ?.    |
|00002c40| 20 20 20 20 20 20 20 20 | 35 20 2b 20 33 20 3d 20 |        |5 + 3 = |
|00002c50| 3f 0d 0d 53 74 65 70 20 | 32 3a 20 41 64 64 20 74 |?..Step |2: Add t|
|00002c60| 68 65 20 6e 75 6d 62 65 | 72 73 3a 0d 20 20 20 20 |he numbe|rs:.    |
|00002c70| 20 20 20 20 20 20 20 20 | 35 20 2b 20 33 20 3d 20 |        |5 + 3 = |
|00002c80| 38 0d 20 0d 52 65 73 75 | 6c 74 3a 20 49 66 20 6e |8. .Resu|lt: If n|
|00002c90| 20 3d 20 35 2c 20 74 68 | 65 6e 20 20 6e 20 2b 20 | = 5, th|en  n + |
|00002ca0| 33 20 3d 20 38 2e 20 0d | 20 20 20 20 20 0d 5f 5f |3 = 8. .|     .__|
|00002cb0| 5f 5f 5f 5f 5f 5f 5f 5f | 5f 5f 5f 5f 5f 5f 5f 5f |________|________|
|00002cc0| 5f 5f 5f 5f 5f 5f 5f 5f | 5f 5f 5f 5f 5f 5f 5f 5f |________|________|
|00002cd0| 5f 5f 5f 5f 5f 0d 45 78 | 61 6d 70 6c 65 20 32 3a |_____.Ex|ample 2:|
|00002ce0| 20 20 49 66 20 20 6e 20 | 2b 20 34 20 3d 20 31 31 |  If  n |+ 4 = 11|
|00002cf0| 2c 20 74 68 65 6e 20 6e | 20 3d 20 3f 0d 20 0d 53 |, then n| = ?. .S|
|00002d00| 74 65 70 20 31 3a 20 53 | 75 62 74 72 61 63 74 20 |tep 1: S|ubtract |
|00002d10| 34 20 66 72 6f 6d 20 62 | 6f 74 68 20 73 69 64 65 |4 from b|oth side|
|00002d20| 73 20 6f 66 20 74 68 65 | 20 65 71 75 61 74 69 6f |s of the| equatio|
|00002d30| 6e 20 74 6f 20 67 65 74 | 20 6e 20 62 79 20 69 74 |n to get| n by it|
|00002d40| 73 65 6c 66 3a 0d 0d 20 | 20 20 20 20 20 20 20 20 |self:.. |        |
|00002d50| 20 20 20 6e 20 2b 20 34 | 20 2d 20 34 20 3d 20 31 |   n + 4| - 4 = 1|
|00002d60| 31 20 2d 20 34 0d 0d 53 | 74 65 70 20 32 3a 20 53 |1 - 4..S|tep 2: S|
|00002d70| 69 6d 70 6c 69 66 79 3a | 0d 20 20 20 20 20 20 20 |implify:|.       |
|00002d80| 20 20 20 20 20 20 20 20 | 20 6e 20 2b 20 30 20 3d |        | n + 0 =|
|00002d90| 20 31 31 20 2d 20 34 0d | 20 20 20 20 20 20 20 20 | 11 - 4.|        |
|00002da0| 20 20 20 20 20 20 20 20 | 20 20 20 20 6e 20 3d 20 |        |    n = |
|00002db0| 37 0d 20 0d 52 65 73 75 | 6c 74 3a 20 49 66 20 6e |7. .Resu|lt: If n|
|00002dc0| 20 2b 20 34 20 3d 20 31 | 31 2c 20 74 68 65 6e 20 | + 4 = 1|1, then |
|00002dd0| 6e 20 3d 20 37 2e 00 00 | 00 00 00 00 00 00 00 00 |n = 7...|........|
|00002de0| 0d 46 61 63 74 6f 72 69 | 6e 67 20 50 6f 6c 79 6e |.Factori|ng Polyn|
|00002df0| 6f 6d 69 61 6c 73 0d 28 | 53 65 65 20 74 68 65 20 |omials.(|See the |
|00002e00| 52 65 66 65 72 65 6e 63 | 65 20 66 6f 72 20 73 70 |Referenc|e for sp|
|00002e10| 65 63 69 61 6c 20 74 69 | 70 73 20 6f 6e 20 66 61 |ecial ti|ps on fa|
|00002e20| 63 74 6f 72 69 6e 67 20 | 71 75 61 64 72 61 74 69 |ctoring |quadrati|
|00002e30| 63 20 65 71 75 61 74 69 | 6f 6e 73 2e 29 0d 0d 45 |c equati|ons.)..E|
|00002e40| 78 61 6d 70 6c 65 3a 20 | 46 61 63 74 6f 72 20 20 |xample: |Factor  |
|00002e50| 32 34 78 a3 7a aa 2d 38 | 78 7a a3 2b 31 36 78 7a |24x.z.-8|xz.+16xz|
|00002e60| 0d 0d 53 74 65 70 20 31 | 3a 20 45 78 61 6d 69 6e |..Step 1|: Examin|
|00002e70| 65 20 65 61 63 68 20 74 | 65 72 6d 20 66 6f 72 20 |e each t|erm for |
|00002e80| 61 20 63 6f 6d 6d 6f 6e | 20 63 6f 6e 73 74 61 6e |a common| constan|
|00002e90| 74 2e 20 45 61 63 68 20 | 74 65 72 6d 20 68 61 73 |t. Each |term has|
|00002ea0| 20 61 6e 20 65 76 65 6e | 20 6d 75 6c 74 69 70 6c | an even| multipl|
|00002eb0| 65 20 6f 66 20 38 2c 20 | 73 6f 20 79 6f 75 20 63 |e of 8, |so you c|
|00002ec0| 61 6e 20 66 61 63 74 6f | 72 20 6f 75 74 20 38 3a |an facto|r out 8:|
|00002ed0| 0d 20 20 20 20 20 20 20 | 20 20 20 38 28 33 78 a3 |.       |   8(3x.|
|00002ee0| 7a aa 2d 78 7a a3 2b 32 | 78 7a aa 29 0d 0d 53 74 |z.-xz.+2|xz.)..St|
|00002ef0| 65 70 20 32 3a 20 44 6f | 20 74 68 65 20 73 61 6d |ep 2: Do| the sam|
|00002f00| 65 20 66 6f 72 20 74 68 | 65 20 68 69 67 68 65 73 |e for th|e highes|
|00002f10| 74 20 70 6f 77 65 72 20 | 6f 66 20 65 61 63 68 20 |t power |of each |
|00002f20| 76 61 72 69 61 62 6c 65 | 20 69 6e 20 45 41 43 48 |variable| in EACH|
|00002f30| 20 74 65 72 6d 2e 20 46 | 61 63 74 6f 72 20 6f 75 | term. F|actor ou|
|00002f40| 74 20 78 3a 0d 20 20 20 | 20 20 20 20 20 20 20 38 |t x:.   |       8|
|00002f50| 78 28 33 78 aa 7a aa 2d | 7a a3 2b 32 7a aa 29 20 |x(3x.z.-|z.+2z.) |
|00002f60| 0d 61 6e 64 20 7a aa 3a | 0d 20 20 20 20 20 20 20 |.and z.:|.       |
|00002f70| 20 20 20 38 78 7a aa 28 | 33 78 aa 2d 7a 2b 32 29 |   8xz.(|3x.-z+2)|
|00002f80| 20 0d 20 20 20 20 20 20 | 20 20 20 0d 53 74 65 70 | .      |   .Step|
|00002f90| 20 33 3a 20 4d 61 6b 65 | 20 73 75 72 65 20 74 68 | 3: Make| sure th|
|00002fa0| 65 72 65 20 61 72 65 20 | 6e 6f 20 61 64 64 69 74 |ere are |no addit|
|00002fb0| 69 6f 6e 61 6c 20 63 6f | 6d 6d 6f 6e 20 66 61 63 |ional co|mmon fac|
|00002fc0| 74 6f 72 73 20 69 6e 20 | 65 61 63 68 20 74 65 72 |tors in |each ter|
|00002fd0| 6d 2e 20 59 6f 75 27 6c | 6c 20 66 69 6e 64 20 74 |m. You'l|l find t|
|00002fe0| 68 61 74 20 74 68 65 20 | 71 75 61 64 72 61 74 69 |hat the |quadrati|
|00002ff0| 63 20 33 78 aa 2d 7a 2b | 32 20 64 6f 65 73 20 6e |c 3x.-z+|2 does n|
|00003000| 6f 74 20 66 61 63 74 6f | 72 2e 0d 20 0d 52 65 73 |ot facto|r.. .Res|
|00003010| 75 6c 74 3a 20 54 68 65 | 20 70 6f 6c 79 6e 6f 6d |ult: The| polynom|
|00003020| 69 61 6c 20 32 34 78 a3 | 7a aa 2d 38 78 7a a3 2b |ial 24x.|z.-8xz.+|
|00003030| 31 36 78 7a 20 63 61 6e | 20 62 65 20 66 61 63 74 |16xz can| be fact|
|00003040| 6f 72 65 64 20 61 73 20 | 66 6f 6c 6c 6f 77 73 3a |ored as |follows:|
|00003050| 0d 20 20 0d 20 20 20 20 | 20 20 20 20 20 20 38 78 |.  .    |      8x|
|00003060| 7a aa 28 33 78 aa 2d 7a | 2b 32 29 20 0d 00 00 00 |z.(3x.-z|+2) ....|
|00003070| 0d 46 69 6e 64 69 6e 67 | 20 43 6f 6d 6d 6f 6e 20 |.Finding| Common |
|00003080| 46 61 63 74 6f 72 73 0d | 0d 45 78 61 6d 70 6c 65 |Factors.|.Example|
|00003090| 20 31 3a 20 46 61 63 74 | 6f 72 3a 20 20 34 78 20 | 1: Fact|or:  4x |
|000030a0| 2b 20 31 32 0d 0d 4c 6f | 6f 6b 20 66 6f 72 20 61 |+ 12..Lo|ok for a|
|000030b0| 20 63 6f 6e 73 74 61 6e | 74 20 61 6e 64 2f 6f 72 | constan|t and/or|
|000030c0| 20 61 20 76 61 72 69 61 | 62 6c 65 20 74 68 61 74 | a varia|ble that|
|000030d0| 20 69 73 20 69 6e 20 45 | 41 43 48 20 74 65 72 6d | is in E|ACH term|
|000030e0| 2e 20 54 68 65 20 76 61 | 72 69 61 62 6c 65 2c 20 |. The va|riable, |
|000030f0| 78 2c 20 69 73 20 69 6e | 20 6f 6e 6c 79 20 74 68 |x, is in| only th|
|00003100| 65 20 66 69 72 73 74 20 | 74 65 72 6d 2c 20 62 75 |e first |term, bu|
|00003110| 74 20 74 68 65 20 63 6f | 6e 73 74 61 6e 74 20 34 |t the co|nstant 4|
|00003120| 20 69 73 20 69 6e 20 62 | 6f 74 68 20 74 65 72 6d | is in b|oth term|
|00003130| 73 3a 20 20 0d 0d 20 20 | 20 20 20 20 20 20 20 20 |s:  ..  |        |
|00003140| 20 20 34 78 20 2b 20 31 | 32 20 3d 20 34 28 78 20 |  4x + 1|2 = 4(x |
|00003150| 2b 20 33 29 20 0d 5f 5f | 5f 5f 5f 5f 5f 5f 5f 5f |+ 3) .__|________|
|00003160| 5f 5f 5f 5f 5f 5f 5f 5f | 5f 5f 5f 5f 5f 5f 5f 5f |________|________|
|00003170| 5f 5f 5f 5f 5f 5f 5f 5f | 5f 5f 5f 5f 5f 20 20 20 |________|_____   |
|00003180| 20 20 20 20 20 0d 45 78 | 61 6d 70 6c 65 20 32 3a |     .Ex|ample 2:|
|00003190| 20 46 61 63 74 6f 72 3a | 20 33 78 aa 20 2b 20 31 | Factor:| 3x. + 1|
|000031a0| 38 78 0d 0d 20 20 20 20 | 20 20 20 20 20 20 20 33 |8x..    |       3|
|000031b0| 78 aa 20 2b 20 31 38 78 | 20 3d 20 33 28 78 aa 20 |x. + 18x| = 3(x. |
|000031c0| 2b 20 36 78 29 20 0d 28 | 33 20 69 73 20 61 20 63 |+ 6x) .(|3 is a c|
|000031d0| 6f 6d 6d 6f 6e 20 66 61 | 63 74 6f 72 2e 29 0d 0d |ommon fa|ctor.)..|
|000031e0| 20 20 20 20 20 20 20 20 | 20 20 20 20 33 28 78 aa |        |    3(x.|
|000031f0| 20 2b 20 36 78 29 20 3d | 20 33 78 28 78 20 2b 20 | + 6x) =| 3x(x + |
|00003200| 36 29 0d 28 78 20 69 73 | 20 61 20 63 6f 6d 6d 6f |6).(x is| a commo|
|00003210| 6e 20 66 61 63 74 6f 72 | 2e 29 0d 0d 00 00 00 00 |n factor|.)......|
|00003220| 0d 49 64 65 6e 74 69 66 | 79 69 6e 67 20 47 72 61 |.Identif|ying Gra|
|00003230| 70 68 73 0d 0d 45 78 61 | 6d 70 6c 65 3a 20 57 68 |phs..Exa|mple: Wh|
|00003240| 61 74 20 69 73 20 74 68 | 69 73 20 67 72 61 70 68 |at is th|is graph|
|00003250| 20 28 69 6e 20 72 65 66 | 65 72 65 6e 63 65 20 74 | (in ref|erence t|
|00003260| 6f 20 74 68 65 20 67 72 | 61 70 68 20 6f 66 20 61 |o the gr|aph of a|
|00003270| 20 66 75 6e 63 74 69 6f | 6e 29 3f 20 0d 0d 53 74 | functio|n)? ..St|
|00003280| 65 70 20 31 3a 20 44 65 | 74 65 72 6d 69 6e 65 20 |ep 1: De|termine |
|00003290| 74 68 65 20 50 4f 57 45 | 52 20 6f 66 20 74 68 65 |the POWE|R of the|
|000032a0| 20 67 72 61 70 68 20 28 | 74 68 65 20 68 69 67 68 | graph (|the high|
|000032b0| 65 73 74 20 65 78 70 6f | 6e 65 6e 74 29 3a 0d 20 |est expo|nent):. |
|000032c0| 0d 53 74 65 70 20 32 3a | 20 43 68 6f 6f 73 65 20 |.Step 2:| Choose |
|000032d0| 61 20 6c 69 6b 65 6c 79 | 20 66 75 6e 63 74 69 6f |a likely| functio|
|000032e0| 6e 20 61 6e 64 20 73 75 | 62 73 74 69 74 75 74 65 |n and su|bstitute|
|000032f0| 20 61 20 66 65 77 20 6b | 65 79 20 76 61 6c 75 65 | a few k|ey value|
|00003300| 73 20 6f 66 20 78 20 74 | 6f 20 64 65 74 65 72 6d |s of x t|o determ|
|00003310| 69 6e 65 20 74 68 65 20 | 63 6f 72 72 65 73 70 6f |ine the |correspo|
|00003320| 6e 64 69 6e 67 20 79 20 | 76 61 6c 75 65 73 2e 20 |nding y |values. |
|00003330| 0d 0d 46 6f 72 20 65 78 | 61 6d 70 6c 65 2c 20 73 |..For ex|ample, s|
|00003340| 75 70 70 6f 73 65 20 79 | 6f 75 20 74 68 69 6e 6b |uppose y|ou think|
|00003350| 20 74 68 65 20 66 75 6e | 63 74 69 6f 6e 20 69 73 | the fun|ction is|
|00003360| 20 79 20 3d 20 31 2f 78 | 2e 20 49 66 20 78 20 3d | y = 1/x|. If x =|
|00003370| 20 30 2c 20 79 20 3d 20 | 31 2f 78 20 69 73 20 6e | 0, y = |1/x is n|
|00003380| 6f 74 20 64 65 66 69 6e | 65 64 2e 20 41 73 20 78 |ot defin|ed. As x|
|00003390| 20 20 62 65 63 6f 6d 65 | 73 20 76 65 72 79 20 6c |  become|s very l|
|000033a0| 61 72 67 65 20 28 70 6f | 73 69 74 69 76 65 20 6f |arge (po|sitive o|
|000033b0| 72 20 6e 65 67 61 74 69 | 76 65 29 2c 20 79 20 62 |r negati|ve), y b|
|000033c0| 65 63 6f 6d 65 73 20 76 | 65 72 79 20 73 6d 61 6c |ecomes v|ery smal|
|000033d0| 6c 2c 20 61 6e 64 20 76 | 69 63 65 20 76 65 72 73 |l, and v|ice vers|
|000033e0| 61 2e 20 0d 20 0d 53 74 | 65 70 20 33 3a 20 56 65 |a. . .St|ep 3: Ve|
|000033f0| 72 69 66 79 20 74 68 61 | 74 20 74 68 6f 73 65 20 |rify tha|t those |
|00003400| 70 6f 69 6e 74 73 20 6f | 6e 20 74 68 65 20 67 72 |points o|n the gr|
|00003410| 61 70 68 20 73 68 6f 77 | 6e 20 6d 61 74 63 68 20 |aph show|n match |
|00003420| 74 68 65 20 66 75 6e 63 | 74 69 6f 6e 20 76 61 6c |the func|tion val|
|00003430| 75 65 73 20 79 6f 75 20 | 63 61 6c 63 75 6c 61 74 |ues you |calculat|
|00003440| 65 64 2e 20 54 68 65 6e | 20 63 6c 69 63 6b 20 74 |ed. Then| click t|
|00003450| 68 65 20 62 75 74 74 6f | 6e 20 77 69 74 68 20 74 |he butto|n with t|
|00003460| 68 61 74 20 65 71 75 61 | 74 69 6f 6e 3a 20 79 20 |hat equa|tion: y |
|00003470| 3d 20 31 2f 78 00 00 00 | 00 00 00 00 00 00 00 00 |= 1/x...|........|
|00003480| 0d 0d 57 6f 72 6b 69 6e | 67 20 77 69 74 68 20 4c |..Workin|g with L|
|00003490| 69 6e 65 61 72 20 43 6f | 6f 72 64 69 6e 61 74 65 |inear Co|ordinate|
|000034a0| 73 0d 0d 45 78 61 6d 70 | 6c 65 3a 20 57 68 69 63 |s..Examp|le: Whic|
|000034b0| 68 20 64 65 73 63 72 69 | 62 65 73 20 74 68 65 20 |h descri|bes the |
|000034c0| 72 65 6c 61 74 69 6f 6e | 73 68 69 70 20 62 65 74 |relation|ship bet|
|000034d0| 77 65 65 6e 20 70 6f 69 | 6e 74 73 20 41 20 61 6e |ween poi|nts A an|
|000034e0| 64 20 42 3f 0d 0d 0d 0d | 0d 0d 0d 0d 0d 0d 20 0d |d B?....|...... .|
|000034f0| 53 74 65 70 20 31 3a 20 | 45 78 61 6d 69 6e 65 20 |Step 1: |Examine |
|00003500| 74 68 65 20 67 72 61 70 | 68 2e 20 54 68 65 20 78 |the grap|h. The x|
|00003510| 2d 63 6f 6f 72 64 69 6e | 61 74 65 20 6f 66 20 62 |-coordin|ate of b|
|00003520| 6f 74 68 20 70 6f 69 6e | 74 73 20 69 73 20 3c 20 |oth poin|ts is < |
|00003530| 30 2e 20 54 68 65 20 79 | 2d 63 6f 6f 72 64 69 6e |0. The y|-coordin|
|00003540| 61 74 65 20 6f 66 20 70 | 6f 69 6e 74 20 41 20 69 |ate of p|oint A i|
|00003550| 73 20 3e 20 30 2c 20 77 | 68 69 6c 65 20 74 68 61 |s > 0, w|hile tha|
|00003560| 74 20 66 6f 72 20 70 6f | 69 6e 74 20 42 20 69 73 |t for po|int B is|
|00003570| 20 3c 20 30 2e 0d 0d 53 | 74 65 70 20 32 3a 20 53 | < 0...S|tep 2: S|
|00003580| 65 6c 65 63 74 20 74 68 | 65 20 61 6e 73 77 65 72 |elect th|e answer|
|00003590| 20 74 68 61 74 20 6d 61 | 74 63 68 65 73 20 74 68 | that ma|tches th|
|000035a0| 65 73 65 20 63 6f 6e 64 | 69 74 69 6f 6e 73 3a 20 |ese cond|itions: |
|000035b0| 41 d0 20 3d 20 42 d0 3b | 20 42 86 20 3d 20 2d 41 |A. = B.;| B. = -A|
|000035c0| 86 2e 0d 0d 0d 0d 0d 0d | 00 00 00 00 00 00 00 00 |........|........|
|000035d0| 0d 41 64 64 69 6e 67 20 | 56 65 63 74 6f 72 73 0d |.Adding |Vectors.|
|000035e0| 0d 56 65 63 74 6f 72 73 | 20 28 61 6e 6f 74 68 65 |.Vectors| (anothe|
|000035f0| 72 20 6e 61 6d 65 20 69 | 73 20 22 72 61 79 73 22 |r name i|s "rays"|
|00003600| 29 20 68 61 76 65 20 62 | 6f 74 68 20 61 20 6c 65 |) have b|oth a le|
|00003610| 6e 67 74 68 20 41 4e 44 | 20 61 20 64 69 72 65 63 |ngth AND| a direc|
|00003620| 74 69 6f 6e 2e 20 0d 20 | 0d 45 78 61 6d 70 6c 65 |tion. . |.Example|
|00003630| 3a 20 57 68 61 74 20 69 | 73 20 76 65 63 74 6f 72 |: What i|s vector|
|00003640| 20 41 44 20 2b 20 76 65 | 63 74 6f 72 20 44 46 20 | AD + ve|ctor DF |
|00003650| 2b 20 76 65 63 74 6f 72 | 20 46 47 3f 0d 0d 53 74 |+ vector| FG?..St|
|00003660| 65 70 20 31 3a 20 54 68 | 65 20 65 6e 64 70 6f 69 |ep 1: Th|e endpoi|
|00003670| 6e 74 20 6f 66 20 41 44 | 2b 44 46 2b 46 47 20 69 |nt of AD|+DF+FG i|
|00003680| 73 20 47 2e 20 41 6d 6f | 6e 67 20 74 68 65 20 70 |s G. Amo|ng the p|
|00003690| 6f 73 73 69 62 6c 65 20 | 61 6e 73 77 65 72 73 2c |ossible |answers,|
|000036a0| 20 79 6f 75 20 73 65 65 | 20 22 76 65 63 74 6f 72 | you see| "vector|
|000036b0| 20 41 47 22 2e 20 53 69 | 6e 63 65 20 74 68 65 20 | AG". Si|nce the |
|000036c0| 65 6e 64 70 6f 69 6e 74 | 20 6f 66 20 76 65 63 74 |endpoint| of vect|
|000036d0| 6f 72 20 41 47 20 69 73 | 20 61 6c 73 6f 20 47 2c |or AG is| also G,|
|000036e0| 20 74 68 69 73 20 69 73 | 20 74 68 65 20 63 6f 72 | this is| the cor|
|000036f0| 72 65 63 74 20 61 6e 73 | 77 65 72 2e 00 00 00 00 |rect ans|wer.....|
|00003700| 57 6f 72 6b 69 6e 67 20 | 77 69 74 68 20 45 78 70 |Working |with Exp|
|00003710| 6f 6e 65 6e 74 73 0d 0d | 45 78 61 6d 70 6c 65 20 |onents..|Example |
|00003720| 31 3a 20 33 bd e7 20 3d | 20 31 2f 39 2e 20 57 68 |1: 3.. =| 1/9. Wh|
|00003730| 61 74 20 69 73 20 79 3f | 0d 0d 53 74 65 70 20 31 |at is y?|..Step 1|
|00003740| 3a 20 52 65 63 61 6c 6c | 20 74 68 61 74 20 31 2f |: Recall| that 1/|
|00003750| 39 20 3d 20 31 2f 33 aa | 20 3d 20 33 bd aa 2e 0d |9 = 1/3.| = 3....|
|00003760| 0d 53 74 65 70 20 32 3a | 20 49 66 20 33 bd e7 20 |.Step 2:| If 3.. |
|00003770| 3d 20 33 bd aa 2c 20 74 | 68 65 6e 20 79 20 3d 20 |= 3.., t|hen y = |
|00003780| 32 2e 0d 0d 5f 5f 5f 5f | 5f 5f 5f 5f 5f 5f 5f 5f |2...____|________|
|00003790| 5f 5f 5f 5f 5f 5f 5f 5f | 5f 5f 5f 5f 5f 5f 5f 5f |________|________|
|000037a0| 5f 5f 5f 5f 5f 5f 5f 5f | 0d 45 78 61 6d 70 6c 65 |________|.Example|
|000037b0| 20 32 3a 20 57 68 61 74 | 20 69 73 20 28 32 79 7a | 2: What| is (2yz|
|000037c0| aa 29 a3 2f 79 7a 3f 0d | 0d 53 74 65 70 20 31 3a |.)./yz?.|.Step 1:|
|000037d0| 20 53 69 6d 70 6c 69 66 | 79 20 74 68 65 20 65 78 | Simplif|y the ex|
|000037e0| 70 72 65 73 73 69 6f 6e | 20 69 6e 20 70 61 72 65 |pression| in pare|
|000037f0| 6e 74 68 65 73 65 73 3a | 0d 0d 20 20 20 20 20 20 |ntheses:|..      |
|00003800| 20 20 20 20 20 28 32 79 | 7a aa 29 a3 2f 79 7a 20 |     (2y|z.)./yz |
|00003810| 3d 20 38 79 a3 7a a4 2f | 79 7a 0d 0d 53 74 65 70 |= 8y.z./|yz..Step|
|00003820| 20 32 3a 20 45 6c 69 6d | 69 6e 61 74 65 20 74 68 | 2: Elim|inate th|
|00003830| 65 20 64 65 6e 6f 6d 69 | 6e 61 74 6f 72 20 62 79 |e denomi|nator by|
|00003840| 20 66 61 63 74 6f 72 69 | 6e 67 20 6f 75 74 20 79 | factori|ng out y|
|00003850| 7a 3a 0d 0d 20 20 20 20 | 20 20 20 20 20 28 38 79 |z:..    |     (8y|
|00003860| aa 7a b0 29 79 7a 20 20 | 3d 20 38 79 aa 7a b0 20 |.z.)yz  |= 8y.z. |
|00003870| 20 20 0d 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |  .     |        |
|00003880| 79 7a 0d 00 00 00 00 00 | 00 00 00 00 00 00 00 00 |yz......|........|
|00003890| 0d 4d 75 6c 74 69 70 6c | 79 69 6e 67 20 77 69 74 |.Multipl|ying wit|
|000038a0| 68 20 45 78 70 6f 6e 65 | 6e 74 73 3a 0d 0d 45 78 |h Expone|nts:..Ex|
|000038b0| 61 6d 70 6c 65 20 31 3a | 20 20 33 a3 20 78 20 32 |ample 1:|  3. x 2|
|000038c0| a2 20 3d 20 3f 0d 0d 53 | 74 65 70 20 31 3a 20 53 |. = ?..S|tep 1: S|
|000038d0| 69 6d 70 6c 69 66 79 20 | 74 68 65 20 66 69 72 73 |implify |the firs|
|000038e0| 74 20 66 61 63 74 6f 72 | 3a 0d 0d 20 20 20 20 20 |t factor|:..     |
|000038f0| 20 33 a3 20 3d 20 33 20 | 78 20 33 20 78 20 33 20 | 3. = 3 |x 3 x 3 |
|00003900| 3d 20 39 20 78 20 33 20 | 3d 20 32 37 0d 0d 53 74 |= 9 x 3 |= 27..St|
|00003910| 65 70 20 32 3a 20 53 69 | 6d 70 6c 69 66 79 20 74 |ep 2: Si|mplify t|
|00003920| 68 65 20 73 65 63 6f 6e | 64 20 66 61 63 74 6f 72 |he secon|d factor|
|00003930| 3a 0d 0d 20 20 20 20 20 | 20 32 a2 20 3d 20 32 20 |:..     | 2. = 2 |
|00003940| 78 20 32 20 78 20 32 20 | 78 20 32 20 3d 20 34 20 |x 2 x 2 |x 2 = 4 |
|00003950| 78 20 34 20 3d 20 31 36 | 0d 0d 53 74 65 70 20 33 |x 4 = 16|..Step 3|
|00003960| 3a 20 4d 75 6c 74 69 70 | 6c 79 20 74 68 65 20 74 |: Multip|ly the t|
|00003970| 77 6f 20 66 61 63 74 6f | 72 73 3a 0d 0d 20 20 20 |wo facto|rs:..   |
|00003980| 20 20 20 20 20 20 20 32 | 37 20 78 20 31 36 20 3d |       2|7 x 16 =|
|00003990| 20 34 33 32 0d 0d 20 20 | 20 0d 5f 5f 5f 5f 5f 5f | 432..  | .______|
|000039a0| 5f 5f 5f 5f 5f 5f 5f 5f | 5f 5f 5f 5f 5f 5f 5f 5f |________|________|
|000039b0| 5f 5f 5f 5f 5f 5f 5f 5f | 5f 5f 5f 5f 5f 5f 5f 20 |________|_______ |
|000039c0| 0d 45 78 61 6d 70 6c 65 | 20 32 3a 20 20 35 aa 20 |.Example| 2:  5. |
|000039d0| 78 20 32 b0 20 3d 20 3f | 0d 0d 20 20 20 35 20 78 |x 2. = ?|..   5 x|
|000039e0| 20 35 20 20 78 20 20 32 | 20 78 20 32 20 78 20 32 | 5  x  2| x 2 x 2|
|000039f0| 20 78 20 32 20 78 20 32 | 20 3d 0d 20 20 20 20 20 | x 2 x 2| =.     |
|00003a00| 32 35 20 20 20 78 20 20 | 20 20 20 20 20 20 20 20 |25   x  |        |
|00003a10| 33 32 20 20 20 20 20 20 | 20 20 3d 20 38 30 30 0d |32      |  = 800.|
|00003a20| 0d 00 00 00 00 00 00 00 | 00 00 00 00 00 00 00 00 |........|........|
|00003a30| 53 69 6d 70 6c 69 66 79 | 69 6e 67 20 45 78 70 72 |Simplify|ing Expr|
|00003a40| 65 73 73 69 6f 6e 73 0d | 0d 53 65 65 20 74 68 65 |essions.|.See the|
|00003a50| 20 52 65 66 65 72 65 6e | 63 65 20 66 6f 72 20 74 | Referen|ce for t|
|00003a60| 68 65 20 64 65 66 69 6e | 69 74 69 6f 6e 20 6f 66 |he defin|ition of|
|00003a70| 20 74 68 65 20 44 69 73 | 74 72 69 62 75 74 69 76 | the Dis|tributiv|
|00003a80| 65 20 50 72 6f 70 65 72 | 74 79 20 6f 66 20 4d 75 |e Proper|ty of Mu|
|00003a90| 6c 74 69 70 6c 69 63 61 | 74 69 6f 6e 20 28 61 6e |ltiplica|tion (an|
|00003aa0| 64 20 73 69 6d 69 6c 61 | 72 20 69 6e 66 6f 72 6d |d simila|r inform|
|00003ab0| 61 74 69 6f 6e 29 2e 0d | 20 0d 45 78 61 6d 70 6c |ation)..| .Exampl|
|00003ac0| 65 20 31 3a 20 4d 75 6c | 74 69 70 6c 79 3a 20 2d |e 1: Mul|tiply: -|
|00003ad0| 33 28 34 72 2d 35 29 20 | 0d 0d 4e 6f 74 69 63 65 |3(4r-5) |..Notice|
|00003ae0| 20 74 68 61 74 20 74 68 | 65 72 65 20 61 72 65 20 | that th|ere are |
|00003af0| 54 57 4f 20 74 65 72 6d | 73 20 69 6e 73 69 64 65 |TWO term|s inside|
|00003b00| 20 74 68 65 20 70 61 72 | 65 6e 74 68 65 73 65 73 | the par|entheses|
|00003b10| 3a 20 34 72 20 61 6e 64 | 20 2d 35 2e 20 4d 75 6c |: 4r and| -5. Mul|
|00003b20| 74 69 70 6c 79 20 65 61 | 63 68 20 74 65 72 6d 20 |tiply ea|ch term |
|00003b30| 62 79 20 2d 33 3a 0d 20 | 0d 20 20 20 20 20 28 2d |by -3:. |.     (-|
|00003b40| 33 29 28 34 72 29 20 2b | 20 28 2d 33 29 28 2d 35 |3)(4r) +| (-3)(-5|
|00003b50| 29 20 3d 0d 20 20 20 20 | 20 20 20 28 2d 31 32 72 |) =.    |   (-12r|
|00003b60| 29 20 2b 20 20 20 28 2b | 31 35 29 20 20 3d 20 2d |) +   (+|15)  = -|
|00003b70| 31 32 72 20 2b 20 31 35 | 20 20 0d 5f 5f 5f 5f 5f |12r + 15|  ._____|
|00003b80| 5f 5f 5f 5f 5f 5f 5f 5f | 5f 5f 5f 5f 5f 5f 5f 5f |________|________|
|00003b90| 5f 5f 5f 5f 5f 5f 5f 5f | 5f 5f 5f 5f 5f 5f 5f 5f |________|________|
|00003ba0| 5f 0d 45 78 61 6d 70 6c | 65 20 32 3a 20 4d 75 6c |_.Exampl|e 2: Mul|
|00003bb0| 74 69 70 6c 79 3a 20 28 | 78 2d 35 29 28 78 2b 32 |tiply: (|x-5)(x+2|
|00003bc0| 29 0d 0d 53 74 65 70 20 | 31 3a 20 55 73 65 20 74 |)..Step |1: Use t|
|00003bd0| 68 65 20 46 4f 49 4c 20 | 28 46 69 72 73 74 2c 20 |he FOIL |(First, |
|00003be0| 4f 75 74 73 69 64 65 2c | 20 49 6e 73 69 64 65 2c |Outside,| Inside,|
|00003bf0| 20 4c 61 73 74 29 20 6d | 65 74 68 6f 64 20 74 6f | Last) m|ethod to|
|00003c00| 20 6d 75 6c 74 69 70 6c | 79 20 65 61 63 68 20 74 | multipl|y each t|
|00003c10| 65 72 6d 20 69 6e 20 74 | 68 65 20 66 69 72 73 74 |erm in t|he first|
|00003c20| 20 66 61 63 74 6f 72 20 | 62 79 20 65 61 63 68 20 | factor |by each |
|00003c30| 74 65 72 6d 20 69 6e 20 | 74 68 65 20 73 65 63 6f |term in |the seco|
|00003c40| 6e 64 3a 0d 20 20 20 20 | 20 20 20 20 20 20 20 28 |nd:.    |       (|
|00003c50| 78 2d 35 29 28 78 2b 32 | 29 20 3d 0d 20 20 20 20 |x-5)(x+2|) =.    |
|00003c60| 20 20 20 20 20 20 20 20 | 78 aa 20 2b 20 32 78 20 |        |x. + 2x |
|00003c70| 2d 20 35 78 20 2d 20 31 | 30 0d 0d 53 74 65 70 20 |- 5x - 1|0..Step |
|00003c80| 32 3a 20 43 6f 6d 62 69 | 6e 65 20 73 69 6d 69 6c |2: Combi|ne simil|
|00003c90| 61 72 20 74 65 72 6d 73 | 3a 0d 20 20 20 20 20 20 |ar terms|:.      |
|00003ca0| 20 20 20 20 20 20 78 aa | 20 2b 20 28 2d 20 33 78 |      x.| + (- 3x|
|00003cb0| 29 20 2d 20 31 30 20 3d | 0d 20 20 20 20 20 20 20 |) - 10 =|.       |
|00003cc0| 20 20 20 20 20 78 aa 20 | 2d 20 33 78 20 2d 20 31 |     x. |- 3x - 1|
|00003cd0| 30 0d 0d 00 00 00 00 00 | 00 00 00 00 00 00 00 00 |0.......|........|
|00003ce0| 0d 54 68 65 20 42 61 6e | 6b 65 72 27 73 20 4e 75 |.The Ban|ker's Nu|
|00003cf0| 6d 62 65 72 3a 20 65 0d | 0d 20 20 20 20 20 20 20 |mber: e.|.       |
|00003d00| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 6e 0d 54 |        |     n.T|
|00003d10| 68 65 20 6c 69 6d 69 74 | 20 6f 66 20 28 31 2b 31 |he limit| of (1+1|
|00003d20| 2f 6e 29 20 3d 20 65 2c | 0d 61 70 70 72 6f 78 69 |/n) = e,|.approxi|
|00003d30| 6d 61 74 65 6c 79 20 32 | 2e 37 32 2e 20 54 68 69 |mately 2|.72. Thi|
|00003d40| 73 20 69 73 20 77 68 79 | 20 65 20 69 73 20 63 61 |s is why| e is ca|
|00003d50| 6c 6c 65 64 20 22 74 68 | 65 20 42 61 6e 6b 65 72 |lled "th|e Banker|
|00003d60| 27 73 20 4e 75 6d 62 65 | 72 2c 22 20 73 69 6e 63 |'s Numbe|r," sinc|
|00003d70| 65 20 69 74 20 70 6c 61 | 63 65 73 20 61 6e 20 75 |e it pla|ces an u|
|00003d80| 70 70 65 72 20 6c 69 6d | 69 74 20 6f 6e 20 68 6f |pper lim|it on ho|
|00003d90| 77 20 6d 75 63 68 20 61 | 6e 20 69 6e 76 65 73 74 |w much a|n invest|
|00003da0| 6f 72 27 73 20 6d 6f 6e | 65 79 20 63 61 6e 20 67 |or's mon|ey can g|
|00003db0| 72 6f 77 2e 0d 0d 00 00 | 00 00 00 00 00 00 00 00 |row.....|........|
|00003dc0| 0d 43 6f 75 6e 74 69 6e | 67 20 4f 62 6a 65 63 74 |.Countin|g Object|
|00003dd0| 73 0d 0d 49 74 27 73 20 | 65 61 73 69 65 72 20 74 |s..It's |easier t|
|00003de0| 6f 20 63 6f 75 6e 74 20 | 6f 62 6a 65 63 74 73 20 |o count |objects |
|00003df0| 69 66 20 79 6f 75 20 74 | 68 69 6e 6b 20 6f 66 20 |if you t|hink of |
|00003e00| 74 68 65 6d 20 69 6e 20 | 62 75 6e 64 6c 65 73 2c |them in |bundles,|
|00003e10| 20 6f 72 20 67 72 6f 75 | 70 73 2e 0d 20 0d 0d 45 | or grou|ps.. ..E|
|00003e20| 78 61 6d 70 6c 65 3a 20 | 48 6f 77 20 6d 61 6e 79 |xample: |How many|
|00003e30| 20 6c 69 67 68 74 73 20 | 64 6f 20 79 6f 75 20 73 | lights |do you s|
|00003e40| 65 65 3f 0d 20 0d 0d 0d | 49 6e 73 74 65 61 64 20 |ee?. ...|Instead |
|00003e50| 6f 66 20 63 6f 75 6e 74 | 69 6e 67 20 31 20 62 79 |of count|ing 1 by|
|00003e60| 20 31 2e 2e 2e 0d 0d 0d | 0d 0d 0d 0d 0d 20 0d 0d | 1......|..... ..|
|00003e70| 54 68 69 6e 6b 20 6f 66 | 20 74 68 65 20 6c 69 67 |Think of| the lig|
|00003e80| 68 74 73 20 69 6e 20 67 | 72 6f 75 70 73 20 6f 66 |hts in g|roups of|
|00003e90| 20 66 69 76 65 2e 0d 0d | 54 68 65 6e 20 61 64 64 | five...|Then add|
|00003ea0| 2d 2d 20 66 69 72 73 74 | 20 74 68 65 20 66 69 76 |-- first| the fiv|
|00003eb0| 65 73 2c 20 74 68 65 6e | 20 74 68 65 20 6f 6e 65 |es, then| the one|
|00003ec0| 73 20 6c 65 66 74 20 6f | 76 65 72 2e 00 00 00 00 |s left o|ver.....|
|00003ed0| 0d 46 69 6e 64 69 6e 67 | 20 4d 69 73 73 69 6e 67 |.Finding| Missing|
|00003ee0| 20 4f 70 65 72 61 74 6f | 72 73 0d 0d 45 78 61 6d | Operato|rs..Exam|
|00003ef0| 70 6c 65 3a 20 46 69 6c | 6c 20 69 6e 20 74 68 65 |ple: Fil|l in the|
|00003f00| 20 6d 69 73 73 69 6e 67 | 20 6f 70 65 72 61 74 6f | missing| operato|
|00003f10| 72 73 2e 0d 20 20 20 20 | 20 20 20 20 20 20 39 20 |rs..    |      9 |
|00003f20| 3f 20 33 20 3f 20 28 2d | 36 29 20 3d 20 39 20 0d |? 3 ? (-|6) = 9 .|
|00003f30| 0d 53 74 65 70 20 31 3a | 20 44 65 63 69 64 65 20 |.Step 1:| Decide |
|00003f40| 77 68 65 74 68 65 72 20 | 65 69 74 68 65 72 20 6f |whether |either o|
|00003f50| 66 20 74 68 65 20 6d 69 | 73 73 69 6e 67 20 6f 70 |f the mi|ssing op|
|00003f60| 65 72 61 74 6f 72 73 20 | 69 73 20 78 20 6f 72 20 |erators |is x or |
|00003f70| d1 20 28 79 6f 75 20 6d | 75 6c 74 69 70 6c 79 20 |. (you m|ultiply |
|00003f80| 6f 72 20 64 69 76 69 64 | 65 20 42 45 46 4f 52 45 |or divid|e BEFORE|
|00003f90| 20 79 6f 75 20 61 64 64 | 20 6f 72 20 73 75 62 74 | you add| or subt|
|00003fa0| 72 61 63 74 29 2e 20 53 | 69 6e 63 65 20 39 78 33 |ract). S|ince 9x3|
|00003fb0| 20 77 6f 75 6c 64 20 6d | 61 6b 65 20 74 6f 6f 20 | would m|ake too |
|00003fc0| 62 69 67 20 61 20 6e 75 | 6d 62 65 72 2c 20 74 72 |big a nu|mber, tr|
|00003fd0| 79 20 39 d1 33 3a 0d 20 | 20 20 20 20 20 20 20 39 |y 9.3:. |       9|
|00003fe0| 20 d1 20 33 20 3f 20 28 | 2d 36 29 20 3d 20 39 0d | . 3 ? (|-6) = 9.|
|00003ff0| 20 0d 44 69 76 69 73 69 | 6f 6e 2c 20 74 68 65 6e | .Divisi|on, then|
|00004000| 2c 20 6c 6f 6f 6b 73 20 | 6c 69 6b 65 20 61 20 67 |, looks |like a g|
|00004010| 6f 6f 64 20 63 68 6f 69 | 63 65 2e 0d 0d 53 74 65 |ood choi|ce...Ste|
|00004020| 70 20 32 3a 20 43 68 6f | 6f 73 65 20 61 20 73 65 |p 2: Cho|ose a se|
|00004030| 63 6f 6e 64 20 6f 70 65 | 72 61 74 6f 72 20 74 6f |cond ope|rator to|
|00004040| 20 6d 61 6b 65 20 74 68 | 65 20 65 71 75 61 74 69 | make th|e equati|
|00004050| 6f 6e 20 61 20 74 72 75 | 65 20 73 74 61 74 65 6d |on a tru|e statem|
|00004060| 65 6e 74 2e 20 4e 65 69 | 74 68 65 72 20 78 20 6f |ent. Nei|ther x o|
|00004070| 72 20 d1 20 77 6f 72 6b | 2c 20 73 6f 20 74 72 79 |r . work|, so try|
|00004080| 20 2b 3a 0d 20 20 20 20 | 20 20 20 0d 20 20 20 20 | +:.    |   .    |
|00004090| 20 20 20 20 39 20 d1 20 | 33 20 2b 28 2d 36 29 20 |    9 . |3 +(-6) |
|000040a0| 3d 20 2d 33 20 ad 20 39 | 0d 0d 53 6f 2c 20 74 68 |= -3 . 9|..So, th|
|000040b0| 65 20 73 65 63 6f 6e 64 | 20 6f 70 65 72 61 74 6f |e second| operato|
|000040c0| 72 20 6d 75 73 74 20 62 | 65 20 2d 20 28 6d 69 6e |r must b|e - (min|
|000040d0| 75 73 29 3a 0d 20 20 20 | 20 20 20 20 20 39 20 d1 |us):.   |     9 .|
|000040e0| 20 33 20 2d 28 2d 36 29 | 20 3d 0d 20 20 20 20 20 | 3 -(-6)| =.     |
|000040f0| 20 20 20 39 20 d1 20 33 | 20 2b 20 36 20 3d 20 39 |   9 . 3| + 6 = 9|
|00004100| 0d 0d 52 65 73 75 6c 74 | 3a 20 54 68 65 20 6d 69 |..Result|: The mi|
|00004110| 73 73 69 6e 67 20 6f 70 | 65 72 61 74 6f 72 73 20 |ssing op|erators |
|00004120| 61 72 65 3a 20 d1 20 61 | 6e 64 20 2d 20 0d 20 20 |are: . a|nd - .  |
|00004130| 20 20 20 20 20 20 0d 20 | 20 20 20 20 20 0d 20 20 |      . |     .  |
|00004140| 20 20 20 20 20 20 20 00 | 00 00 00 00 00 00 00 00 |       .|........|
|00004150| 0d 0d 49 6e 20 6d 61 74 | 68 2c 20 65 61 63 68 20 |..In mat|h, each |
|00004160| 73 79 6d 62 6f 6c 20 61 | 6e 64 20 6f 70 65 72 61 |symbol a|nd opera|
|00004170| 74 6f 72 20 68 61 73 20 | 61 6e 20 65 78 61 63 74 |tor has |an exact|
|00004180| 20 61 6e 64 20 73 70 65 | 63 69 61 6c 20 6d 65 61 | and spe|cial mea|
|00004190| 6e 69 6e 67 2e 20 20 0d | 20 0d 54 6f 20 72 65 76 |ning.  .| .To rev|
|000041a0| 69 65 77 20 74 68 65 20 | 64 69 66 66 65 72 65 6e |iew the |differen|
|000041b0| 74 20 6d 61 74 68 20 73 | 79 6d 62 6f 6c 73 20 69 |t math s|ymbols i|
|000041c0| 6e 20 74 68 65 20 52 65 | 66 65 72 65 6e 63 65 2c |n the Re|ference,|
|000041d0| 20 63 6c 69 63 6b 20 74 | 68 65 20 62 6f 6f 6b 20 | click t|he book |
|000041e0| 69 63 6f 6e 20 62 65 6c | 6f 77 2e 00 00 00 00 00 |icon bel|ow......|
|000041f0| 0d 43 68 65 63 6b 69 6e | 67 20 66 6f 72 20 44 69 |.Checkin|g for Di|
|00004200| 76 69 73 69 62 69 6c 69 | 74 79 0d 20 0d 53 65 65 |visibili|ty. .See|
|00004210| 20 74 68 65 20 52 65 66 | 65 72 65 6e 63 65 20 28 | the Ref|erence (|
|00004220| 63 6c 69 63 6b 20 74 68 | 65 20 62 6f 6f 6b 20 69 |click th|e book i|
|00004230| 63 6f 6e 20 62 65 6c 6f | 77 29 20 66 6f 72 20 74 |con belo|w) for t|
|00004240| 69 70 73 20 6f 6e 20 64 | 69 76 69 73 69 62 69 6c |ips on d|ivisibil|
|00004250| 69 74 79 20 6f 66 20 6e | 75 6d 62 65 72 73 2e 00 |ity of n|umbers..|
|00004260| 0d 57 6f 72 6b 69 6e 67 | 20 77 69 74 68 20 46 61 |.Working| with Fa|
|00004270| 63 74 6f 72 69 61 6c 73 | 0d 20 0d 45 78 61 6d 70 |ctorials|. .Examp|
|00004280| 6c 65 3a 20 57 68 61 74 | 20 69 73 20 34 21 20 2b |le: What| is 4! +|
|00004290| 20 32 21 3f 0d 0d 53 74 | 65 70 20 31 3a 20 4d 75 | 2!?..St|ep 1: Mu|
|000042a0| 6c 74 69 70 6c 79 20 6f | 75 74 20 65 61 63 68 20 |ltiply o|ut each |
|000042b0| 66 61 63 74 6f 72 69 61 | 6c 20 69 6e 20 74 68 65 |factoria|l in the|
|000042c0| 20 70 72 6f 62 6c 65 6d | 3a 0d 0d 20 20 20 20 20 | problem|:..     |
|000042d0| 20 20 20 20 20 20 20 20 | 20 20 20 34 21 20 2b 20 |        |   4! + |
|000042e0| 32 21 20 20 3d 20 0d 20 | 20 20 20 20 20 20 20 20 |2!  = . |        |
|000042f0| 20 20 34 78 33 78 32 78 | 31 20 2b 20 32 78 31 20 |  4x3x2x|1 + 2x1 |
|00004300| 3d 0d 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |=.      |        |
|00004310| 20 20 32 34 20 2b 20 32 | 0d 0d 53 74 65 70 20 32 |  24 + 2|..Step 2|
|00004320| 3a 20 41 64 64 20 74 68 | 65 20 70 72 6f 64 75 63 |: Add th|e produc|
|00004330| 74 73 2e 0d 20 0d 20 20 | 20 20 20 20 20 20 20 20 |ts.. .  |        |
|00004340| 20 32 34 20 2b 20 32 20 | 3d 20 32 36 0d 0d 20 0d | 24 + 2 |= 26.. .|
|00004350| 52 65 73 75 6c 74 3a 20 | 20 20 20 34 21 20 2b 20 |Result: |   4! + |
|00004360| 32 21 20 3d 20 32 36 20 | 20 00 00 00 00 00 00 00 |2! = 26 | .......|
|00004370| 54 75 72 6e 69 6e 67 20 | 45 6e 67 6c 69 73 68 20 |Turning |English |
|00004380| 69 6e 74 6f 20 41 6c 67 | 65 62 72 61 0d 0d 45 78 |into Alg|ebra..Ex|
|00004390| 61 6d 70 6c 65 20 31 3a | 49 66 20 31 20 67 61 6c |ample 1:|If 1 gal|
|000043a0| 6c 6f 6e 20 6f 66 20 70 | 61 69 6e 74 20 63 6f 76 |lon of p|aint cov|
|000043b0| 65 72 73 20 33 30 66 74 | aa 2c 20 77 68 69 63 68 |ers 30ft|., which|
|000043c0| 20 65 78 70 72 65 73 73 | 69 6f 6e 20 73 68 6f 77 | express|ion show|
|000043d0| 73 20 68 6f 77 20 6d 61 | 6e 79 20 67 61 6c 6c 6f |s how ma|ny gallo|
|000043e0| 6e 73 20 79 6f 75 20 6e | 65 65 64 20 74 6f 20 70 |ns you n|eed to p|
|000043f0| 61 69 6e 74 20 32 30 30 | 30 66 74 aa 3f 0d 20 0d |aint 200|0ft.?. .|
|00004400| 54 68 69 73 20 69 73 20 | 61 20 63 6c 61 73 73 69 |This is |a classi|
|00004410| 63 20 70 72 6f 70 6f 72 | 74 69 6f 6e 20 70 72 6f |c propor|tion pro|
|00004420| 62 6c 65 6d 2c 20 69 6e | 20 77 68 69 63 68 20 74 |blem, in| which t|
|00004430| 68 65 20 72 61 74 69 6f | 20 6f 66 20 74 68 65 20 |he ratio| of the |
|00004440| 71 75 61 6e 74 69 74 69 | 65 73 20 63 61 6e 20 62 |quantiti|es can b|
|00004450| 65 20 65 78 70 72 65 73 | 73 65 64 20 61 73 20 66 |e expres|sed as f|
|00004460| 6f 6c 6c 6f 77 73 3a 20 | 20 33 30 2f 31 20 3d 20 |ollows: | 30/1 = |
|00004470| 32 30 30 30 2f 78 0d 59 | 6f 75 20 63 61 6e 20 74 |2000/x.Y|ou can t|
|00004480| 68 65 6e 20 73 6f 6c 76 | 65 20 66 6f 72 20 74 68 |hen solv|e for th|
|00004490| 65 20 75 6e 6b 6e 6f 77 | 6e 2c 20 78 2e 0d 5f 5f |e unknow|n, x..__|
|000044a0| 5f 5f 5f 5f 5f 5f 5f 5f | 5f 5f 5f 5f 5f 5f 5f 5f |________|________|
|000044b0| 5f 5f 5f 5f 5f 5f 5f 5f | 5f 5f 5f 5f 5f 5f 5f 5f |________|________|
|000044c0| 5f 5f 5f 0d 45 78 61 6d | 70 6c 65 20 32 3a 20 4f |___.Exam|ple 2: O|
|000044d0| 6e 65 20 61 6e 67 6c 65 | 20 6f 66 20 61 20 74 72 |ne angle| of a tr|
|000044e0| 69 61 6e 67 6c 65 20 69 | 73 20 37 30 98 2e 20 41 |iangle i|s 70.. A|
|000044f0| 6e 6f 74 68 65 72 20 69 | 73 20 68 61 6c 66 20 61 |nother i|s half a|
|00004500| 73 20 6c 61 72 67 65 2e | 20 57 68 61 74 20 69 73 |s large.| What is|
|00004510| 20 74 68 65 20 6d 65 61 | 73 75 72 65 20 6f 66 20 | the mea|sure of |
|00004520| 74 68 65 20 74 68 69 72 | 64 20 61 6e 67 6c 65 3f |the thir|d angle?|
|00004530| 0d 0d 53 74 65 70 20 31 | 3a 20 49 64 65 6e 74 69 |..Step 1|: Identi|
|00004540| 66 79 20 74 68 65 20 75 | 6e 6b 6e 6f 77 6e 20 28 |fy the u|nknown (|
|00004550| 74 68 65 20 74 68 69 72 | 64 20 61 6e 67 6c 65 29 |the thir|d angle)|
|00004560| 20 61 6e 64 20 61 73 73 | 69 67 6e 20 61 20 76 61 | and ass|ign a va|
|00004570| 72 69 61 62 6c 65 20 74 | 6f 20 69 74 3a 20 78 0d |riable t|o it: x.|
|00004580| 0d 53 74 65 70 20 32 3a | 20 45 78 70 72 65 73 73 |.Step 2:| Express|
|00004590| 20 74 68 65 20 74 68 72 | 65 65 20 61 6e 67 6c 65 | the thr|ee angle|
|000045a0| 73 20 69 6e 20 61 6c 67 | 65 62 72 61 69 63 20 74 |s in alg|ebraic t|
|000045b0| 65 72 6d 73 2c 20 75 73 | 69 6e 67 20 76 61 72 69 |erms, us|ing vari|
|000045c0| 61 62 6c 65 20 78 20 28 | 72 65 63 61 6c 6c 20 74 |able x (|recall t|
|000045d0| 68 61 74 20 74 68 65 20 | 73 75 6d 20 6f 66 20 61 |hat the |sum of a|
|000045e0| 20 74 72 69 61 6e 67 6c | 65 27 73 20 61 6e 67 6c | triangl|e's angl|
|000045f0| 65 73 20 3d 20 31 38 30 | 29 3a 20 20 20 20 37 30 |es = 180|):    70|
|00004600| 20 2b 20 37 30 2f 32 20 | 2b 20 78 20 3d 20 31 38 | + 70/2 |+ x = 18|
|00004610| 30 0d 28 4e 6f 74 69 63 | 65 20 74 68 65 20 73 6d |0.(Notic|e the sm|
|00004620| 61 6c 6c 65 72 20 61 6e | 67 6c 65 20 69 73 20 65 |aller an|gle is e|
|00004630| 78 70 72 65 73 73 65 64 | 20 69 6e 20 74 65 72 6d |xpressed| in term|
|00004640| 73 20 6f 66 20 74 68 65 | 20 6c 61 72 67 65 72 20 |s of the| larger |
|00004650| 6f 6e 65 2e 29 20 0d 0d | 53 74 65 70 20 33 3a 20 |one.) ..|Step 3: |
|00004660| 49 73 6f 6c 61 74 65 20 | 78 20 6f 6e 20 6f 6e 65 |Isolate |x on one|
|00004670| 20 73 69 64 65 20 6f 66 | 20 74 68 65 20 65 71 75 | side of| the equ|
|00004680| 61 74 69 6f 6e 20 74 6f | 20 73 6f 6c 76 65 3a 20 |ation to| solve: |
|00004690| 78 20 3d 20 31 38 30 20 | 2d 20 28 37 30 2b 37 30 |x = 180 |- (70+70|
|000046a0| 2f 32 29 20 20 20 20 20 | 20 20 20 20 20 0d 20 20 |/2)     |     .  |
|000046b0| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |        |        |
|000046c0| 20 78 20 3d 20 37 35 98 | 0d 00 00 00 00 00 00 00 | x = 75.|........|
|000046d0| 53 6f 6c 76 69 6e 67 20 | 57 6f 72 64 20 50 72 6f |Solving |Word Pro|
|000046e0| 62 6c 65 6d 73 0d 0d 45 | 78 61 6d 70 6c 65 20 31 |blems..E|xample 1|
|000046f0| 3a 20 4d 61 72 79 20 68 | 61 64 20 24 31 30 2e 20 |: Mary h|ad $10. |
|00004700| 53 68 65 20 67 6f 74 20 | 24 34 39 20 6d 6f 72 65 |She got |$49 more|
|00004710| 20 66 6f 72 20 68 65 72 | 20 62 69 72 74 68 64 61 | for her| birthda|
|00004720| 79 2e 20 20 48 6f 77 20 | 6d 75 63 68 20 64 6f 65 |y.  How |much doe|
|00004730| 73 20 73 68 65 20 68 61 | 76 65 20 6e 6f 77 3f 0d |s she ha|ve now?.|
|00004740| 0d 53 74 65 70 20 31 3a | 20 52 65 61 64 20 74 68 |.Step 1:| Read th|
|00004750| 65 20 70 72 6f 62 6c 65 | 6d 20 63 61 72 65 66 75 |e proble|m carefu|
|00004760| 6c 6c 79 20 74 6f 20 64 | 65 63 69 64 65 20 77 68 |lly to d|ecide wh|
|00004770| 61 74 20 6f 70 65 72 61 | 74 69 6f 6e 20 69 73 20 |at opera|tion is |
|00004780| 6e 65 65 64 65 64 2e 20 | 54 68 65 20 77 6f 72 64 |needed. |The word|
|00004790| 20 22 6d 6f 72 65 22 20 | 69 73 20 61 20 63 6c 75 | "more" |is a clu|
|000047a0| 65 20 74 68 61 74 20 79 | 6f 75 20 73 68 6f 75 6c |e that y|ou shoul|
|000047b0| 64 20 41 44 44 20 28 2b | 29 2e 20 20 0d 53 74 65 |d ADD (+|).  .Ste|
|000047c0| 70 20 32 3a 20 57 72 69 | 74 65 20 74 68 65 20 70 |p 2: Wri|te the p|
|000047d0| 72 6f 62 6c 65 6d 20 75 | 73 69 6e 67 20 61 72 69 |roblem u|sing ari|
|000047e0| 74 68 6d 65 74 69 63 2c | 20 61 6e 64 20 74 68 65 |thmetic,| and the|
|000047f0| 6e 20 73 69 6d 70 6c 69 | 66 79 3a 0d 0d 20 20 20 |n simpli|fy:..   |
|00004800| 20 20 20 20 20 20 20 20 | 20 20 20 31 30 20 2b 20 |        |   10 + |
|00004810| 34 39 20 3d 20 3f 20 20 | 0d 20 20 20 20 20 20 20 |49 = ?  |.       |
|00004820| 20 20 20 20 20 20 20 31 | 30 20 2b 20 34 39 20 3d |       1|0 + 49 =|
|00004830| 20 35 39 20 20 0d 5f 5f | 5f 5f 5f 5f 5f 5f 5f 5f | 59  .__|________|
|00004840| 5f 5f 5f 5f 5f 5f 5f 5f | 5f 5f 5f 5f 5f 5f 5f 5f |________|________|
|00004850| 5f 5f 5f 5f 5f 5f 5f 5f | 5f 5f 5f 5f 5f 5f 0d 45 |________|______.E|
|00004860| 78 61 6d 70 6c 65 20 32 | 3a 20 20 4d 61 72 79 20 |xample 2|:  Mary |
|00004870| 73 70 65 6e 74 20 24 32 | 34 20 6f 6e 20 67 69 66 |spent $2|4 on gif|
|00004880| 74 73 20 6f 66 20 65 71 | 75 61 6c 20 76 61 6c 75 |ts of eq|ual valu|
|00004890| 65 20 66 6f 72 20 34 20 | 6f 66 20 68 65 72 20 66 |e for 4 |of her f|
|000048a0| 72 69 65 6e 64 73 2e 20 | 20 48 6f 77 20 6d 75 63 |riends. | How muc|
|000048b0| 68 20 64 69 64 20 65 61 | 63 68 20 67 69 66 74 20 |h did ea|ch gift |
|000048c0| 63 6f 73 74 3f 0d 0d 53 | 74 65 70 20 31 3a 20 52 |cost?..S|tep 1: R|
|000048d0| 65 61 64 20 61 6e 64 20 | 64 65 63 69 64 65 2e 20 |ead and |decide. |
|000048e0| 54 68 65 20 77 6f 72 64 | 20 22 65 71 75 61 6c 22 |The word| "equal"|
|000048f0| 20 69 73 20 61 20 63 6c | 75 65 20 74 68 61 74 20 | is a cl|ue that |
|00004900| 79 6f 75 20 73 68 6f 75 | 6c 64 20 44 49 56 49 44 |you shou|ld DIVID|
|00004910| 45 20 28 d1 29 2e 20 20 | 0d 20 0d 53 74 65 70 20 |E (.).  |. .Step |
|00004920| 32 3a 20 57 72 69 74 65 | 20 74 68 65 20 70 72 6f |2: Write| the pro|
|00004930| 62 6c 65 6d 20 75 73 69 | 6e 67 20 61 72 69 74 68 |blem usi|ng arith|
|00004940| 6d 65 74 69 63 2c 20 61 | 6e 64 20 73 69 6d 70 6c |metic, a|nd simpl|
|00004950| 69 66 79 3a 0d 20 20 20 | 20 20 20 20 20 20 20 20 |ify:.   |        |
|00004960| 20 20 20 20 32 34 20 d1 | 20 34 20 3d 20 3f 20 20 |    24 .| 4 = ?  |
|00004970| 0d 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |.       |        |
|00004980| 32 34 20 d1 20 34 20 3d | 20 36 20 20 0d 00 00 00 |24 . 4 =| 6  ....|
|00004990| 0d 53 6f 6c 76 69 6e 67 | 20 4c 6f 67 61 72 69 74 |.Solving| Logarit|
|000049a0| 68 6d 2a 20 50 72 6f 62 | 6c 65 6d 73 0d 0d 45 78 |hm* Prob|lems..Ex|
|000049b0| 61 6d 70 6c 65 3a 20 6c | 6f 67 da e2 20 36 34 20 |ample: l|og.. 64 |
|000049c0| 3d 20 3f 20 0d 28 48 69 | 6e 74 3a 20 6c 6f 67 da |= ? .(Hi|nt: log.|
|000049d0| e2 20 32 20 3d 20 30 2e | 33 30 31 29 0d 0d 53 74 |. 2 = 0.|301)..St|
|000049e0| 65 70 20 31 3a 20 52 65 | 63 61 6c 6c 69 6e 67 20 |ep 1: Re|calling |
|000049f0| 74 68 61 74 20 36 34 20 | 3d 20 32 a4 2c 20 72 65 |that 64 |= 2., re|
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|00004a10| 6d 3a 0d 20 20 20 20 20 | 20 20 20 20 6c 6f 67 da |m:.     |    log.|
|00004a20| e2 20 32 a4 20 3d 20 3f | 0d 20 0d 53 74 65 70 20 |. 2. = ?|. .Step |
|00004a30| 32 3a 20 53 69 6e 63 65 | 20 6c 6f 67 b6 20 75 fb |2: Since| log. u.|
|00004a40| 20 3d 20 78 6c 6f 67 b6 | 20 75 20 0d 28 61 20 67 | = xlog.| u .(a g|
|00004a50| 65 6e 65 72 61 6c 20 70 | 72 6f 70 65 72 74 79 20 |eneral p|roperty |
|00004a60| 6f 66 20 6c 6f 67 61 72 | 69 74 68 6d 73 29 2c 20 |of logar|ithms), |
|00004a70| 74 68 65 6e 0d 20 20 20 | 20 20 20 20 20 20 6c 6f |then.   |      lo|
|00004a80| 67 da e2 20 32 a4 20 3d | 20 36 28 6c 6f 67 da e2 |g.. 2. =| 6(log..|
|00004a90| 20 32 29 0d 20 20 20 20 | 20 20 20 20 20 20 20 20 | 2).    |        |
|00004aa0| 20 20 20 20 20 20 3d 20 | 36 28 30 2e 33 30 31 29 |      = |6(0.301)|
|00004ab0| 0d 20 20 20 20 20 20 20 | 20 20 20 20 0d 52 65 73 |.       |    .Res|
|00004ac0| 75 6c 74 3a 20 6c 6f 67 | da e2 20 36 34 20 3d 20 |ult: log|.. 64 = |
|00004ad0| 31 2e 38 30 36 20 0d 0d | 0d 2a 4c 6f 67 61 72 69 |1.806 ..|.*Logari|
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|00004b00| 63 73 20 63 61 6c 63 75 | 6c 61 74 69 6f 6e 73 2e |cs calcu|lations.|
|00004b10| 20 4f 6e 65 20 6b 65 79 | 20 74 6f 20 77 6f 72 6b | One key| to work|
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|00004b30| 68 6d 73 20 69 73 20 74 | 6f 20 6b 65 65 70 20 69 |hms is t|o keep i|
|00004b40| 6e 20 6d 69 6e 64 20 74 | 68 65 20 72 65 6c 61 74 |n mind t|he relat|
|00004b50| 69 6f 6e 73 68 69 70 20 | 62 65 74 77 65 65 6e 20 |ionship |between |
|00004b60| 74 68 65 6d 20 61 6e 64 | 20 65 78 70 6f 6e 65 6e |them and| exponen|
|00004b70| 74 69 61 6c 20 65 78 70 | 72 65 73 73 69 6f 6e 73 |tial exp|ressions|
|00004b80| 3a 20 49 66 20 41 e7 20 | 3d 20 78 2c 20 74 68 65 |: If A. |= x, the|
|00004b90| 6e 20 6c 6f 67 b6 20 78 | 20 3d 20 79 20 28 72 65 |n log. x| = y (re|
|00004ba0| 61 64 20 22 6c 6f 67 20 | 62 61 73 65 20 41 20 6f |ad "log |base A o|
|00004bb0| 66 20 78 20 69 73 20 79 | 22 29 2e 53 65 65 20 74 |f x is y|").See t|
|00004bc0| 68 65 20 52 65 66 65 72 | 65 6e 63 65 20 74 6f 20 |he Refer|ence to |
|00004bd0| 72 65 76 69 65 77 20 74 | 68 65 20 62 61 73 69 63 |review t|he basic|
|00004be0| 20 6c 6f 67 61 72 69 74 | 68 6d 69 63 20 70 72 6f | logarit|hmic pro|
|00004bf0| 70 65 72 74 69 65 73 2e | 0d 00 00 00 00 00 00 00 |perties.|........|
|00004c00| 0d 4c 65 61 72 6e 69 6e | 67 20 4f 64 64 20 61 6e |.Learnin|g Odd an|
|00004c10| 64 20 45 76 65 6e 20 4e | 75 6d 62 65 72 73 0d 0d |d Even N|umbers..|
|00004c20| 4f 44 44 20 6e 75 6d 62 | 65 72 73 20 61 72 65 3a |ODD numb|ers are:|
|00004c30| 20 31 20 33 20 35 20 37 | 20 39 20 31 31 20 31 33 | 1 3 5 7| 9 11 13|
|00004c40| 20 31 35 20 2e 2e 2e 20 | 0d 20 20 20 20 20 20 20 | 15 ... |.       |
|00004c50| 20 20 20 20 20 20 20 20 | 20 20 28 74 68 65 79 20 |        |  (they |
|00004c60| 67 6f 20 6f 6e 20 66 6f | 72 65 76 65 72 21 29 0d |go on fo|rever!).|
|00004c70| 0d 0d 45 56 45 4e 20 6e | 75 6d 62 65 72 73 20 61 |..EVEN n|umbers a|
|00004c80| 72 65 3a 20 32 20 34 20 | 36 20 38 20 31 30 20 31 |re: 2 4 |6 8 10 1|
|00004c90| 32 20 31 34 20 2e 2e 2e | 0d 20 20 20 20 20 20 20 |2 14 ...|.       |
|00004ca0| 20 20 20 20 20 20 20 20 | 20 20 20 28 66 6f 72 65 |        |   (fore|
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|00004cc0| 73 65 65 20 61 20 70 61 | 74 74 65 72 6e 3a 0d 0d |see a pa|ttern:..|
|00004cd0| 31 2e 20 4f 44 44 20 6e | 75 6d 62 65 72 73 20 45 |1. ODD n|umbers E|
|00004ce0| 4e 44 20 77 69 74 68 20 | 31 20 33 20 35 20 37 20 |ND with |1 3 5 7 |
|00004cf0| 6f 72 20 39 2e 0d 0d 32 | 2e 20 45 56 45 4e 20 6e |or 9...2|. EVEN n|
|00004d00| 75 6d 62 65 72 73 20 45 | 4e 44 20 77 69 74 68 20 |umbers E|ND with |
|00004d10| 32 20 34 20 36 20 38 20 | 6f 72 20 30 2e 0d 20 20 |2 4 6 8 |or 0..  |
|00004d20| 20 20 20 20 20 20 0d 41 | 6c 73 6f 2c 20 77 68 65 |      .A|lso, whe|
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|00004d40| 6e 20 6e 75 6d 62 65 72 | 73 20 62 79 20 32 2c 20 |n number|s by 2, |
|00004d50| 74 68 65 20 72 65 73 75 | 6c 74 20 69 73 20 61 20 |the resu|lt is a |
|00004d60| 77 68 6f 6c 65 20 6e 75 | 6d 62 65 72 2e 20 28 46 |whole nu|mber. (F|
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|00004d80| 20 32 20 3d 20 32 34 2e | 29 0d 0d 45 78 61 6d 70 | 2 = 24.|)..Examp|
|00004d90| 6c 65 73 3a 0d 20 20 20 | 20 20 20 20 31 32 33 20 |les:.   |    123 |
|00004da0| 69 73 20 6f 64 64 2e 20 | 28 49 74 20 65 6e 64 73 |is odd. |(It ends|
|00004db0| 20 77 69 74 68 20 61 20 | 33 2e 29 0d 20 20 20 20 | with a |3.).    |
|00004dc0| 20 20 20 31 32 34 20 69 | 73 20 65 76 65 6e 2e 20 |   124 i|s even. |
|00004dd0| 28 49 74 20 65 6e 64 73 | 20 77 69 74 68 20 61 20 |(It ends| with a |
|00004de0| 34 2e 29 0d 0d 20 20 20 | 20 20 20 20 31 2c 32 33 |4.)..   |    1,23|
|00004df0| 34 2c 35 36 37 20 69 73 | 20 6f 64 64 2e 0d 20 20 |4,567 is| odd..  |
|00004e00| 20 20 20 20 20 33 34 2c | 30 30 33 2c 31 31 33 38 |     34,|003,1138|
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|00004e20| 0d 43 6f 75 6e 74 69 6e | 67 20 4f 62 6a 65 63 74 |.Countin|g Object|
|00004e30| 73 0d 0d 49 74 27 73 20 | 65 61 73 69 65 72 20 74 |s..It's |easier t|
|00004e40| 6f 20 63 6f 75 6e 74 20 | 6f 62 6a 65 63 74 73 20 |o count |objects |
|00004e50| 69 66 20 79 6f 75 20 0d | 74 68 69 6e 6b 20 6f 66 |if you .|think of|
|00004e60| 20 74 68 65 6d 20 69 6e | 20 62 75 6e 64 6c 65 73 | them in| bundles|
|00004e70| 2c 20 6f 72 20 67 72 6f | 75 70 73 2e 0d 20 0d 0d |, or gro|ups.. ..|
|00004e80| 20 0d 0d 20 00 00 00 00 | 00 00 00 00 00 00 00 00 | .. ....|........|
|00004e90| 0d 45 6e 74 65 72 69 6e | 67 20 4e 75 6d 62 65 72 |.Enterin|g Number|
|00004ea0| 73 20 6f 6e 20 61 20 4b | 65 79 20 50 61 64 0d 0d |s on a K|ey Pad..|
|00004eb0| 45 78 61 6d 70 6c 65 3a | 20 45 6e 74 65 72 20 74 |Example:| Enter t|
|00004ec0| 68 69 73 20 6e 75 6d 62 | 65 72 3a 0d 20 20 20 20 |his numb|er:.    |
|00004ed0| 20 20 20 20 20 74 68 72 | 65 65 20 74 68 6f 75 73 |     thr|ee thous|
|00004ee0| 61 6e 64 20 66 6f 75 72 | 74 65 65 6e 20 20 0d 0d |and four|teen  ..|
|00004ef0| 53 74 65 70 20 31 3a 20 | 45 6e 74 65 72 20 74 68 |Step 1: |Enter th|
|00004f00| 65 20 68 69 67 68 65 73 | 74 20 70 6c 61 63 65 20 |e highes|t place |
|00004f10| 76 61 6c 75 65 2c 20 74 | 68 65 20 74 68 6f 75 73 |value, t|he thous|
|00004f20| 61 6e 64 73 3a 20 43 6c | 69 63 6b 20 22 33 22 2e |ands: Cl|ick "3".|
|00004f30| 0d 20 20 20 20 20 20 20 | 20 20 0d 53 74 65 70 20 |.       |  .Step |
|00004f40| 32 3a 20 45 6e 74 65 72 | 20 74 68 65 20 6e 65 78 |2: Enter| the nex|
|00004f50| 74 20 68 69 67 68 65 73 | 74 2c 20 74 68 65 20 68 |t highes|t, the h|
|00004f60| 75 6e 64 72 65 64 73 3a | 20 43 6c 69 63 6b 20 22 |undreds:| Click "|
|00004f70| 30 22 2e 0d 20 20 0d 49 | 4d 50 4f 52 54 41 4e 54 |0"..  .I|MPORTANT|
|00004f80| 21 20 59 6f 75 20 64 6f | 6e 27 74 20 73 65 65 20 |! You do|n't see |
|00004f90| 74 68 65 20 77 6f 72 64 | 20 22 68 75 6e 64 72 65 |the word| "hundre|
|00004fa0| 64 22 20 69 6e 20 74 68 | 65 20 70 72 6f 62 6c 65 |d" in th|e proble|
|00004fb0| 6d 2e 20 54 68 69 73 20 | 6d 65 61 6e 73 20 74 68 |m. This |means th|
|00004fc0| 65 72 65 20 61 72 65 20 | 4e 4f 20 68 75 6e 64 72 |ere are |NO hundr|
|00004fd0| 65 64 73 2e 20 53 6f 20 | 79 6f 75 20 4d 55 53 54 |eds. So |you MUST|
|00004fe0| 20 63 6c 69 63 6b 20 22 | 30 22 20 66 6f 72 20 74 | click "|0" for t|
|00004ff0| 68 65 20 68 75 6e 64 72 | 65 64 73 27 20 70 6c 61 |he hundr|eds' pla|
|00005000| 63 65 2e 0d 0d 53 74 65 | 70 20 33 3a 20 45 6e 74 |ce...Ste|p 3: Ent|
|00005010| 65 72 20 74 68 65 20 6e | 65 78 74 20 68 69 67 68 |er the n|ext high|
|00005020| 65 73 74 2c 20 74 68 65 | 20 74 65 6e 73 3a 20 43 |est, the| tens: C|
|00005030| 6c 69 63 6b 20 22 31 22 | 2e 0d 0d 53 74 65 70 20 |lick "1"|...Step |
|00005040| 34 3a 20 45 6e 74 65 72 | 20 74 68 65 20 6c 61 73 |4: Enter| the las|
|00005050| 74 2c 20 74 68 65 20 6f | 6e 65 73 3a 20 43 6c 69 |t, the o|nes: Cli|
|00005060| 63 6b 20 22 34 22 2e 0d | 0d 0d 52 65 73 75 6c 74 |ck "4"..|..Result|
|00005070| 3a 20 20 33 30 31 34 20 | 20 20 20 20 0d 0d 00 00 |:  3014 |    ....|
|00005080| 20 0d 57 6f 72 6b 69 6e | 67 20 77 69 74 68 20 50 | .Workin|g with P|
|00005090| 6f 73 69 74 69 76 65 20 | 26 20 4e 65 67 61 74 69 |ositive |& Negati|
|000050a0| 76 65 20 4e 75 6d 62 65 | 72 73 0d 0d 45 78 61 6d |ve Numbe|rs..Exam|
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|000050c0| 35 20 2b 20 33 3f 0d 20 | 0d 20 20 20 20 20 20 54 |5 + 3?. |.      T|
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|000050e0| 65 72 20 6c 69 6e 65 3a | 0d 20 5f 5f 5f 5f 5f 5f |er line:|. ______|
|000050f0| 5f 5f 5f 5f 5f 5f 5f 5f | 5f 5f 5f 5f 5f 5f 5f 5f |________|________|
|00005100| 5f 5f 5f 5f 5f 5f 5f 5f | 5f 5f 5f 5f 5f 5f 5f 5f |________|________|
|00005110| 0d 20 2e 2e 2e 20 2d 33 | 20 20 2d 32 20 20 2d 31 |. ... -3|  -2  -1|
|00005120| 20 20 20 30 20 20 20 31 | 20 20 20 32 20 20 20 33 |   0   1|   2   3|
|00005130| 20 20 20 34 20 2e 2e 2e | 0d 0d 53 74 61 72 74 20 |   4 ...|..Start |
|00005140| 61 74 20 2d 35 20 61 6e | 64 20 67 6f 20 52 49 47 |at -5 an|d go RIG|
|00005150| 48 54 20 33 20 74 69 6d | 65 73 20 28 62 65 63 61 |HT 3 tim|es (beca|
|00005160| 75 73 65 20 79 6f 75 27 | 72 65 20 61 64 64 69 6e |use you'|re addin|
|00005170| 67 29 2e 20 20 54 68 65 | 20 72 65 73 75 6c 74 20 |g).  The| result |
|00005180| 69 73 20 2d 32 2e 20 20 | 20 0d 0d 0d 45 78 61 6d |is -2.  | ...Exam|
|00005190| 70 6c 65 20 32 3a 20 57 | 68 61 74 20 69 73 20 2d |ple 2: W|hat is -|
|000051a0| 31 37 20 2d 20 28 2d 36 | 29 3f 0d 20 0d 53 75 62 |17 - (-6|)?. .Sub|
|000051b0| 74 72 61 63 74 69 6e 67 | 20 61 20 2d 36 20 69 73 |tracting| a -6 is|
|000051c0| 20 74 68 65 20 73 61 6d | 65 20 61 73 20 41 44 44 | the sam|e as ADD|
|000051d0| 49 4e 47 20 2b 36 2e 20 | 53 74 61 72 74 20 61 74 |ING +6. |Start at|
|000051e0| 20 2d 31 37 20 61 6e 64 | 20 67 6f 20 52 49 47 48 | -17 and| go RIGH|
|000051f0| 54 20 36 20 74 69 6d 65 | 73 20 28 62 65 63 61 75 |T 6 time|s (becau|
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|000052c0| 2d 31 38 2c 20 6f 72 20 | 31 38 98 20 43 4f 4c 44 |-18, or |18. COLD|
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|000052e0| 0d 49 64 65 6e 74 69 66 | 79 69 6e 67 20 50 72 69 |.Identif|ying Pri|
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|00005330| 20 20 20 35 37 20 20 20 | 20 20 20 39 34 20 20 20 |   57   |   94   |
|00005340| 20 20 20 36 31 20 20 20 | 20 20 20 20 37 37 0d 0d |   61   |    77..|
|00005350| 0d 53 74 65 70 20 31 3a | 20 45 6c 69 6d 69 6e 61 |.Step 1:| Elimina|
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|000053c0| 74 65 70 20 32 3a 20 4c | 6f 6f 6b 20 66 6f 72 20 |tep 2: L|ook for |
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|00005510| 0d 48 6f 6c 64 20 74 68 | 65 20 6d 6f 75 73 65 20 |.Hold th|e mouse |
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|00005560| 0d 00 00 00 00 00 00 00 | 00 00 00 00 00 00 00 00 |........|........|
|00005570| 55 6e 64 65 72 73 74 61 | 6e 64 69 6e 67 20 53 63 |Understa|nding Sc|
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|00005680| 5f 5f 5f 5f 5f 5f 5f 5f | 5f 5f 5f 5f 5f 5f 5f 5f |________|________|
|00005690| 5f 5f 5f 5f 5f 5f 5f 5f | 5f 5f 5f 5f 5f 5f 5f 5f |________|________|
|000056a0| 5f 5f 5f 5f 5f 5f 5f 20 | 20 20 0d 45 78 61 6d 70 |_______ |  .Examp|
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|000056f0| 74 68 65 20 64 65 63 69 | 6d 61 6c 20 70 6f 69 6e |the deci|mal poin|
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|00005730| 20 72 65 73 75 6c 74 20 | 62 79 20 31 30 bd a4 2c | result |by 10..,|
|00005740| 20 73 69 6e 63 65 20 79 | 6f 75 20 68 61 64 20 74 | since y|ou had t|
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|000057a0| 2a 20 43 6f 72 72 65 63 | 74 20 73 63 69 65 6e 74 |* Correc|t scient|
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|00005860| 0d 0d 00 00 00 00 00 00 | 00 00 00 00 00 00 00 00 |........|........|
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|00005890| 32 35 30 34 35 38 2c 20 | 31 39 32 36 36 2c 20 31 |250458, |19266, 1|
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|000058c0| 20 20 20 20 20 20 20 20 | 34 38 32 20 20 20 31 31 |        |482   11|
|000058d0| 34 20 20 20 31 30 38 20 | 20 20 20 38 37 0d 0d 53 |4   108 |   87..S|
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|00005a10| 6e 64 3a 20 32 35 30 34 | 35 38 20 d1 20 31 39 32 |nd: 2504|58 . 192|
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|00005a60| 20 44 69 76 69 64 65 20 | 74 68 65 20 6c 61 73 74 | Divide |the last|
|00005a70| 20 6e 75 6d 62 65 72 20 | 62 79 20 31 33 3a 20 31 | number |by 13: 1|
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|00005a90| 52 65 73 75 6c 74 3a 20 | 54 68 65 20 6e 65 78 74 |Result: |The next|
|00005aa0| 20 6e 75 6d 62 65 72 20 | 69 6e 20 74 68 65 20 73 | number |in the s|
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|00005ac0| 20 20 0d 0d 54 68 65 20 | 61 62 6f 76 65 20 69 73 |  ..The |above is|
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|00005b30| 0d 20 20 35 33 2e 39 34 | 2c 20 31 34 36 2e 31 37 |.  53.94|, 146.17|
|00005b40| 2c 20 20 33 39 36 2e 31 | 31 2c 20 31 30 37 33 2e |,  396.1|1, 1073.|
|00005b50| 34 36 2c 20 2e 2e 2e 0d | 20 20 28 65 a2 29 2c 20 |46, ....|  (e.), |
|00005b60| 20 20 28 65 b0 29 2c 20 | 20 20 28 65 a4 29 2c 20 |  (e.), |  (e.), |
|00005b70| 20 20 20 20 28 65 a6 29 | 2c 20 20 2e 2e 2e 20 20 |    (e.)|,  ...  |
|00005b80| 0d 46 69 67 75 72 69 6e | 67 20 4f 75 74 20 53 65 |.Figurin|g Out Se|
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|00005ba0| 78 61 6d 70 6c 65 20 31 | 3a 20 20 31 30 2c 20 20 |xample 1|:  10,  |
|00005bb0| 31 34 2c 20 20 31 38 2c | 20 20 32 32 2c 2e 2e 2e |14,  18,|  22,...|
|00005bc0| 0d 20 20 20 20 20 20 20 | 20 20 61 64 64 20 20 20 |.       |  add   |
|00005bd0| 34 20 20 20 20 34 20 20 | 20 20 34 20 0d 28 49 6e |4    4  |  4 .(In|
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|00005c10| 20 32 3a 20 20 31 30 2c | 20 20 37 2c 20 20 34 2c | 2:  10,|  7,  4,|
|00005c20| 20 20 31 2c 20 20 2d 32 | 2c 2e 2e 0d 20 20 20 20 |  1,  -2|,...    |
|00005c30| 73 75 62 74 72 61 63 74 | 20 20 20 33 20 20 20 33 |subtract|   3   3|
|00005c40| 20 20 20 33 20 20 20 33 | 0d 28 33 20 69 73 20 73 |   3   3|.(3 is s|
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|00005c70| 20 20 20 0d 0d 45 78 61 | 6d 70 6c 65 20 33 3a 20 |   ..Exa|mple 3: |
|00005c80| 20 31 30 2c 20 34 30 2c | 20 31 36 30 2c 20 36 34 | 10, 40,| 160, 64|
|00005c90| 30 2c 2e 2e 0d 20 20 20 | 20 20 6d 75 6c 74 69 70 |0,...   |  multip|
|00005ca0| 6c 79 20 20 34 20 20 20 | 34 20 20 20 20 34 0d 20 |ly  4   |4    4. |
|00005cb0| 20 20 20 20 0d 0d 45 78 | 61 6d 70 6c 65 20 34 3a |    ..Ex|ample 4:|
|00005cc0| 20 20 31 32 2c 20 20 34 | 2c 20 20 34 2f 33 2c 20 |  12,  4|,  4/3, |
|00005cd0| 20 34 2f 39 2c 2e 2e 0d | 20 20 20 20 20 64 69 76 | 4/9,...|     div|
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|00005d70| 0d 57 6f 72 6b 69 6e 67 | 20 77 69 74 68 20 53 65 |.Working| with Se|
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|00005df0| 73 6a 6f 69 6e 74 20 20 | 65 6d 70 74 79 20 20 20 |sjoint  |empty   |
|00005e00| 20 69 6e 66 69 6e 69 74 | 65 20 20 20 20 66 69 6e | infinit|e    fin|
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|00005e30| 74 77 6f 20 73 65 74 73 | 20 68 61 76 65 20 61 6e |two sets| have an|
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|00005f60| 76 65 72 79 20 69 72 72 | 61 74 69 6f 6e 61 6c 20 |very irr|ational |
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|00005fa0| 69 6e 66 69 6e 69 74 65 | 20 6e 75 6d 62 65 72 20 |infinite| number |
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|00006040| 20 6d 6f 72 65 2e 0d 0d | 20 20 20 20 0d 20 20 20 | more...|    .   |
|00006050| 20 53 71 75 61 72 65 20 | 20 20 20 20 20 20 20 20 | Square |        |
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|000060e0| 0d 0d 0d 0d 20 20 20 20 | 52 68 6f 6d 62 75 73 20 |....    |Rhombus |
|000060f0| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |        |        |
|00006100| 20 20 45 6c 6c 69 70 73 | 65 0d 0d 0d 0d 0d 20 20 |  Ellips|e.....  |
|00006110| 20 20 0d 00 00 00 00 00 | 00 00 00 00 00 00 00 00 |  ......|........|
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|00006140| 20 6d 6f 72 65 2e 0d 0d | 20 20 20 20 20 20 20 20 | more...|        |
|00006150| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |        |        |
|00006160| 20 20 20 52 65 67 75 6c | 61 72 20 0d 20 20 20 20 |   Regul|ar .    |
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|00006280| 0d 00 00 00 00 00 00 00 | 00 00 00 00 00 00 00 00 |........|........|
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|00006390| 63 61 67 6f 6e 3a 0d 41 | 20 70 6f 6c 79 67 6f 6e |cagon:.A| polygon|
|000063a0| 20 77 69 74 68 20 31 32 | 20 73 69 64 65 73 2e 0d | with 12| sides..|
|000063b0| 0d 59 6f 75 27 6c 6c 20 | 6e 6f 74 69 63 65 20 74 |.You'll |notice t|
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+--------+-------------------------+-------------------------+--------+--------+