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    Data Nodal

    Nama batang Nodal i Nodal j Alpha Panjang (mm)

    batang 1 1 2 0 4000

    batang 2 2 3 0 4000

    batang 3 3 4 0 4000batang 4 4 5 0 4000

    batang 5 1 6 42.77 2720

    batang 6 6 7 42.77 2720

    batang 7 6 2 317.23 2720

    batang 8 7 2 270 3700

    batang 9 7 8 0 4000

    batang 10 2 8 42.77 5440

    batang 11 8 3 270 3700

    batang 12 8 9 0 4000

    batang 13 8 4 317.23 5440batang 14 9 4 270 3700

    batang 15 9 10 317.23 2720

    batang 16 4 10 42.77 2720

    batang 17 10 5 317.23 2720

     !an"#o!ma"i mat!i$"

    %l&m&n 1

    1 0 0 0

     1 0 1 0 0

    0 0 1 0

    0 0 0 1

    %l&m&n 2

    1 0 0 0

     2 0 1 0 0

    0 0 1 0

    0 0 0 1

    %l&m&n 3

    1 0 0 0

     3 0 1 0 0

    0 0 1 0

    0 0 0 1

    %l&m&n 4

    1 0 0 0

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     4 0 1 0 0

    0 0 1 0

    0 0 0 1

    %l&m&n 5

    0.7340855185 0.679057 0 0

     5 '0.6790570311 0.734086 0 00 0 0.734086 0.679057

    0 0 '0.679057 0.734086

    %l&m&n 6

    0.7340855185 0.679057 0 0

     6 '0.6790570311 0.734086 0 0

    0 0 0.734086 0.679057

    0 0 '0.679057 0.734086

    %l&m&n 70.7340855185 '0.679057 0 0

     7 0.6790570311 0.734086 0 0

    0 0 0.734086 '0.679057

    0 0 0.679057 0.734086

    %l&m&n 8

    '1.83772%'016 '1 0 0

     8 1 '1.8%'016 0 0

    0 0 '1.8%'016 '1

    0 0 1 '1.8%'016

    %l&m&n 9

    1 0 0 0

     9 0 1 0 0

    0 0 1 0

    0 0 0 1

    %l&m&n 10

    0.7340855185 0.679057 0 0

     10 '0.6790570311 0.734086 0 0

    0 0 0.734086 0.679057

    0 0 '0.679057 0.734086

    %l&m&n 11

    '1.83772%'016 '1 0 0

     11 1 '1.8%'016 0 0

    0 0 '1.8%'016 '1

    0 0 1 '1.8%'016

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    %l&m&n 12

    1 0 0 0

     12 0 1 0 0

    0 0 1 0

    0 0 0 1

    %l&m&n 13

    0.7340855185 '0.679057 0 0

     13 0.6790570311 0.734086 0 0

    0 0 0.734086 '0.679057

    0 0 0.679057 0.734086

    %l&m&n 14

    '1.83772%'016 '1 0 0

     14 1 '1.8%'016 0 0

    0 0 '1.8%'016 '10 0 1 '1.8%'016

    %l&m&n 15

    0.7340855185 '0.679057 0 0

     15 0.6790570311 0.734086 0 0

    0 0 0.734086 '0.679057

    0 0 0.679057 0.734086

    %l&m&n 16

    0.7340855185 0.679057 0 0

     16 '0.6790570311 0.734086 0 0

    0 0 0.734086 0.679057

    0 0 '0.679057 0.734086

    %l&m&n 17

    0.7340855185 '0.679057 0 0

     17 0.6790570311 0.734086 0 0

    0 0 0.734086 '0.679057

    0 0 0.679057 0.734086

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    &nt$ !"" 2

    A%*+ Alpha !ad

    210300 0

    210300 0

    210300 0210300 0

    309264.71 0.7464773211

    309264.71 0.7464773211

    309264.71 5.5367079861

    227351.35 4.7123889804

    210300 0

    154632.35 0.7464773211

    227351.35 4.7123889804

    210300 0

    154632.35 5.5367079861227351.35 4.7123889804

    309264.71 5.5367079861

    309264.71 0.7464773211

    309264.71 5.5367079861

    ,g

      t!an"#o!ma"i

    1 0 0 0 1

    0 1 0 0 0

    0 0 1 0 '1

    0 0 0 1 0

    1 0 0 0 1

    0 1 0 0 0

    0 0 1 0 '1

    0 0 0 1 0

    1 0 0 0 1

    0 1 0 0 0

    0 0 1 0 '1

    0 0 0 1 0

    1 0 0 0 1

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    0 1 0 0 0

    0 0 1 0 '1

    0 0 0 1 0

    0.7340855 '0.6790570311 0 0 0.5388815485

    0.679057 0.7340855185 0 0 0.49848593280 0 0.7340855 '0.6790570311 '0.538881549

    0 0 0.679057 0.7340855185 '0.498485933

    0.7340855 '0.6790570311 0 0 0.5388815485

    0.679057 0.7340855185 0 0 0.4984859328

    0 0 0.7340855 '0.6790570311 '0.538881549

    0 0 0.679057 0.7340855185 '0.498485933

    0.7340855 0.6790570311 0 0 0.5388815485

    '0.679057 0.7340855185 0 0 '0.498485933

    0 0 0.7340855 0.6790570311 '0.538881549

    0 0 '0.679057 0.7340855185 0.4984859328

    '1.8%'016 1 0 0 3.37722%'032

    '1 '1.83772%'016 0 0 1.83772%'016

    0 0 '1.8%'016 1 '3.37722%'032

    0 0 '1 '1.83772%'016 '1.83772%'016

    1 0 0 0 1

    0 1 0 0 0

    0 0 1 0 '1

    0 0 0 1 0

    0.7340855 '0.6790570311 0 0 0.5388815485

    0.679057 0.7340855185 0 0 0.4984859328

    0 0 0.7340855 '0.6790570311 '0.538881549

    0 0 0.679057 0.7340855185 '0.498485933

    '1.8%'016 1 0 0 3.37722%'032

    '1 '1.83772%'016 0 0 1.83772%'016

    0 0 '1.8%'016 1 '3.37722%'032

    0 0 '1 '1.83772%'016 '1.83772%'016

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    1 0 0 0 1

    0 1 0 0 0

    0 0 1 0 '1

    0 0 0 1 0

    0.7340855 0.6790570311 0 0 0.5388815485

    '0.679057 0.7340855185 0 0 '0.498485933

    0 0 0.7340855 0.6790570311 '0.538881549

    0 0 '0.679057 0.7340855185 0.4984859328

    '1.8%'016 1 0 0 3.37722%'032

    '1 '1.83772%'016 0 0 1.83772%'016

    0 0 '1.8%'016 1 '3.37722%'0320 0 '1 '1.83772%'016 '1.83772%'016

    0.7340855 0.6790570311 0 0 0.5388815485

    '0.679057 0.7340855185 0 0 '0.498485933

    0 0 0.7340855 0.6790570311 '0.538881549

    0 0 '0.679057 0.7340855185 0.4984859328

    0.7340855 '0.6790570311 0 0 0.5388815485

    0.679057 0.7340855185 0 0 0.4984859328

    0 0 0.7340855 '0.6790570311 '0.538881549

    0 0 0.679057 0.7340855185 '0.498485933

    0.7340855 0.6790570311 0 0 0.5388815485

    '0.679057 0.7340855185 0 0 '0.498485933

    0 0 0.7340855 0.6790570311 '0.538881549

    0 0 '0.679057 0.7340855185 0.4984859328

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    D

    %l&m&n 1   u1 v1

    0 '1 0 210300 0

    0 0 0 0 0

    0 1 0 '210300 0

    0 0 0 0 0

    %l&m&n 2 2 -2

    0 '1 0 210300 0

    0 0 0 0 0

    0 1 0 '210300 0

    0 0 0 0 0

    %l&m&n 3 3 -3

    0 '1 0 210300 0

    0 0 0 0 0

    0 1 0 '210300 0

    0 0 0 0 0

    %l&m&n 4 4 -4

    0 '1 0 210300 0

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    0 0 0 0 0

    0 1 0 '210300 0

    0 0 0 0 0

    %l&m&n 5 1 -1

    0.4984859328 '0.538882 '0.498486 166657.04361 154164.1

    0.4611184515 '0.498486 '0.461118 154164.10539 142607.7'0.498485933 0.538882 0.4984859 '166657.0436 '154164

    '0.461118451 0.498486 0.4611185 '154164.1054 '142608

    %l&m&n 6 6 -6

    0.4984859328 '0.538882 '0.498486 166657.04361 154164.1

    0.4611184515 '0.498486 '0.461118 154164.10539 142607.7

    '0.498485933 0.538882 0.4984859 '166657.0436 '154164

    '0.461118451 0.498486 0.4611185 '154164.1054 '142608

    %l&m&n 7 6 -6'0.498485933 '0.538882 0.4984859 166657.04361 '154164

    0.4611184515 0.498486 '0.461118 '154164.1054 142607.7

    0.4984859328 0.538882 '0.498486 '166657.0436 154164.1

    '0.461118451 '0.498486 0.4611185 154164.10539 '142608

    %l&m&n 8 7 -7

    1.83772%'016 '3.4%'032 '1.8%'016 7.67817%'027 4.18%'011

    1 '1.8%'016 '1 4.17809%'011 227351.4

    '1.83772%'016 3.38%'032 1.84%'016 '7.67817%'027 '4.2%'011

    '1 1.84%'016 1 '4.17809%'011 '227351

    %l&m&n 9 7 -7

    0 '1 0 210300 0

    0 0 0 0 0

    0 1 0 '210300 0

    0 0 0 0 0

    %l&m&n 10 2 -2

    0.4984859328 '0.538882 '0.498486 83328.521807 77082.05

    0.4611184515 '0.498486 '0.461118 77082.052694 71303.83

    '0.498485933 0.538882 0.4984859 '83328.52181 '77082.05

    '0.461118451 0.498486 0.4611185 '77082.05269 '71303.83

    %l&m&n 11 8 -8

    1.83772%'016 '3.4%'032 '1.8%'016 7.67817%'027 4.18%'011

    1 '1.8%'016 '1 4.17809%'011 227351.4

    '1.83772%'016 3.38%'032 1.84%'016 '7.67817%'027 '4.2%'011

    '1 1.84%'016 1 '4.17809%'011 '227351

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    %l&m&n 12 8 -8

    0 '1 0 210300 0

    0 0 0 0 0

    0 1 0 '210300 0

    0 0 0 0 0

    %l&m&n 13 8 -8

    '0.498485933 '0.538882 0.4984859 83328.521807 '77082.05

    0.4611184515 0.498486 '0.461118 '77082.05269 71303.83

    0.4984859328 0.538882 '0.498486 '83328.52181 77082.05

    '0.461118451 '0.498486 0.4611185 77082.052694 '71303.83

    %l&m&n 14 9 -9

    1.83772%'016 '3.4%'032 '1.8%'016 7.67817%'027 4.18%'011

    1 '1.8%'016 '1 4.17809%'011 227351.4

    '1.83772%'016 3.38%'032 1.84%'016 '7.67817%'027 '4.2%'011'1 1.84%'016 1 '4.17809%'011 '227351

    %l&m&n 15 9 -9

    '0.498485933 '0.538882 0.4984859 166657.04361 '154164

    0.4611184515 0.498486 '0.461118 '154164.1054 142607.7

    0.4984859328 0.538882 '0.498486 '166657.0436 154164.1

    '0.461118451 '0.498486 0.4611185 154164.10539 '142608

    %l&m&n 16 4 4

    0.4984859328 '0.538882 '0.498486 166657.04361 154164.1

    0.4611184515 '0.498486 '0.461118 154164.10539 142607.7

    '0.498485933 0.538882 0.4984859 '166657.0436 '154164

    '0.461118451 0.498486 0.4611185 '154164.1054 '142608

    %l&m&n 17 10 -10

    '0.498485933 '0.538882 0.4984859 166657.04361 '154164

    0.4611184515 0.498486 '0.461118 '154164.1054 142607.7

    0.4984859328 0.538882 '0.498486 '166657.0436 154164.1

    '0.461118451 '0.498486 0.4611185 154164.10539 '142608

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    u2 v2

    '210300 0 u1   1 -1

    0 0 v1   1 1 376957 154164.105389

    210300 0 u2   /1 -1 154164.1 142607.662269

    0 0 v2   2 2 '210300 0

    /2 -2 0 0

    3 -3 3 3 0 0

    '210300 0 u2   /3 -3 0 0

    0 0 v2   4 4 0 0

    210300 0 u3   /4 -4 0 0

    0 0 v3   5 5 0 0

    /5 -5 0 0

    4 -4 6 6 '166657 '154164.10539

    '210300 0 u3   /6 -6 '154164 '142607.66227

    0 0 -3 7 7 0 0

    210300 0 4 /7 -7 0 0

    0 0 -4 8 8 0 0

    /8 -8 0 0

    5 -5 9 9 0 0

    '210300 0 4 /9 -9 0 0

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    0 0 -4 10 10 0 0

    210300 0 5 /10 -10 0 0

    0 0 -5

    6 -6

    '166657 '154164 1 1 376957 154164.105389

    '154164 '142608 -1 /1 154164.1 142607.662269166657 154164.1 6 2 '210300 0

    154164.1 142607.7 -6 /2 0 0

    3 0 0

    7 -7 /3 0 0

    '166657 '154164 6 4 0 0

    '154164 '142608 -6 /4 0 0

    166657 154164.1 7 5 0 0

    154164.1 142607.7 -7 /5 0 0

    6 '166657 '154164.10539

    2 -2 /6 '154164 '142607.66227'166657 154164.1 6 7 0 0

    154164.1 '142608 -6 /7 0 0

    166657 '154164 2 8 0 0

    '154164 142607.7 -2 /8 0 0

    9 0 0

    2 -2 /9 0 0

    '7.7%'027 '4.2%'011 7 10 0 0

    '4.2%'011 '227351 -7 /10 0 0

    7.68%'027 4.18%'0112

    4.18%'011 227351.4-2

    2

    8 -8 2 670585.56542

    '210300 0 7 -2 '77082.052694

    0 0 -7 3 '210300

    210300 0 8 -3 0

    0 0 -8 4 0

    -4 0

    8 -8 5 0

    '83328.52 '77082.05 2 6 '166657.04361

    '77082.05 '71303.83 -2 -6 154164.105389

    83328.52 77082.05 8 7 '7.678166%'027

    77082.05 71303.83 -8 -7 '4.178087%'011

    8 '83328.521807

    3 -3 -8 '77082.052694

    '7.7%'027 '4.2%'011 8 9 0

    '4.2%'011 '227351 -8 -9 0

    7.68%'027 4.18%'011 3 10 0

    4.18%'011 227351.4 -3 -10 0

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    9 -9

    '210300 0 8 4.755112%'006

    0 0 -8 '3.855337%'006

    210300 0 9 4.755112%'006

    0 0 -9 '2.570225%'006

    4.755112%'0064 -4 '1.285112%'006

    '83328.52 77082.05 8 4.755112%'006

    77082.05 '71303.83 -8 4.160723%'006

    83328.52 '77082.05 4 '4.497894%'006

    '77082.05 71303.83 -4 3.566334%'006

    '3.855337%'006

    4 -4 3.566334%'006

    '7.7%'027 '4.2%'011 9 '2.570225%'006

    '4.2%'011 '227351 -9 3.566334%'006

    7.68%'027 4.18%'011 4 '1.285112%'0064.18%'011 227351.4 -4 4.160723%'006

    '6.425562%'007

    10 -10

    '166657 154164.1 9 di"pla&m&nt

    154164.1 '142608 -9

    166657 '154164 10   u2   0.4550985506

    '154164 142607.7-10   v2   '2.7462893406

    u3   0.952930148

    10 -10   v3   '3.6322351047

    '166657 '154164 4   u4   1.4507617453

    '154164 '142608 -4   v4   '2.6818782544

    166657 154164.110   u5   1.8446382322

    154164.1 142607.7-10   u6   1.2878765393

    v6   '1.8794317979

    5 -5   u7   1.4001011968

    '166657 154164.110   v7   '2.5213468181

    154164.1 '142608 -10   u8   0.9694914717

    166657 '154164 5   v8   '3.4857657751

    '154164 142607.7-5   u9   0.5756149848

    v9   '2.4464586753

    u10   0.6557913076

    v10   '1.8224860984

    !&a$"i

    '210300

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    0

    0

    1 '20600

    /1'33.3 69477.0405609/5'33.3 76622.9594391

    1 '20600

    /1 102777.040561

    /5 109922.959439

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    o-&!all "tin&""

    2 -2 3 -3 4

    '210300 0 0 0 0

    0 0 0 0 0

    670585.56542 '77082.052694 '210300 0 0

    '77082.052694 441262.844755 0 0 0

    '210300 0 420600 4.178087%'011 '210300

    0 0 4.178087%'011 227351.351351 0

    0 0 '210300 0 670585.56542

    0 0 0 0 77082.0526945

    0 0 0 0 '210300

    0 0 0 0 0

    '166657.04361 154164.105389 0 0 0

    154164.105389 '142607.66227 0 0 0

    '7.678166%'027 '4.178087%'011 0 0 0

    '4.178087%'011 '227351.35135 0 0 0

    '83328.521807 '77082.052694 '7.678166%'027 '4.178087%'011 '83328.521807

    '77082.052694 '71303.831135 '4.178087%'011 '227351.35135 77082.0526945

    0 0 0 0 '7.678166%'027

    0 0 0 0 '4.178087%'011

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    0 0 0 0 '166657.04361

    0 0 0 0 '154164.10539

    !&a!!ang&m&nt

    '210300 0 0 0 0

    0 0 0 0 0670585.56542 '77082.052694 '210300 0 0

    '77082.052694 441262.844755 0 0 0

    '210300 0 420600 4.178087%'011 '210300

    0 0 4.178087%'011 227351.351351 0

    0 0 '210300 0 670585.56542

    0 0 0 0 77082.0526945

    0 0 0 0 '210300

    0 0 0 0 0

    '166657.04361 154164.105389 0 0 0

    154164.105389 '142607.66227 0 0 0'7.678166%'027 '4.178087%'011 0 0 0

    '4.178087%'011 '227351.35135 0 0 0

    '83328.521807 '77082.052694 '7.678166%'027 '4.178087%'011 '83328.521807

    '77082.052694 '71303.831135 '4.178087%'011 '227351.35135 77082.0526945

    0 0 0 0 '7.678166%'027

    0 0 0 0 '4.178087%'011

    0 0 0 0 '166657.04361

    0 0 0 0 '154164.10539

    -2 3 -3 4 -4

    '77082.052694 '210300 0 0 0

    441262.844755 0 0 0 0

    0 420600 4.178087%'011 '210300 0

    0 4.178087%'011 227351.351351 0 0

    0 '210300 0 670585.56542 77082.0526945

    0 0 0 77082.0526945 441262.844755

    0 0 0 '210300 0

    154164.105389 0 0 0 0

    '142607.66227 0 0 0 0

    '4.178087%'011 0 0 0 0

    '227351.35135 0 0 0 0

    '77082.052694 '7.678166%'027 '4.178087%'011 '83328.521807 77082.0526945

    '71303.831135 '4.178087%'011 '227351.35135 77082.0526945 '71303.831135

    0 0 0 '7.678166%'027 '4.178087%'011

    0 0 0 '4.178087%'011 '227351.35135

    0 0 0 '166657.04361 '154164.10539

    0 0 0 '154164.10539 '142607.66227

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    '3.855337%'006 4.755112%'006 '2.570225%'006 4.755112%'006 '1.285112%'006

    2.299219%'005 '6.425562%'006 2.032551%'005 '8.995787%'006 1.210182%'005

    '6.425562%'006 9.510223%'006 '7.710675%'006 9.510223%'006 '3.855337%'006

    2.032551%'005 '7.710675%'006 3.729325%'005 '1.285112%'005 2.032551%'005

    '8.995787%'006 9.510223%'006 '1.285112%'005 1.426534%'005 '6.425562%'0061.210182%'005 '3.855337%'006 2.032551%'005 '6.425562%'006 2.299219%'005

    '1.028090%'005 9.510223%'006 '1.542135%'005 1.426534%'005 '1.028090%'005

    '1.012952%'005 5.349501%'006 '9.064401%'006 6.538279%'006 '5.429054%'006

    1.620957%'005 '0.000005783 1.330507%'005 '7.068119%'006 7.622068%'006

    '8.487192%'006 5.943890%'006 '1.028090%'005 8.321446%'006 '6.934157%'006

    1.969333%'005 '6.425562%'006 1.812628%'005 '8.995787%'006 1.100220%'005

    '4.631855%'006 5.943890%'006 '7.710675%'006 8.321446%'006 '0.000005649

    2.032551%'005 '7.710675%'006 3.289477%'005 '1.285112%'005 2.032551%'005

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    20/46

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  • 8/17/2019 Matriks Rahardian Gusta

    21/46

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  • 8/17/2019 Matriks Rahardian Gusta

    22/46

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  • 8/17/2019 Matriks Rahardian Gusta

    23/46

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  • 8/17/2019 Matriks Rahardian Gusta

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    0 '154164.10539 '142607.66227 0 0

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  • 8/17/2019 Matriks Rahardian Gusta

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  • 8/17/2019 Matriks Rahardian Gusta

    26/46

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  • 8/17/2019 Matriks Rahardian Gusta

    27/46

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    28/46

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  • 8/17/2019 Matriks Rahardian Gusta

    29/46

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  • 8/17/2019 Matriks Rahardian Gusta

    30/46

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  • 8/17/2019 Matriks Rahardian Gusta

    31/46

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  • 8/17/2019 Matriks Rahardian Gusta

    32/46

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  • 8/17/2019 Matriks Rahardian Gusta

    33/46

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  • 8/17/2019 Matriks Rahardian Gusta

    34/46

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  • 8/17/2019 Matriks Rahardian Gusta

    35/46

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  • 8/17/2019 Matriks Rahardian Gusta

    36/46

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  • 8/17/2019 Matriks Rahardian Gusta

    37/46

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  • 8/17/2019 Matriks Rahardian Gusta

    38/46

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  • 8/17/2019 Matriks Rahardian Gusta

    39/46

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  • 8/17/2019 Matriks Rahardian Gusta

    40/46

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    0 210300 0 0.95293

    0 0 0 '3.632235

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    154164.1 '166657 '154164 0

    142607.7 '154164 '142608 0

    '154164 166657 154164.1 1.287877

    '142608 154164.1 142607.7 '1.879432

    154164.1 '166657 '154164 1.287877

    142607.7 '154164 '142608 '1.879432

    '154164 166657 154164.1 1.400101

    '142608 154164.1 142607.7 '2.521347

    '154164 '166657 154164.1 1.287877

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    142607.7 154164.1 '142608 '1.879432

    154164.1 166657 '154164 0.455099

    '142608 '154164 142607.7 '2.746289

    4.18%'011 '7.7%'027 '4.2%'011 1.400101

    227351.4 '4.2%'011 '227351 '2.521347

    '4.2%'011 7.68%'027 4.18%'011 0.455099

    '227351 4.18%'011 227351.4 '2.746289

    0 '210300 0 1.400101

    0 0 0 '2.521347

    0 210300 0 0.969491

    0 0 0 '3.485766

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    77082.05 '83328.52 '77082.05 0.45509971303.83 '77082.05 '71303.83 '2.746289

    '77082.05 83328.52 77082.05 0.969491

    '71303.83 77082.05 71303.83 '3.485766

    4.18%'011 '7.7%'027 '4.2%'011 0.969491

    227351.4 '4.2%'011 '227351 '3.485766

    '4.2%'011 7.68%'027 4.18%'011 0.95293

    '227351 4.18%'011 227351.4 '3.632235

    0 '210300 0 0.969491

    0 0 0 '3.485766

    0 210300 0 0.575615

    0 0 0 '2.446459

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    44/46

    '77082.05 '83328.52 77082.05 0.969491

    71303.83 77082.05 '71303.83 '3.485766

    77082.05 83328.52 '77082.05 1.450762

    '71303.83 '77082.05 71303.83 '2.681878

    4.18%'011 '7.7%'027 '4.2%'011 0.575615

    227351.4 '4.2%'011 '227351 '2.446459

    '4.2%'011 7.68%'027 4.18%'011 1.450762

    '227351 4.18%'011 227351.4 '2.681878

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    45/46

    '154164 '166657 154164.1 0.575615

    142607.7 154164.1 '142608 '2.446459

    154164.1 166657 '154164 0.655791

    '142608 '154164 142607.7 '1.822486

    154164.1 '166657 '154164 1.450762

    142607.7 '154164 '142608 '2.681878

    '154164 166657 154164.1 0.655791

    '142608 154164.1 142607.7 '1.822486

    '154164 '166657 154164.1 0.655791

    142607.7 154164.1 '142608 '1.822486

    154164.1 166657 '154164 1.844638

    '142608 '154164 142607.7 0

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