Wyrównać przedstawiona na szkicu sieć metodą pośredniczącą.Obliczyc najprawdopodobniejsze wartości współrzędnych punktów 1 i 2, ich błędy średnie oraz średni błąd odległości między punktami A i 2 po wyrównaniu. |
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Przyjąć: |
błąd średni obserwacji kąta mα=6" |
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błąd średni obserwanej długości md= 0,0446 m |
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X |
Y |
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A |
14788,16 |
21532,51 |
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B |
15247,88 |
23507,23 |
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Obserwacje w stopniach |
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α 1 = |
92,96861111 |
1,62260836487568 |
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α 2 = |
52,97638889 |
0,924612411947444 |
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α 3 = |
36,89055556 |
0,643861657411901 |
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α 4 = |
35,63944444 |
0,622025649059587 |
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α 5 = |
55,92833333 |
0,976133561761384 |
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α 6 = |
51,54138889 |
0,899566937181326 |
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α 7 = |
34,05444444 |
0,594362180415476 |
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mα = |
6 |
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d 8 = |
1986,69 |
m |
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md = |
0,0446 |
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Przybliżone wartości współrzędnych punktów 1 i 2 |
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15247,88 |
23507,23 |
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14788,16 |
21532,51 |
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-1 |
-0,0518585 |
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1 |
1,4795264 |
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X |
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Y |
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P1 |
16154,64 |
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21138,77 |
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γ = |
52,9769444500001 |
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Σ = |
180,000000 |
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15247,88 |
23507,23 |
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16154,64 |
21138,77 |
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-1 |
1,3323323 |
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1 |
0,7942572 |
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X |
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Y |
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P2 |
16700,28 |
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23049,03 |
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γ = |
91,56805555 |
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Σ = |
180,000000 |
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Oblicznie kątów i długości ze współrzędnych |
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AL. |
BL |
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AP |
BP |
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tgα 1 = |
1366,48 |
-393,74 |
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αprz = |
92,96872064 |
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139,37 |
-40,16 |
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2368,46 |
459,72 |
1974,72 |
0 |
αob = |
92,96861111 |
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23,07 |
99,08 |
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393,74 |
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αprz - αob = |
0,39 |
" |
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tgα 2 = |
-906,76 |
2368,46 |
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αprz = |
52,9768568224628 |
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-29,08 |
75,96 |
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-1366,48 |
393,74 |
0 |
αob = |
52,97638889 |
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-139,37 |
40,16 |
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αprz - αob = |
1,68 |
" |
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tgα 3 = |
545,64 |
1910,26 |
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αprz = |
36,8905168439364 |
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28,52 |
99,83 |
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-906,76 |
2368,46 |
0 |
αob = |
36,89055556 |
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-29,08 |
75,96 |
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αprz - αob = |
-0,14 |
" |
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tgα 4 = |
-1912,12 |
-1516,52 |
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αprz = |
35,6404657584136 |
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-66,22 |
-52,52 |
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-545,64 |
-1910,26 |
0 |
αob = |
35,63944444 |
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-28,52 |
-99,83 |
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αprz - αob = |
3,68 |
" |
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tgα 5 = |
-1452,40 |
458,20 |
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αprz = |
55,9275885302861 |
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-129,16 |
40,75 |
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-1912,12 |
-1516,52 |
0 |
αob = |
55,92833333 |
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-66,22 |
-52,52 |
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αprz - αob = |
-2,68 |
" |
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tgα 6 = |
906,76 |
-2368,46 |
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αprz = |
51,5414288673639 |
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29,08 |
-75,96 |
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1452,40 |
-458,20 |
0 |
αob = |
51,54138889 |
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129,16 |
-40,75 |
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αprz - αob = |
0,14 |
" |
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tgα 7 = |
-459,72 |
-1974,72 |
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αprz = |
34,0544225337651 |
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-23,07 |
-99,08 |
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906,76 |
-2368,46 |
0 |
αob = |
34,05444444 |
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29,08 |
-75,96 |
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αprz - αob = |
-0,08 |
" |
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Azymut |
A1-2 = |
74,0587240740888 |
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cosA1-2 = |
0,2747 |
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sinA1-2 = |
0,9615 |
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Δx |
Δy |
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cosA1-2 |
sinA1-2 |
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dprz = |
1986,66 |
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1 - 2 |
545,64 |
1910,26 |
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dob = |
1986,69 |
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0,2747 |
0,9615 |
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dprz - dob = |
-0,03 |
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Równania poprawk w postaci form |
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dxL |
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dyL |
dxP |
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dyP |
dxC |
dyC |
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AL. |
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BL |
- AP |
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- BP |
- (AL.-AP) |
- (BL.-BP) |
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V1 = |
dx1 |
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dy1 |
0 |
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0 |
0 |
0 |
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0,39 |
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139,37 |
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-40,16 |
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1 |
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V2 = |
0 |
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0 |
0 |
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0 |
dx1 |
dy1 |
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1,68 |
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-29,08 |
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75,96 |
139,37 |
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-40,16 |
-110,30 |
-35,80 |
1 |
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V3 = |
dx2 |
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dy2 |
0 |
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0 |
dx1 |
dy1 |
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-0,14 |
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28,52 |
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99,83 |
29,08 |
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-75,96 |
-57,60 |
-23,88 |
1 |
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V4 = |
0 |
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0 |
dx1 |
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dy1 |
dx2 |
dy2 |
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3,68 |
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-66,22 |
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-52,52 |
28,52 |
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99,83 |
37,70 |
-47,31 |
1 |
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V5 = |
0 |
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0 |
0 |
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0 |
dx2 |
dy2 |
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-2,68 |
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-129,16 |
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40,75 |
66,22 |
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52,52 |
62,94 |
-93,27 |
1 |
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V6 = |
dx1 |
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dy1 |
dx2 |
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dy2 |
0 |
0 |
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0,14 |
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29,08 |
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-75,96 |
-129,16 |
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40,75 |
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1 |
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V7 = |
0 |
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0 |
dx1 |
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dy1 |
0 |
0 |
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-0,08 |
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- |
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-29,08 |
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75,96 |
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1 |
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V8 = |
dx1 |
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dy1 |
dx2 |
dy2 |
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-0,03 |
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-0,27 |
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-0,96 |
0,27 |
0,96 |
2 |
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Azumut |
AA -2 = |
38,4182583156752 |
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cosAA -2 = |
0,7835 |
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f = |
0 |
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0 |
dx2 |
dy2 |
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sinAA -2 = |
0,6214 |
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-0,7835 |
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-0,6214 |
0,7835 |
0,6214 |
2 |
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Postać algebraiczna równań poprawek |
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-0,0143 |
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-0,0063 |
-0,0059 |
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0,0043 |
1 |
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dx1 |
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dy1 |
dx2 |
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dy2 |
1 |
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1,85 |
V1 |
-40,16 |
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-139,37 |
0 |
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0 |
0,39 |
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1,50 |
V2 |
-35,80 |
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110,30 |
0 |
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0 |
1,68 |
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-0,88 |
V3 |
-23,88 |
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57,60 |
99,83 |
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-28,52 |
-0,14 |
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2,55 |
V4 |
99,83 |
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-28,52 |
-47,31 |
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-37,70 |
3,68 |
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-2,40 |
V5 |
0 |
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0 |
-93,27 |
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-62,94 |
-2,68 |
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1,73 |
V6 |
-75,96 |
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-29,08 |
40,75 |
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129,16 |
0,14 |
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-1,35 |
V7 |
75,96 |
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29,08 |
0 |
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0 |
-0,08 |
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-0,017 |
V8 |
-0,2747 |
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-0,9615 |
0,2747 |
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0,9615 |
-0,03 |
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-0,0143 |
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-0,0063 |
-0,0059 |
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0,0043 |
1 |
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dx1 |
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dy1 |
dx2 |
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dy2 |
1 |
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0,3 |
V1 |
-6,693 |
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-23,229 |
0 |
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0 |
0,066 |
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0,3 |
V2 |
-5,966 |
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18,383 |
0 |
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0 |
0,281 |
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-0,1 |
V3 |
-3,980 |
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9,599 |
16,639 |
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-4,753 |
-0,023 |
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0,4 |
V4 |
16,639 |
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-4,753 |
-7,886 |
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-6,284 |
0,613 |
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-0,4 |
V5 |
0 |
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0 |
-15,544 |
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-10,490 |
-0,447 |
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0,3 |
V6 |
-12,659 |
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-4,847 |
6,791 |
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21,527 |
0,024 |
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-0,2 |
V7 |
12,659 |
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4,847 |
0 |
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0 |
-0,013 |
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-0,4 |
V8 |
-6,158 |
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-21,559 |
6,158 |
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21,559 |
-0,673 |
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dx1 |
dy1 |
dx2 |
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dy2 |
1 |
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100 * τ |
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f |
Σ |
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731,509 |
184,004 |
-321,314 |
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-490,922 |
11,846 |
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100 |
0 |
0 |
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0 |
0 |
215,123 |
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1504,021 |
31,516 |
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-584,890 |
14,821 |
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0 |
100 |
0 |
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0 |
0 |
1249,471 |
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664,702 |
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412,502 |
-2,252 |
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0 |
0 |
100 |
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0 |
0,7835 |
885,939 |
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1100,336 |
-13,038 |
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0 |
0 |
0 |
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100 |
0,6214 |
524,610 |
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dx1 |
dy1 |
dx2 |
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dy2 |
1 |
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100 * 1/R |
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φ |
S |
Σ1 |
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27,046 |
6,803 |
-11,880 |
|
-18,151 |
0,438 |
|
3,697 |
0 |
0 |
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0 |
0 |
7,954 |
7,954 |
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|
38,180 |
2,942 |
|
-12,085 |
0,310 |
|
-0,659 |
2,619 |
0 |
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0 |
0 |
31,308 |
31,308 |
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|
22,692 |
|
10,243 |
0,090 |
|
2,021 |
-0,340 |
4,407 |
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0 |
0,035 |
39,147 |
39,147 |
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|
22,802 |
-0,099 |
|
1,686 |
1,541 |
-1,980 |
|
4,386 |
0,012 |
28,347 |
28,347 |
|
-0,0143 |
-0,0063 |
-0,0059 |
|
0,0043 |
1 |
|
-0,0143 |
-0,0063 |
-0,0059 |
|
0,0043 |
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kontrola warunku V^2=min |
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V2 |
0,8062 |
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0,000000 |
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0,000000 |
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L2 – Λ2 = |
0,8062 |
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V · Λ= |
0,000000 |
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0,000000 |
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L2 – Λ2 = |
0,8062 |
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Obliczamy najprawdopodobniejsze wartości punktów 1 i 2 |
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X1 = |
16154,626 |
Y1 = |
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21138,764 |
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X2 = |
16700,274 |
Y2 = |
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23049,034 |
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XA = |
14788,16 |
YA = |
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21532,51 |
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XB = |
15247,88 |
YB = |
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23507,23 |
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αi w = αi ob. + Vi |
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Kontrola ostateczna |
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di w = di ob. + di |
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α 1 = |
92,96912 |
tgα 1 = |
|
1366,466 |
-393,746 |
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α 1 = |
92,96911 |
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459,719999999999 |
1974,72 |
0 |
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α 2 = |
52,97681 |
tgα 2 = |
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-906,746 |
2368,466 |
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α 2 = |
52,97681 |
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-1366,466 |
393,746 |
0 |
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α 3 = |
36,89031 |
tgα 3 = |
|
545,648 |
1910,270 |
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α 3 = |
36,89032 |
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-906,746 |
2368,466 |
0 |
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α 4 = |
35,64015 |
tgα 4 = |
|
-1912,114 |
-1516,524 |
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α 4 = |
35,64016 |
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-545,648 |
-1910,270 |
0 |
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α 5 = |
55,92767 |
tgα 5 = |
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-1452,394 |
458,196 |
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α 5 = |
55,92767 |
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-1912,114 |
-1516,524 |
0 |
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α 6 = |
51,54187 |
tgα 6 = |
|
906,746 |
-2368,466 |
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α 6 = |
51,54185 |
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1452,394 |
-458,196 |
0 |
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α 7 = |
34,05407 |
tgα 7 = |
|
-459,719999999999 |
-1974,72 |
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α 7 = |
34,05408 |
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906,746 |
-2368,466 |
0 |
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Δx |
Δy |
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d = |
1986,673 |
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d1-2 = |
545,648 |
1910,270 |
= |
1986,671 |
m |
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mo = |
0,3394 |
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mX2 = |
0,0165 |
m |
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mX1 = |
0,0125 |
m |
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mY2 = |
0,0181 |
m |
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mY1 = |
0,0092 |
m |
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md = |
|
m |
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