polinomial pangkat 3
TRANSCRIPT
Mata Kuliah Rekyasa Perhitungan Cadangan
PERHITUNGAN CADANGAN DENGAN
METODE POLINOMIAL PANGKAT TIGA
OLEH :
MUHAMMAD SUKARDI
D62107026
PROGRAM STUDI TEKNIK PERTAMBANGAN FAKULTAS TEKNIK
UNIVERSITAS HASANUDDIN
MAKASSAR 2010
A. PENAMPANG 1-1’
1. Nilai Segmen
PENAMPANG 1-1’ SEGMEN X Y
0 0 70 1 25 75 2 50 50 3 75 65 4 100 55 5 125 60 6 150 35
2. Diketahui
H0 = X1 - X0 = 25.00 H1 = X2 - X1 = 25.00 H2 = X3 - X2 = 25.00 H3 = X4 - X3 = 25.00 H4 = X5 - X4 = 25.00 H5 = X6 - X5 = 25.00
3. Maka matriks [H] [C] = [A] adalah :
4. Perhitungan Eliminasi Gauss Jordan membuat matriks baru
M21 = H21/H11 = 25.00
a21 baru = a21 - M21 (a11) = 25 - (25 x 1) = 0.00 a22 baru = a22 - M21 (a12) = 25 - (25 x 0) = 100.00 a23 baru = a23 - M21 (a13) = 25 - (25 x 0) = 25.00 A21 baru = A21 - M21 (A11) = 3.6 - (25 x 0) = -3.60
M32 = H32/H22 = 0.25
a0 = 70.00 a1 = 75.00 a2 = 50.00 a3 = 65.00 a4 = 55.00 a5 = 60.00 a6 = 35.00
a32 baru = a32 - M32 (a22) = 25 - (0.25 x 100) = 0 a33 baru = a33 - M32 (a23) = 100 - (0.25 x 25) = 93.75 a34 baru = a34 - M32 (a24) = 25 - (0.25 x 25) = 25.00 A31 baru = A31 - M21 (A21) = 4.8 - (0.25 x-3.6) = 5.70
M43 = H43/H33 = 0.25
a43 baru = a43 - M43 (a33) = 25 - (0.25 x 100) = 0 a44 baru = a44 - M43 (a34) = 100 - (0.25 x 25) = 93.75 a45 baru = a45 - M43 (a35) = 25 - (0.25 x 25) = 25.00 A41 baru = A41 - M43 (A31) = 3 - (0.25 x 4.8) =
-4.20
M54 = H54/H44 = 0.25
a54 baru = a54 - M54 (a44) = 25 - (0.25 x 100) = 0 a55 baru = a55 - M54 (a45) = 100 - (0.25 x 25) = 93.75 a56 baru = a56 - M54 (a46) = 25 - (0.25 x 25) = 25.00 A51 baru = A51 - M54 (A41) = 1.8 - (0.25 x 3) =
2.55
Matriks baru
5. Substitusi mundur untuk mendapatkan nilai C
C5 = 0
93.75C4 + 25C5 = 2.55 C4 = 0.02720 93.75C3 + 25C4 = - 4.2 C3 = -0.05205
93.75C2 + 25C3 = 5.7 C2 = 0.07468 93.75C1 + 25C2 = - 3.6 C1 = -0.05467
C0 = 0
6. Mencari nilai b dengan rumus :
b0 = 0.66
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b1 = -0.71 b2 = -0.21 b3 = 0.24 b4 = -0.25 b5 = -1.00
7. Mencari nilai d dengan rumus :
d0 = -0.000729 d1 = 0.001725 d2 = -0.001690 d3 = 0.001057 d4 = -0.000363 d5 = 0.000000
8. Perhitungan luas penampang :
A0 = 1883.69 A1 = 1536.44 A2 = 1408.04 A3 = 1532.36 A4 = 1402.08 A5 = 1187.50
Luas penampang 1-1’ diperoleh dari penjumlahan A0, A1, A2, A3, A4 dan A5
A penampang 1-1’ = A0+ A1+ A2+ A3+ A4+ A5
= 8.950,11 m2
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B. PENAMPANG 2-2’
1. Nilai Segmen
PENAMPANG 2 SEGMEN X Y
0 0 60 1 25 80 2 50 55 3 75 70 4 100 55 5 125 70 6 150 45
2. Diketahui
H0 = X1 - X0 = 25.00 a0 = 60.00
H1 = X2 - X1 = 25.00 a1 = 80.00
H2 = X3 - X2 = 25.00 a2 = 55.00
H3 = X4 - X3 = 25.00 a3 = 70.00
H4 = X5 - X4 = 25.00 a4 = 55.00
H5 = X6 - X5 = 25.00 a5 = 70.00
a6 = 45.00
3. Maka matriks [H] [C] = [A] adalah :
4. Perhitungan Eliminasi Gauss Jordan membuat matriks baru
M21 = H21/H11 = 25.00
a21 baru = a21 - M21 (a11) = 25 - (25 x 1) = 0.00 a22 baru = a22 - M21 (a12) = 25 - (25 x 0) = 100.00 a23 baru = a23 - M21 (a13) = 25 - (25 x 0) = 25.00 A21 baru = A21 - M21 (A11) = 5.4 - (25 x 0) = -5.40
M32 = H32/H22 = 0.25
a32 baru = a32 - M32 (a22) = 25 - (0.25 x 100) = 0 a33 baru = a33 - M32 (a23) = 100 - (0.25 x 25) = 93.75 a34 baru = a34 - M32 (a24) = 25 - (0.25 x 25) = 25.00
A31 baru = A31 - M21 (A21) = 4.8 - (0.25 x5.4) = 6.15
M43 = H43/H33 = 0.25
a43 baru = a43 - M43 (a33) = 25 - (0.25 x 100) = 0 a44 baru = a44 - M43 (a34) = 100 - (0.25 x 25) = 93.75 a45 baru = a45 - M43 (a35) = 25 - (0.25 x 25) = 25.00 A41 baru = A41 - M43 (A31) = 3.6 - (0.25 x 4.8) = -4.80
M54 = H54/H44 = 0.25
a54 baru = a54 - M54 (a44) = 25 - (0.25 x 100) = 0 a55 baru = a55 - M54 (a45) = 100 - (0.25 x 25) = 93.75 a56 baru = a56 - M54 (a46) = 25 - (0.25 x 25) = 25.00 A51 baru = A51 - M54 (A41) = 3.6 - (0.25 x 3.6) = 4.50
Matriks baru
5. Substitusi mundur untuk mendapatkan nilai C
C5 = 0 93.75C4 + 25C5 =4.5 C4 = 0.04800
93.75C3 + 25C4 = -4.8 C3 = -
0.06400 93.75C2 + 25C3 = 6.15 C2 = 0.08267
93.75C1 + 25C2 = -5.40 C1 = -
0.07467
C0 = 0
6. Mencari nilai b dengan rumus : 11 23
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b0 = 1.4222 b1 = -0.44 b2 = -0.24 b3 = 0.07 b4 = -0.20 b5 = -1.00
7. Mencari nilai d dengan rumus :
d0 = -0.000996 d1 = 0.002098 d2 = -0.001956 d3 = 0.001493 d4 = -0.000640 d5 = 0.000000
8. Perhitungan luas penampang :
A0 = 1847.22 A1 = 1677.08 A2 = 1538.19 A3 = 1583.33 A4 = 1500.00 A5 = 1437.50
Luas penampang 2-2’ diperoleh dari penjumlahan A0, A1, A2, A3, A4 dan A5
A penampang 2-2’ = A0+ A1+ A2+ A3+ A4+ A5
= 9.583,33 m2
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C. PENAMPANG 3-3’
1. Nilai Segmen
PENAMPANG 3 SEGMEN X Y
0 0 70 1 25 75 2 50 65 3 75 85 4 100 65 5 125 80 6 150 45
2. Diketahui
a0 = 70.00 a1 = 75.00 a2 = 65.00 a3 = 85.00 a4 = 65.00 a5 = 80.00 a6 = 45.00
3. Maka matriks [H] [C] = [A] adalah :
4. Perhitungan Eliminasi Gauss Jordan membuat matriks baru
M21 = H21/H11 = 25.00
a21 baru = a21 - M21 (a11) = 25 - (25 x 1) = 0.00 a22 baru = a22 - M21 (a12) = 25 - (25 x 0) = 100.00 a23 baru = a23 - M21 (a13) = 25 - (25 x 0) = 25.00 A21 baru = A21 - M21 (A11) = 1.8 - (25 x 0) = -1.80
M32 = H32/H22 = 0.25
a32 baru = a32 - M32 (a22) = 25 - (0.25 x 100) = 0 a33 baru = a33 - M32 (a23) = 100 - (0.25 x 25) = 93.75
H0 = X1 - X0 = 25.00 H1 = X2 - X1 = 25.00 H2 = X3 - X2 = 25.00 H3 = X4 - X3 = 25.00 H4 = X5 - X4 = 25.00 H5 = X6 - X5 = 25.00
a34 baru = a34 - M32 (a24) = 25 - (0.25 x 25) = 25.00 A31 baru = A31 - M21 (A21) = 3,6 - (0.25 x-1,8) = 4.05
M43 = H43/H33 = 0.25
a43 baru = a43 - M43 (a33) = 25 - (0.25 x 100) = 0 a44 baru = a44 - M43 (a34) = 100 - (0.25 x 25) = 93.75 a45 baru = a45 - M43 (a35) = 25 - (0.25 x 25) = 25.00
A41 baru = A41 - M43 (A31) = 4,8- (0.25 x3,6) = -5.70
M54 = H54/H44 = 0.25
a54 baru = a54 - M54 (a44) = 25 - (0.25 x 100) = 0 a55 baru = a55 - M54 (a45) = 100 - (0.25 x 25) = 93.75 a56 baru = a56 - M54 (a46) = 25 - (0.25 x 25) = 25.00 A51 baru = A51 - M54 (A41) = 4,2 - (0.25 x -4,8) = 5.40
Matriks baru
5. Substitusi mundur untuk mendapatkan nilai C
C5 = 0 93.75C4 + 25C5 =5,4 C4 = 0.05760
93.75C3 + 25C4 = -5,7 C3 = -0.07616 93.75C2 + 25C3 = 4,05 C2 = 0.06351
93.75C1 + 25C2 = -1,80 C1 = -0.03388 C0 = 0
6. Mencari nilai b dengan rumus :
b0 = 0.4823 b1 = -0.36 b2 = 0.38 b3 = -0.01 b4 = -0.36
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b5 = -1.40
7. Mencari nilai d dengan rumus :
d0 = -0.000452 d1 = 0.001298 d2 = -0.001862 d3 = 0.001783 d4 = -0.000768 d5 = 0.000000
8. Perhitungan luas penampang :
A0 = 1856.61 A1 = 1711.42 A2 = 1891.47 A3 = 1899.17 A4 = 1737.50 A5 = 1562.50
Luas penampang 3-3 diperoleh dari penjumlahan A0, A1, A2, A3, A4 dan A5
A penampang 3-3’ = A0+ A1+ A2+ A3+ A4+ A5
= 10.658,67 m2
D. PENAMPANG 4-4’
1. Nilai Segmen
PENAMPANG 4 SEGMEN X Y
0 0 75 1 25 70 2 50 65 3 75 80 4 100 65 5 125 90 6 150 50
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2. Diketahui
a0 = 75.00 a1 = 70.00 a2 = 65.00 a3 = 80.00 a4 = 65.00 a5 = 90.00 a6 = 50.00
3. Maka matriks [H] [C] = [A] adalah :
4. Perhitungan Eliminasi Gauss Jordan membuat matriks baru
M21 = H21/H11 = 25.00
a21 baru = a21 - M21 (a11) = 25 - (25 x 1) = 0.00 a22 baru = a22 - M21 (a12) = 25 - (25 x 0) = 100.00 a23 baru = a23 - M21 (a13) = 25 - (25 x 0) = 25.00 A21 baru = A21 - M21 (A11) = 0 - (25 x 0) = 0.00
M32 = H32/H22 = 0.25
a32 baru = a32 - M32 (a22) = 25 - (0.25 x 100) = 0 a33 baru = a33 - M32 (a23) = 100 - (0.25 x 25) = 93.75 a34 baru = a34 - M32 (a24) = 25 - (0.25 x 25) = 25.00 A31 baru = A31 - M21 (A21) = 2,4 - (0.25 x 0) = 2.40
M43 = H43/H33 = 0.25
a43 baru = a43 - M43 (a33) = 25 - (0.25 x 100) = 0 a44 baru = a44 - M43 (a34) = 100 - (0.25 x 25) = 93.75 a45 baru = a45 - M43 (a35) = 25 - (0.25 x 25) = 25.00
A41 baru = A41 - M43 (A31) = 3.6 - (0.25 x2,4) = -4.20
M54 = H54/H44 = 0.25
H0 = X1 - X0 = 25.00 H1 = X2 - X1 = 25.00 H2 = X3 - X2 = 25.00 H3 = X4 - X3 = 25.00 H4 = X5 - X4 = 25.00 H5 = X6 - X5 = 25.00
a54 baru = a54 - M54 (a44) = 25 - (0.25 x 100) = 0 a55 baru = a55 - M54 (a45) = 100 - (0.25 x 25) = 93.75 a56 baru = a56 - M54 (a46) = 25 - (0.25 x 25) = 25.00 A51 baru = A51 - M54 (A41) = 4,8- (0.25 x -3.6) = 5.70
Matriks baru
5. Substitusi mundur untuk mendapatkan nilai C
C5 = 0
93.75C4 + 25C5 = 5,70 C4 = 0.06080 93.75C3 + 25C4 = -4.20 C3 = -0.06101 93.75C2 + 25C3 = 2,40 C2 = 0.04187
93.75C1 + 25C2 = 0 C1 = -0.01047
C0 = 0
6. Mencari nilai b dengan rumus :
b0 = -0.1128 b1 = -0.37 b2 = 0.41 b3 = -0.09 b4 = -0.01 b5 = -1.60
7. Mencari nilai d dengan rumus :
d0 = -0.000140 d1 = 0.000698 d2 = -0.001372 d3 = 0.001624 d4 = -0.000811 d5 = 0.000000
8. Perhitungan luas penampang :
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A0 = 1826.13 A1 = 1646.61 A2 = 1837.43 A3 = 1812.78 A4 = 1858.33 A5 = 1750.00
Luas penampang 4-4’ diperoleh dari penjumlahan A0, A1, A2, A3, A4 dan A5
A penampang 4-4’ = A0+ A1+ A2+ A3+ A4+ A5
= 10.731,28 m2
E. PENAMPANG 5-5’
1. Nilai Segmen
PENAMPANG 5 SEGMEN X Y
0 0 80 1 25 75 2 50 75 3 75 75 4 100 75 5 125 100 6 150 50
2. Diketahui
a0 = 80.00 a1 = 75.00 a2 = 75.00 a3 = 75.00 a4 = 75.00 a5 = 100.00 a6 = 50.00
H0 = X1 - X0 = 25.00 H1 = X2 - X1 = 25.00 H2 = X3 - X2 = 25.00 H3 = X4 - X3 = 25.00 H4 = X5 - X4 = 25.00 H5 = X6 - X5 = 25.00
3. Maka matriks [H] [C] = [A] adalah :
4. Perhitungan Eliminasi Gauss Jordan membuat matriks baru
M21 = H21/H11 = 25.00
a21 baru = a21 - M21 (a11) = 25 - (25 x 1) = 0.00 a22 baru = a22 - M21 (a12) = 25 - (25 x 0) = 100.00 a23 baru = a23 - M21 (a13) = 25 - (25 x 0) = 25.00 A21 baru = A21 - M21 (A11) = 0.6 - (25 x 0) = 0.60
M32 = H32/H22 = 0.25
a32 baru = a32 - M32 (a22) = 25 - (0.25 x 100) = 0 a33 baru = a33 - M32 (a23) = 100 - (0.25 x 25) = 93.75 a34 baru = a34 - M32 (a24) = 25 - (0.25 x 25) = 25.00 A31 baru = A31 - M21 (A21) = 0 - (0.25 x0.6) = -0.15
M43 = H43/H33 = 0.25
a43 baru = a43 - M43 (a33) = 25 - (0.25 x 100) = 0 a44 baru = a44 - M43 (a34) = 100 - (0.25 x 25) = 93.75 a45 baru = a45 - M43 (a35) = 25 - (0.25 x 25) = 25.00 A41 baru = A41 - M43 (A31) = 0 - (0.25 x 0) = 0.00
M54 = H54/H44 = 0.25
a54 baru = a54 - M54 (a44) = 25 - (0.25 x 100) = 0 a55 baru = a55 - M54 (a45) = 100 - (0.25 x 25) = 93.75 a56 baru = a56 - M54 (a46) = 25 - (0.25 x 25) = 25.00 A51 baru = A51 - M54 (A41) = 3 - (0.25 x0) = 3.00
Matriks baru
5. Substitusi mundur untuk mendapatkan nilai C
C5 = 0
93.75C4 + 25C5 = 3 C4 = 0.03200 93.75C3 + 25C4 = 0 C3 = -0.00853
93.75C2 + 25C3 = -0.15 C2 = 0.00068
93.75C1 + 25C2 = 0,60 C1 = 0.00583 C0 = 0
6. Mencari nilai b dengan rumus :
b0 = -0.2486 b1 = -0.10 b2 = 0.06 b3 = -0.12 b4 = 0.47 b5 = -2.00
7. Mencari nilai d dengan rumus :
d0 = 0.000078 d1 = -0.000069 d2 = -0.000123 d3 = 0.000540 d4 = -0.000427 d5 = 0.000000
8. Perhitungan luas penampang :
A0 = 1929.91 A1 = 1866.53
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A2 = 1885.23 A3 = 1844.44 A4 = 2145.83 A5 = 1875.00
Luas penampang 5-5’ diperoleh dari penjumlahan A0, A1, A2, A3, A4 dan A5
A penampang 5-5’ = A0+ A1+ A2+ A3+ A4+ A5
= 11.546,94 m2
F. PENAMPANG 6-6’
1. Nilai Segmen
PENAMPANG 6 SEGMEN X Y
0 0 65 1 25 70 2 50 75 3 75 65 4 100 85 5 125 90 6 150 50
2. Diketahui
a0 = 65.00 a1 = 70.00 a2 = 75.00 a3 = 65.00 a4 = 85.00 a5 = 90.00 a6 = 50.00
3. Maka matriks [H] [C] = [A] adalah :
H0 = X1 - X0 = 25.00 H1 = X2 - X1 = 25.00 H2 = X3 - X2 = 25.00 H3 = X4 - X3 = 25.00 H4 = X5 - X4 = 25.00 H5 = X6 - X5 = 25.00
4. Perhitungan Eliminasi Gauss Jordan membuat matriks baru
M21 = H21/H11 = 25.00
a21 baru = a21 - M21 (a11) = 25 - (25 x 1) = 0.00 a22 baru = a22 - M21 (a12) = 25 - (25 x 0) = 100.00 a23 baru = a23 - M21 (a13) = 25 - (25 x 0) = 25.00 A21 baru = A21 - M21 (A11) = 0- (25 x 0) = 0.00
M32 = H32/H22 = 0.25
a32 baru = a32 - M32 (a22) = 25 - (0.25 x 100) = 0 a33 baru = a33 - M32 (a23) = 100 - (0.25 x 25) = 93.75 a34 baru = a34 - M32 (a24) = 25 - (0.25 x 25) = 25.00 A31 baru = A31 - M21 (A21) = 1.8 - (0.25 x0) = -1.80
M43 = H43/H33 = 0.25
a43 baru = a43 - M43 (a33) = 25 - (0.25 x 100) = 0 a44 baru = a44 - M43 (a34) = 100 - (0.25 x 25) = 93.75 a45 baru = a45 - M43 (a35) = 25 - (0.25 x 25) = 25.00 A41 baru = A41 - M43 (A31) = 3.6 - (0.25 x -1.8) = 4.05
M54 = H54/H44 = 0.25
a54 baru = a54 - M54 (a44) = 25 - (0.25 x 100) = 0 a55 baru = a55 - M54 (a45) = 100 - (0.25 x 25) = 93.75 a56 baru = a56 - M54 (a46) = 25 - (0.25 x 25) = 25.00 A51 baru = A51 - M54 (A41) = 1.8 - (0.25 x 3.6) = -2.70
Matriks baru
5. Substitusi mundur untuk mendapatkan nilai C
C5 = 0 93.75C4 + 25C5 = 0 C4 = -0.02880
93.75C3 + 25C4 = -1.8 C3 = 0.05088 93.75C2 + 25C3 = 4,05 C2 = -0.03277
93.75C1 + 25C2 = -2,70 C1 = 0.00819 C0 = 0
6. Mencari nilai b dengan rumus :
b0 = 0.1317 b1 = 0.34 b2 = -0.28 b3 = 0.19 b4 = 0.68 b5 = -1.60
7. Mencari nilai d dengan rumus :
d0 = 0.000109 d1 = -0.000546 d2 = 0.001115 d3 = -0.001062 d4 = 0.000384 d5 = 0.000000
8. Perhitungan luas penampang :
A0 = 1676.83 A1 = 1844.50 A2 = 1726.42 A3 = 1846.25 A4 = 2225.00 A5 = 1750.00
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Luas penampang 6-6’ diperoleh dari penjumlahan A0, A1, A2, A3, A4 dan A5
A penampang 6-6’ = A0+ A1+ A2+ A3+ A4+ A5
=11.069,00 m2
F. PENAMPANG 7-7’
1. Nilai Segmen
PENAMPANG 7 SEGMEN X Y
0 0 70 1 25 55 2 50 70 3 75 55 4 100 70 5 125 70 6 150 45
2. Diketahui
a0 = 70.00 a1 = 55.00 a2 = 70.00 a3 = 55.00 a4 = 70.00 a5 = 70.00 a6 = 45.00
3. Maka matriks [H] [C] = [A] adalah :
4. Perhitungan Eliminasi Gauss Jordan membuat matriks baru
M21 = H21/H11 = 25.00
H0 = X1 - X0 = 25.00 H1 = X2 - X1 = 25.00 H2 = X3 - X2 = 25.00 H3 = X4 - X3 = 25.00 H4 = X5 - X4 = 25.00 H5 = X6 - X5 = 25.00
a21 baru = a21 - M21 (a11) = 25 - (25 x 1) = 0.00 a22 baru = a22 - M21 (a12) = 25 - (25 x 0) = 100.00 a23 baru = a23 - M21 (a13) = 25 - (25 x 0) = 25.00 A21 baru = A21 - M21 (A11) = 3,60 - (25 x 0) = 3.60
M32 = H32/H22 = 0.25
a32 baru = a32 - M32 (a22) = 25 - (0.25 x 100) = 0 a33 baru = a33 - M32 (a23) = 100 - (0.25 x 25) = 93.75 a34 baru = a34 - M32 (a24) = 25 - (0.25 x 25) = 25.00 A31 baru = A31 - M21 (A21) = 3,6 - (0.25 x3,60) = -4.50
M43 = H43/H33 = 0.25
a43 baru = a43 - M43 (a33) = 25 - (0.25 x 100) = 0 a44 baru = a44 - M43 (a34) = 100 - (0.25 x 25) = 93.75 a45 baru = a45 - M43 (a35) = 25 - (0.25 x 25) = 25.00 A41 baru = A41 - M43 (A31) = 3.6 - (0.25 x-3,6) = 4.50
M54 = H54/H44 = 0.25
a54 baru = a54 - M54 (a44) = 25 - (0.25 x 100) = 0 a55 baru = a55 - M54 (a45) = 100 - (0.25 x 25) = 93.75 a56 baru = a56 - M54 (a46) = 25 - (0.25 x 25) = 25.00 A51 baru = A51 - M54 (A41) = 1,8 - (0.25 x 3.6) = -2.70
Matriks baru
5. Substitusi mundur untuk mendapatkan nilai C
C5 = 0 93.75C4 + 25C5 =-2,70 C4 = -0.02880
93.75C3 + 25C4 = 4,5 C3 = 0.05568 93.75C2 + 25C3 = -4,5 C2 = -0.06285 93.75C1 + 25C2 = 3,60 C1 = 0.05171
C0 = 0
6. Mencari nilai b dengan rumus :
b0 = -1.0309 b1 = 0.26 b2 = -0.02 b3 = -0.09 b4 = 0.48 b5 = -1.00
7. Mencari nilai d dengan rumus :
d0 = 0.000689 d1 = -0.001527 d2 = 0.001580 d3 = -0.001126 d4 = 0.000384 d5 = 0.000000
8. Perhitungan luas penampang :
A0 = 1.495.17 A1 = 1.577.00 A2 = 1.571.83 A3 = 1.527.50 A4 = 1.787.50 A5 = 1.437.50
Luas penampang 7-7’ diperoleh dari penjumlahan A0, A1, A2, A3, A4 dan A5
A penampang 7-7’ = A0+ A1+ A2+ A3+ A4+ A5
= 9.396,50 m2
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F. PENAMPANG 8-8’
1. Nilai Segmen
PENAMPANG 8 SEGMEN X Y
0 0 65 1 25 60 2 50 60 3 75 55 4 100 60 5 125 60 6 150 45
2. Diketahui
a0 = 65.00 a1 = 60.00 a2 = 60.00 a3 = 55.00 a4 = 60.00 a5 = 60.00 a6 = 45.00
3. Maka matriks [H] [C] = [A] adalah :
4. Perhitungan Eliminasi Gauss Jordan membuat matriks baru
M21 = H21/H11 = 25.00
a21 baru = a21 - M21 (a11) = 25 - (25 x 1) = 0.00 a22 baru = a22 - M21 (a12) = 25 - (25 x 0) = 100.00 a23 baru = a23 - M21 (a13) = 25 - (25 x 0) = 25.00 A21 baru = A21 - M21 (A11) = 0,6 - (25 x 0) = 0.60
M32 = H32/H22 = 0.25
a32 baru = a32 - M32 (a22) = 25 - (0.25 x 100) = 0 a33 baru = a33 - M32 (a23) = 100 - (0.25 x 25) = 93.75
H0 = X1 - X0 = 25.00 H1 = X2 - X1 = 25.00 H2 = X3 - X2 = 25.00 H3 = X4 - X3 = 25.00 H4 = X5 - X4 = 25.00 H5 = X6 - X5 = 25.00
a34 baru = a34 - M32 (a24) = 25 - (0.25 x 25) = 25.00
A31 baru = A31 - M21 (A21) = 0,6 - (0.25 x0,6) = -0.75
M43 = H43/H33 = 0.25
a43 baru = a43 - M43 (a33) = 25 - (0.25 x 100) = 0 a44 baru = a44 - M43 (a34) = 100 - (0.25 x 25) = 93.75 a45 baru = a45 - M43 (a35) = 25 - (0.25 x 25) = 25.00 A41 baru = A41 - M43 (A31) = 1,2 - (0.25 x-0,6) = 1.35
M54 = H54/H44 = 0.25
a54 baru = a54 - M54 (a44) = 25 - (0.25 x 100) = 0 a55 baru = a55 - M54 (a45) = 100 - (0.25 x 25) = 93.75 a56 baru = a56 - M54 (a46) = 25 - (0.25 x 25) = 25.00 A51 baru = A51 - M54 (A41) = 0,6 - (0.25 x 1,2) = -0.90
Matriks baru
5. Substitusi mundur untuk mendapatkan nilai C
C5 = 0 93.75C4 + 25C5 =-0,90 C4 = -0.00960 93.75C3 + 25C4 = 1,35 C3 = 0.01696
93.75C2 + 25C3 = -0,75 C2 = -0.01252 93.75C1 + 25C2 = 0,60 C1 = 0.00913
C0 = 0
6. Mencari nilai b dengan rumus :
b0 = -0.2761 b1 = -0.05 b2 = -0.13 b3 = 0.00 b4 = 0.16 b5 = -0.60
7. Mencari nilai d dengan rumus :
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d0 = 0.000122 d1 = -0.000289 d2 = 0.000393 d3 = -0.000354 d4 = 0.000128 d5 = 0.000000
8. Perhitungan luas penampang :
A0 = 1550.61 A1 = 1504.42 A2 = 1431.72 A3 = 1427.92 A4 = 1512.50 A5 = 1312.50
Luas penampang 8-8’ diperoleh dari penjumlahan A0, A1, A2, A3, A4 dan A5
A penampang 8-8’ = A0+ A1+ A2+ A3+ A4+ A5
= 8.739,67 m2
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HASIL PERHITUNGAN
1. Perhitungan Luas Penampang Dengan Aplikasi Polinomial Pangkat Tiga
No PENAMPANG LUAS (meter2) 1 1-1' 8.950,11 2 2-2' 9.583,33 3 3-3' 10.658,67 4 4-4' 10.731,28 5 5-5' 11.546,94 6 6-6' 11.069,00 7 7-7' 9.396,30 8 8-8' 8.739,67
TOTAL 80.675,30
2. Perhitungan Cadangan
Perhitungan volume dengan metode End Area dilakukan terhadap dua penampang yang saling berdekatan. Kemudian hasil perhitungan volume dikalikan dengan faktor tonase batubara yaitu 1.3 ton/m3.
NO Penampang Jarak (m) Volume (meter3) Tonase (ton)
1 1-2’ 25 231.668,00 3.011.684,00
2 2-3’ 25 253.025,00 3.289.325,00
3 3-4’ 25 267.374,38 3.475.866,88
4 4-5’ 25 278.477,75 3.620.210,75
5 5-6’ 25 282.699,25 3.675.090,25
6 6-7’ 25 255.816,25 3.325.611,25
7 7-8’ 25 226.699,63 2.947.095,13
TOTAL 1.795.760,25 23.344.883,25
PETA DASAR
0 1 2 3 4 5 6 7 8 9 100
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