Trs: Tugas Matematika Rekayasa II ke-2

Nama : Safitri Npm : 0953010008 Progdi : Teknik Sipil Mata Kuliah : Matematika Rekayasa II Dosen : Ir. Hendrata Wibisana,.MT 1.       Diketahui : x y 1 1.8 2 2.8 3 3.8 4 5.8 5 9 6 14.8                         Ditanya :      Buatlah model :        Y = ax2 + bx                                                                 Y = ax2 + bx + c                                                                 Y = ax3 + bx2 + cx + d Jawab : x y x² x³ x⁴ x⁵ x⁶ xy x²y x³y 1 1.8 1 1 1 1 1 1.8 1.8 1.8 2 2.8 4 8 16 32 64 5.6 11.2 22.4 3 3.8 9 27 81 243 729 11.4 34.2 102.6 4 5.8 16 64 256 1024 4096 23.2 92.8 371.2 5 9 25 125 625 3125 15625 45 225 1125 6 14.8 36 216 1296 7776 46656 88.8 532.8 3196.8 ∑ 21 38 91 441 2275 12201 67171 175.8 897.8 4819.8                            jadi nilai a = 0.333, b = 0.32è Y = 0.333x2+ 0.32x                           jadi nilai a = 0.586, b = -1.654, c = 3.24 è Y = 0.586x2 – 1.654x + 3.24                       jadi nilai a = 130.857, b = -1.395 x 103, c = 4.298 x 103, d = -3.496 x 103 è Y = 130.857x3 – 0.001395x2 + 0.004298x – 0.003496

FW: Tugas Ke-2 Matematika Rekayasa I / Fransiskus X E Lie / 0953210064

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From: andrew_lie@hotmail.com
To: hendrata2008.artikel@blogger.com
Subject: Tugas Ke-2 Matematika Rekayasa I / Fransiskus X E Lie / 0953210064
Date: Sat, 9 Apr 2011 18:25:47 +0700

Tugas Ke-2

Matematika Rekayasa I

Fransiskus X E Lie / 0953210064

X	Y	X²	X³	X⁴	X⁵	X⁶	Xy	X²Y	X³Y
1	1.7	1	1	1	1	1	1.7	1.7	1.7
2	2.7	4	8	16	32	64	5.4	10.8	21.6
3	3.7	9	27	81	243	729	11.1	33.3	99.9
4	5.7	16	64	256	1024	4096	22.8	91.2	364.8
5	9.7	25	125	625	3125	15625	48.5	242.5	1212.5
6	14.7	36	216	1296	7776	46656	88.2	529.2	3175.2
21	38.2	91	441	2275	12201	67171	177.7	908.7	4875.7

Ditanya Model Matematika    A) Y = Ax² + Bx

                                             B) Y = Ax² + Bx + C

                                             C) Y = Ax³ + Bx² + Cx + D

                                        Jadi Model Matematikanya :

                                        Y = 0.074x³–1.206x²+0.862x+0.733

FW: TUGAS KE-3 MATEMATIKA REKAYASA II / Fransiskus X E Lie / 0953210064

TUGAS KE-3 MATEMATIKA REKAYASA II

Fransiskus X E Lie / 0953210064

x	Y
1	124
3	254
5	374
7	554
9	764
11	984
13	1264
15	1484
64	5802

Buatlah analisa ketepatan untuk model

Y = ax + b

Y = ax² + bx       

Y = ax² + bx + c

Tentukan yang mana yang paling teliti ?

Jawab :

x	Y	X2	X*Y
1	124	1	124
3	254	9	762
5	374	25	1870
7	554	49	3878
9	764	81	6876
11	984	121	10824
13	1264	169	16432
15	1484	225	22260
64	5802	680	63026

A). Y = ax + b

Pers. Nominal

64 (98.869) + 8 b  =  5802

b = -65.702

Pers. Least quare  Y = 98.869x – 65.702

X	Y	Ŷ	X-Ŷ	(Y-Ŷ)^2
1	124	33.167	-32.167	8250.634
3	254	230.905	-227.905	533.379
5	374	428.643	-423.643	2985.857
7	554	626.381	-619.381	5239.009
9	764	824.119	-815.119	3614.294
11	984	1021.857	-1010.857	1433.152
13	1264	1219.595	-1206.595	1971.804
15	1484	1417.333	-1402.333	4444.489
				28472.619

B). Y = ax² + bx

Pers. Least quare  Y = 98.869x² – 65.702x

X	Y	Ŷ	X-Ŷ	(Y-Ŷ)^2
1	124	33.17	-32.17	8250.63
3	254	692.72	-689.72	192470.85
5	374	2143.22	-2138.22	3130121.72
7	554	4384.67	-4377.67	14674009.66
9	764	7417.07	-7408.07	44263353.73
11	984	11240.43	-11229.43	105194294.81
13	1264	15854.74	-15841.74	212889547.84
15	1484	21260.00	-21245.00	391089978.24
				771442027.48