Examples

Physics and engineering equations
$$\Delta P = \rho \cdot g_{m/s} \cdot \Delta h$$
ρ Δh ΔP
0.95 3.75 34.9374375
0.8 7.75 60.8034
0.55 5.25 28.3177125
0.25 4.5 11.032875
0.9 7.5 66.19725
0.4 3.25 12.7491
0.15 2.25 3.3098625
0.75 2.5 18.388125
0.2 4.0 7.8456
0.45 2.75 12.1361625
0.3 0.75 2.206575
0.65 1.5 9.561825
0.05 0.5 0.245175
0.5 6.5 31.87275
0.0 0.25 0.0
0.6 1.25 7.35525
0.85 4.25 35.4277875
0.1 7.25 7.110075
0.7 5.75 39.473175
0.35 5.5 18.878475
$$E = m \cdot c^{2}$$
m E
50 4.4937759e+18
170 1.527883806e+19
70 6.29128626e+18
190 1.707634842e+19
10 8.9875518e+17
90 8.08879662e+18
80 7.19004144e+18
40 3.59502072e+18
120 1.078506216e+19
130 1.168381734e+19
180 1.617759324e+19
110 9.88630698e+18
30 2.69626554e+18
160 1.438008288e+19
20 1.79751036e+18
95 8.53817421e+18
75 6.74066385e+18
140 1.258257252e+19
150 1.34813277e+19
100 8.9875518e+18
$$I_{x} = \frac{1}{12} \cdot b \cdot h^{3}$$
b h Ix
32.5 25.0 40625.0
20.0 77.5 744775.0
25.0 72.5 762156.25
65.0 85.0 3193450.0
70.0 67.5 1722262.5
97.5 32.5 267759.375
47.5 60.0 820800.0
27.5 12.5 4296.875
45.0 35.0 154350.0
87.5 55.0 1164625.0
67.5 15.0 18225.0
35.0 57.5 532306.25
15.0 20.0 9600.0
52.5 82.5 2358365.625
42.5 37.5 179296.875
77.5 95.0 5315725.0
30.0 87.5 1607812.5
95.0 92.5 6015043.75
85.0 70.0 2332400.0
37.5 90.0 2187000.0
$$F = k \cdot \Delta l$$
k Δl F
1.9 10.0 19.0
1.3 50.0 65.0
0.6 92.5 55.5
1.05 87.5 91.875
1.4 95.0 133.0
0.3 75.0 22.5
1.8 15.0 27.0
0.35 62.5 21.875
0.65 40.0 26.0
1.5 97.5 146.25
1.35 82.5 111.375
0.45 17.5 7.875
1.45 80.0 116.0
0.55 45.0 24.75
1.25 67.5 84.375
0.8 70.0 56.0
0.5 77.5 38.75
1.1 22.5 24.75
0.75 27.5 20.625
0.2 85.0 17.0
$$A = b \cdot h$$
b h A
60.0 30.0 1800.0
77.5 97.5 7556.25
32.5 50.0 1625.0
45.0 75.0 3375.0
80.0 60.0 4800.0
95.0 25.0 2375.0
47.5 37.5 1781.25
57.5 27.5 1581.25
22.5 45.0 1012.5
50.0 12.5 625.0
12.5 10.0 125.0
17.5 77.5 1356.25
85.0 20.0 1700.0
37.5 22.5 843.75
65.0 72.5 4712.5
10.0 40.0 400.0
87.5 70.0 6125.0
92.5 57.5 5318.75
70.0 42.5 2975.0
75.0 67.5 5062.5
$$W = F \cdot \Delta s \cdot cos(\Theta)$$
F Δs cos(Θ) W
85.0 10.0 0.95 807.5
70.0 80.0 0.7 3920.0
12.5 50.0 0.2 125.0
50.0 95.0 0.85 4037.5
37.5 32.5 -1.0 -1218.75
82.5 70.0 0.9 5197.5
77.5 92.5 -0.1 -716.875
40.0 45.0 -0.7 -1260.0
25.0 87.5 -0.6 -1312.5
95.0 37.5 -0.95 -3384.375
45.0 82.5 -0.8 -2970.0
42.5 85.0 -0.15 -541.875
90.0 12.5 -0.2 -225.0
67.5 52.5 0.75 2657.8125
80.0 90.0 0.05 360.0
87.5 30.0 -0.35 -918.75
22.5 47.5 -0.9 -961.875
27.5 40.0 -0.25 -275.0
35.0 77.5 0.25 678.125
20.0 55.0 -0.5 -550.0
$$P = \frac{n \cdot R \cdot T}{v}$$
n T v P
100 418 8.75 39720.0224457
10 413 4.0 8584.822435
445 408 2.0 754799.20644
55 443 3.25 62333.9016215
130 428 4.25 108852.76064
355 383 8.0 141311.789634
430 458 6.0 272912.821687
310 393 3.0 337655.82478
115 373 4.75 75085.1960442
340 448 3.5 361851.30496
490 378 5.25 293339.01744
325 463 7.0 178734.162007
295 388 8.5 111963.39848
250 423 1.0 879268.7385
370 438 9.5 141838.289672
220 453 7.75 106920.366023
460 468 3.75 477324.441984
85 398 1.5 187521.900227
175 433 6.5 96929.0251462
205 403 5.75 119462.698047
$$T = 2 \cdot \pi \cdot \frac{L}{g}$$
L T
97.5 19.8113466989
82.5 18.2237884229
80.0 17.9455463061
50.0 14.1872000458
35.0 11.8698631668
57.5 15.2140770969
72.5 17.083651116
87.5 18.7679015608
67.5 16.484036852
17.5 8.39326073699
85.0 18.4978457324
40.0 12.6894174851
20.0 8.97277315306
37.5 12.2864756483
52.5 14.5375540376
12.5 7.09360002292
60.0 15.5412989859
45.0 13.4591597296
10.0 6.34470874257
25.0 10.0318653585
$$M = \frac{1}{n} \cdot \sum_{i=1}^{n} x_{i}$$
x1 x2 x3 m
69 36 3 36.0
31 24 2 19.0
23 26 6 18.333
65 31 17 37.667
20 41 12 24.333
49 11 1 20.333
51 22 13 28.667
63 15 7 28.333
40 12 4 18.667
30 45 15 30.0
97 28 18 47.667
11 14 16 13.667
59 40 11 36.667
46 13 14 24.333
50 40 17 35.667
47 35 8 30.0
95 48 9 50.667
85 46 10 47.0
34 19 5 19.333
10 10 10 10.0
$$A = 4 \cdot \pi \cdot r^{2}$$
r A
35.0 15393.8008
18.5 4300.839448
0.5 3.141592
24.0 7238.227968
1.0 12.566368
27.5 9503.3158
49.5 30790.743192
30.5 11689.863832
47.5 28352.8678
22.0 6082.122112
26.0 8494.864768
25.5 8171.280792
38.5 18626.498968
13.0 2123.716192
11.5 1661.902168
15.5 3019.069912
17.0 3631.680352
4.5 254.468952
21.5 5808.803608
33.5 14102.606488
$$A = 2 \cdot \pi \cdot r^{2} + 2 \cdot pi \cdot r \cdot h$$
r h A
21.5 29 6821.967028
48.5 24 22093.24574
12.0 48 4523.89248
32.5 3 7249.22354
38.5 1 9555.152068
42.5 7 13218.24834
47.0 5 15356.101696
24.0 20 6635.042304
46.0 6 15029.376128
20.5 40 7792.718956
37.0 16 12321.323824
9.5 32 2477.145292
9.0 30 2205.397584
10.0 14 1507.96416
16.0 25 4121.768704
0.5 41 130.376068
45.5 47 26444.35066
36.0 0 8143.006464
18.0 42 6785.83872
28.5 10 6894.223644
$$E = \frac{ k \Delta l^{2}}{2}$$
k Δl E
1.35 25.0 421.875
0.05 87.5 191.40625
1.15 42.5 1038.59375
0.6 82.5 2041.875
0.25 40.0 200.0
0.95 95.0 4286.875
1.8 37.5 1265.625
1.5 45.0 1518.75
0.4 35.0 245.0
1.6 85.0 5780.0
1.25 57.5 2066.40625
0.75 75.0 2109.375
0.8 12.5 62.5
1.55 20.0 310.0
0.1 55.0 151.25
0.45 30.0 202.5
1.9 70.0 4655.0
1.85 97.5 8793.28125
0.65 60.0 1170.0
0.3 47.5 338.4375
$$\rho = \frac{m}{V}$$
m V ρ
1.0 0.5 2.0
8.25 0.55 15.0
4.75 0.6 7.916
7.0 1.0 7.0
9.75 0.05 195.0
6.0 0.3 20.0
6.25 0.7 8.928
2.5 0.9 2.777
1.25 0.4 3.125
4.0 0.15 26.666
7.25 0.1 72.5
4.5 0.95 4.736
1.75 0.75 2.333
3.0 0.25 12.0
7.75 0.85 9.117
8.75 0.45 19.444
7.5 0.35 21.428
9.0 0.8 11.25
6.5 0.2 32.5
6.75 0.65 10.384
$$ \beta = 10 dB \cdot log(\frac{I}{I_{0}})$$
I I0 β
8.6e-07 1.6e-11 108.92098946
5.04e-06 4.2e-11 116.952470218
7.29e-06 3.8e-11 121.644279443
5.4e-07 7.6e-11 88.6859107825
2.5e-07 6.2e-11 83.020818118
7.09e-06 6e-11 116.798513363
6.32e-06 4.6e-11 118.305883696
1.89e-06 8e-12 123.726458454
4.98e-06 8.1e-11 110.264912943
1.63e-06 9e-11 98.0428090245
2.24e-06 3e-11 112.207890422
7.99e-06 9.8e-11 113.087338391
5.98e-06 3.5e-11 120.485830644
3.34e-06 3e-12 139.228690763
6.12e-06 5.3e-11 116.567807409
2.08e-06 8.9e-11 100.592420819
4.85e-06 4.4e-11 116.10299629
8.34e-06 9.4e-11 113.932789921
7.03e-06 6.3e-11 116.225625374
9.89e-06 7.7e-11 117.632292817
Non-representable equations
$$ R_{t} = \frac{1}{\frac{1}{R_{1}} + \frac{1}{R_{2}}}$$
R1 R2 Rt
10 10 5
100 10 9.09
100 50 1.96
20 1000 19.61
60 125 40.54
20 30 12.0
140 55 39.49
130 135 66.23
170 95 60.94
40 60 24.0
90 145 55.53
30 35 16.15
10 50 8.33
80 115 47.18
110 80 46.32
100 75 42.86
150 120 66.67
180 105 66.32
$$ c = \sqrt{a^{2} + b^{2}}$$
a b c
148 25 150.096635539
140 125 187.683243791
52 40 65.6048778674
132 10 132.378245947
72 30 78.0
92 100 135.882302012
142 65 156.169779407
80 20 82.4621125124
10 70 70.7106781187
44 130 137.244307714
120 85 147.054411699
68 75 101.237344888
30 95 99.6242942259
62 45 76.6093989012
70 120 138.924439894
32 135 138.740765458
22 55 59.2368128785
88 80 118.928549979
$$ W = F \cdot \Delta s \cdot cos(\Theta)$$
F Δs Θ W
40 30 3.89 -879.328265823
10 20 5.25 102.417095448
850 80 0.19 66776.287988
480 10 0.25 4650.77962421
770 45 2.79 -32530.3002581
100 90 5.58 6865.07651478
490 55 2.46 -20928.5691412
930 65 0.79 42547.4493312
650 15 3.31 -9612.06641539
500 50 0.49 22058.3214653
840 35 3.0 -29105.7794001
620 40 2.88 -23956.2869475
450 95 0.42 39034.5521984
670 85 5.72 48154.5750533
210 70 1.58 -135.292086051
750 75 5.66 45676.3249939
990 60 0.1 59103.2474175
270 25 0.61 5532.62412046
$$ x_{0} = \frac{ -b - \sqrt{b^{2} - 4 \cdot a \cdot c} }{2 \cdot a}$$
a b c x0
6 42 19 -17.50115
17 54 13 -75.83945
4 52 12 -3.760287
2 36 15 -1.707143
11 56 10 -22.42339
10 26 9 -41.11805
5 50 11 -5.626636
1 20 14 -0.7263815
8 18 5 -20.77500
3 40 4 -0.9068531
7 28 1 -1.765910
14 58 7 -24.38763
16 24 8 -128.0
18 44 3 -22.74405
13 16 2 -23.86261
12 32 16 -96.0
3 20 11 -5.443941
16 26 1 -10.09092
8 48 5 -6.786609
$$ e = \sqrt{1 - \frac{b^{2}}{a^{2}}}$$
a b e
38 18 0.880694764773
34 5 0.989127748282
22 4 0.983332166036
30 17 0.823947139621
26 10 0.923076923077
48 19 0.918322368356
39 9 0.973008510821
12 11 0.399652626943
37 13 0.936243679767
35 15 0.903507902905
14 14 0.0
16 8 0.866025403784
47 1 0.999773627615
11 7 0.77138921584
23 16 0.718378767037
41 6 0.98923413613
32 2 0.998044963917
18 3 0.986013297183
13 12 0.384615384615
$$ \Delta T = \frac{\Delta t}{ \sqrt{ 1 - \frac{v^{2}}{c^{2}} } } $$
Δt v ΔT
494000 140000 494000.053866
245000 110000 245000.016492
76000 158000 76000.010555
191000 143000 191000.021729
143000 93000 143000.006881
259000 97000 259000.013557
272000 49000 272000.003633
10000 121000 10000.0008145
126000 127000 126000.011306
79000 103000 79000.0046626
246000 40000 246000.00219
123000 69000 123000.003258
177000 48000 177000.002269
49000 105000 49000.0030054
453000 106000 453000.028316
279000 167000 279000.043288
491000 96000 491000.025174
236000 29000 236000.001104
168000 198000 168000.036641

Contact

Mentor:
Prof. Dr. Fabrício Olivetti de França
folivetti@ufabc.edu.br

Mentee:
Guilherme Seidyo Imai Aldeia
guilherme.aldeia@ufabc.edu.br

Universidade Federal do ABC
Avenida dos Estados, 5001 - Bairro Santa Terezinha, Santo André - CEP: 09210-580
+55 11 4996-0001

2020 Guilherme Seidyo Imai Aldeia