Advanced Search

Michael703939

0 Reputation

One Badge

9 years, 78 days
Contact Michael703939

MaplePrimes Activity


These are replies submitted by Michael703939

Theta...

Michael703939 0
April 15 2016
0 0

@Doug Meade Yeah sorry about the order. But if you look at first plot you see it ranges from 0 to pi/2. The problem is that I want to set values of theta to only be in the range of 0.7 to 1.2, or the constraint in line 18. I've already given the plot between those points but the plot continues below 0.7. What I want is to assign a minimum value for theta which is in my code theta_0L

Does that make sense?

@roman_pearce  the equation I'm plo...

Michael703939 0
April 15 2016
0 5

@roman_pearce  the equation I'm plotting is v_0. I vary the value of l by delta L and doing this gives us 2 other graphs to plot. I need to place constraints on the possible values of theta for the calculations. Sorry it's so messy, it's my first time with maple. It's more relevant towards the bottom. Thanks

> 

v_0 := sqrt(g*l/(2*cos(theta)^2*(tan(theta)-h/l)));

4.533966806*(1/(cos(theta)^2*(tan(theta)-.1287878788)))^(1/2)

 (1)
> 

g := 9.81;

9.81

 (2)
> 

l := 4.191;

4.191

 (3)
> 

h := .53975;

.53975

 (4)
> 

plot(v_0, theta = arctan(2*h/l) .. (1/2)*Pi, labels = [theta[0], "v_0"]);

 
> 

evalf((1/2)*Pi)

1.570796327

 (5)
> 

q := diff(v_0, theta)

(1/4)*2^(1/2)*(2*g*l*sin(theta)/(cos(theta)^3*(tan(theta)-h/l))-g*l*(1+tan(theta)^2)/(cos(theta)^2*(tan(theta)-h/l)^2))/(g*l/(cos(theta)^2*(tan(theta)-h/l)))^(1/2)

 (6)
> 

p := solve(q = 0, theta)

arctan((h+(h^2+l^2)^(1/2))/l), -arctan((-h+(h^2+l^2)^(1/2))/l)

 (7)
> 

NULL
> 

r := simplify((1/4)*sqrt(2)*g*l(-2*cos(theta)*(sin(theta))(tan(theta)*l-h)+cos(theta)^2*l(1+tan(theta)^2))^2/(sqrt(g*l/(cos(theta)^2)(tan(theta)-h/l))*(cos(theta)^4)(tan(theta)*l-h)^2)):
> 

r1 := solve(r = 0, theta)

"r1:="

 (8)
> 

simplify((g*l+g*(sqrt(h^2+l^2)+h)/l)/(2*sqrt(h^2+l^2)/l))

(1/2)*g*(l^2+(h^2+l^2)^(1/2)+h)/(h^2+l^2)^(1/2)

 (9)
> 

display(p0, p2, p1);

 
> 

v_01 := sqrt(g*l_1/(2*cos(theta)^2*(tan(theta)-h/l_1)));

4.593082298*(1/(cos(theta)^2*(tan(theta)-.1254940711)))^(1/2)

 (10)
> 

delta_L := .11

.11

 (11)
> 

l_1 := l+delta_L

4.301

 (12)
> 

l_2 := l-delta_L

4.081

 (13)
> 

v_02 := sqrt(g*l_2/(2*cos(theta)^2*(tan(theta)-h/l_2)));

4.474070294*(1/(cos(theta)^2*(tan(theta)-.1322592502)))^(1/2)

 (14)
> 

p1 := plot(v_01, theta = .7 .. 1.2, labels = [theta[0], "v_0"]);

PLOT(CURVES(Matrix(200, 2, {(1, 1) = .7, (1, 2) = 7.093084242764435, (2, 1) = .7026288025125628, (2, 2) = 7.086620675775125, (3, 1) = .7049161095226131, (3, 2) = 7.081102480530271, (4, 1) = .7074884254773869, (4, 2) = 7.075013526096419, (5, 1) = .7100777924120603, (5, 2) = 7.06900840731167, (6, 1) = .7126548525376883, (6, 2) = 7.063154821863709, (7, 1) = .715044117160804, (7, 2) = 7.057836792897891, (8, 1) = .7175180622864321, (8, 2) = 7.052440192528355, (9, 1) = .7200766198743718, (9, 2) = 7.046976018780917, (10, 1) = .7226269721356784, (10, 2) = 7.041647127993424, (11, 1) = .7252503229145728, (11, 2) = 7.036287718031497, (12, 1) = .7275609717085427, (12, 2) = 7.0316691127364335, (13, 1) = .7301622149748743, (13, 2) = 7.026583359329854, (14, 1) = .7327741391959799, (14, 2) = 7.021597301149085, (15, 1) = .735291212160804, (15, 2) = 7.016906069434941, (16, 1) = .7375769555527638, (16, 2) = 7.012742268390181, (17, 1) = .7402949255276381, (17, 2) = 7.007909841998061, (18, 1) = .7425974026130653, (18, 2) = 7.003916623779827, (19, 1) = .7452757308291457, (19, 2) = 6.999387000849144, (20, 1) = .7476465051256281, (20, 2) = 6.995480667398853, (21, 1) = .7502476202763819, (21, 2) = 6.9913057677794175, (22, 1) = .7527244970100502, (22, 2) = 6.987437761985273, (23, 1) = .755308858040201, (23, 2) = 6.983513230981202, (24, 1) = .7576821082160804, (24, 2) = 6.980009042810422, (25, 1) = .7602419791457286, (25, 2) = 6.976335967934418, (26, 1) = .762900965603015, (26, 2) = 6.972637454358238, (27, 1) = .7652156211306532, (27, 2) = 6.969514421221273, (28, 1) = .7677155125125628, (28, 2) = 6.966242036651852, (29, 1) = .7702981449246231, (29, 2) = 6.962970669682251, (30, 1) = .772824746884422, (30, 2) = 6.959877437622741, (31, 1) = .7752693641959798, (31, 2) = 6.956985141061887, (32, 1) = .777983694924623, (32, 2) = 6.95388925413351, (33, 1) = .7804226418090452, (33, 2) = 6.951210835063762, (34, 1) = .7830267381909547, (34, 2) = 6.948458746361424, (35, 1) = .785386436557789, (35, 2) = 6.94606074071225, (36, 1) = .7879662101507537, (36, 2) = 6.943543028757963, (37, 1) = .7903935760552763, (37, 2) = 6.941272953037757, (38, 1) = .7929308728391959, (38, 2) = 6.939002316970225, (39, 1) = .7954115442211055, (39, 2) = 6.936883161219639, (40, 1) = .7980085772613065, (40, 2) = 6.934771152258781, (41, 1) = .8005098287437186, (41, 2) = 6.932839853724348, (42, 1) = .8030677196482412, (42, 2) = 6.930968946380936, (43, 1) = .8056044299246231, (43, 2) = 6.92921731670889, (44, 1) = .8079354032160804, (44, 2) = 6.9276987090343445, (45, 1) = .8106069616582914, (45, 2) = 6.926065166858673, (46, 1) = .8129964353768844, (46, 2) = 6.9247007345508695, (47, 1) = .8155441127386934, (47, 2) = 6.923346316218511, (48, 1) = .8179825650502512, (48, 2) = 6.922146834404955, (49, 1) = .8206901529648241, (49, 2) = 6.920925828493466, (50, 1) = .8230347251507537, (50, 2) = 6.9199626652532995, (51, 1) = .8256958355527637, (51, 2) = 6.9189752141153305, (52, 1) = .8281211487939698, (52, 2) = 6.9181730976900955, (53, 1) = .8307740603266331, (53, 2) = 6.917402459967642, (54, 1) = .833063074321608, (54, 2) = 6.916827099263139, (55, 1) = .8356699940703517, (55, 2) = 6.916272823262096, (56, 1) = .8381881498492462, (56, 2) = 6.915839483754284, (57, 1) = .8407046605778894, (57, 2) = 6.915506579015508, (58, 1) = .843211913517588, (58, 2) = 6.915274431416316, (59, 1) = .8456205986683416, (59, 2) = 6.915144954877564, (60, 1) = .8482244511055276, (60, 2) = 6.915108084188651, (61, 1) = .8507061112814069, (61, 2) = 6.915172629428633, (62, 1) = .8533179417587939, (62, 2) = 6.915345646686094, (63, 1) = .8556822772864321, (63, 2) = 6.915595222213557, (64, 1) = .8582953106532663, (64, 2) = 6.91597383422912, (65, 1) = .860798141281407, (65, 2) = 6.916437705866125, (66, 1) = .8632948799497487, (66, 2) = 6.916999182346416, (67, 1) = .8659027331658291, (67, 2) = 6.91769100404791, (68, 1) = .8683046611809044, (68, 2) = 6.918423498843522, (69, 1) = .8707645640201005, (69, 2) = 6.919268468519871, (70, 1) = .8734805890452261, (70, 2) = 6.920312943619157, (71, 1) = .8759397272361809, (71, 2) = 6.92135969842378, (72, 1) = .8784546566582914, (72, 2) = 6.92252965923269, (73, 1) = .8810122751005025, (73, 2) = 6.923822754106763, (74, 1) = .8833632241457287, (74, 2) = 6.925103340836926, (75, 1) = .8858692596984924, (75, 2) = 6.926565559578838, (76, 1) = .8883562191457286, (76, 2) = 6.928115910960763, (77, 1) = .8910164927135678, (77, 2) = 6.92988394767715, (78, 1) = .8933640688944723, (78, 2) = 6.931538461260198, (79, 1) = .8960726844723618, (79, 2) = 6.933557484501278, (80, 1) = .8985170012060301, (80, 2) = 6.935480913136843, (81, 1) = .9009355248492462, (81, 2) = 6.937478937309775, (82, 1) = .903536214723618, (82, 2) = 6.939733001283127, (83, 1) = .9061474249246231, (83, 2) = 6.942106477194272, (84, 1) = .9085232395728643, (84, 2) = 6.944362239129867, (85, 1) = .9110462491959799, (85, 2) = 6.946858411471669, (86, 1) = .91350846, (86, 2) = 6.949394643615943, (87, 1) = .9161775224874371, (87, 2) = 6.952256063953172, (88, 1) = .9184870036180904, (88, 2) = 6.954826372599609, (89, 1) = .9211395266582914, (89, 2) = 6.957886825614928, (90, 1) = .9236330377638191, (90, 2) = 6.960869767476564, (91, 1) = .9261024642713567, (91, 2) = 6.963925412430593, (92, 1) = .9285738552261307, (92, 2) = 6.967084950707954, (93, 1) = .931094517562814, (93, 2) = 6.970412380474594, (94, 1) = .9337663774120603, (94, 2) = 6.974055459733338, (95, 1) = .9362162112562813, (95, 2) = 6.9775011444837, (96, 1) = .9386345118341708, (96, 2) = 6.981001669831852, (97, 1) = .9412196353517588, (97, 2) = 6.98485305673477, (98, 1) = .943799131281407, (98, 2) = 6.988809154637988, (99, 1) = .9461143820603015, (99, 2) = 6.992456568073293, (100, 1) = .9488569635678392, (100, 2) = 6.996895894548904, (101, 1) = .9511518285929648, (101, 2) = 7.000709840781704, (102, 1) = .9538359310050251, (102, 2) = 7.0052860001433, (103, 1) = .9563976467336683, (103, 2) = 7.009769967100728, (104, 1) = .9586849537437185, (104, 2) = 7.0138701677145, (105, 1) = .9612572696984925, (105, 2) = 7.018590580762424, (106, 1) = .9638466366331657, (106, 2) = 7.023459694562421, (107, 1) = .9664236967587939, (107, 2) = 7.028423198550875, (108, 1) = .9688129613819094, (108, 2) = 7.033130260270049, (109, 1) = .9712869065075377, (109, 2) = 7.038111399615335, (110, 1) = .9738454640954773, (110, 2) = 7.043378253467943, (111, 1) = .9763958163567839, (111, 2) = 7.048745552809203, (112, 1) = .9790191671356783, (112, 2) = 7.054389368044188, (113, 1) = .9813298159296482, (113, 2) = 7.059464220828983, (114, 1) = .9839310591959798, (114, 2) = 7.065294246778572, (115, 1) = .9865429834170854, (115, 2) = 7.071273533829643, (116, 1) = .9890600563819095, (116, 2) = 7.077155201022298, (117, 1) = .9913457997738693, (117, 2) = 7.082598528508975, (118, 1) = .9940637697487437, (118, 2) = 7.089198539566066, (119, 1) = .9963662468341707, (119, 2) = 7.094898503717816, (120, 1) = .9990445750502512, (120, 2) = 7.101655365558439, (121, 1) = 1.0014153493467337, (121, 2) = 7.1077504843648045, (122, 1) = 1.0040164644974874, (122, 2) = 7.114561913621076, (123, 1) = 1.0064933412311556, (123, 2) = 7.121169483380752, (124, 1) = 1.0090777022613064, (124, 2) = 7.128190959581999, (125, 1) = 1.011450952437186, (125, 2) = 7.134754006027289, (126, 1) = 1.0140108233668341, (126, 2) = 7.141957548554035, (127, 1) = 1.0166698098241205, (127, 2) = 7.1495776595345735, (128, 1) = 1.0189844653517588, (128, 2) = 7.156325979857871, (129, 1) = 1.0214843567336682, (129, 2) = 7.163735412085862, (130, 1) = 1.0240669891457286, (130, 2) = 7.171523037151533, (131, 1) = 1.0265935911055277, (131, 2) = 7.179273422627264, (132, 1) = 1.0290382084170853, (132, 2) = 7.186897231180621, (133, 1) = 1.0317525391457285, (133, 2) = 7.19550719813778, (134, 1) = 1.0341914860301507, (134, 2) = 7.203374800656853, (135, 1) = 1.0367955824120603, (135, 2) = 7.211913279285594, (136, 1) = 1.0391552807788944, (136, 2) = 7.219774554766509, (137, 1) = 1.041735054371859, (137, 2) = 7.228505129938665, (138, 1) = 1.044162420276382, (138, 2) = 7.236850772688807, (139, 1) = 1.0466997170603014, (139, 2) = 7.245711091135137, (140, 1) = 1.049180388442211, (140, 2) = 7.254509867949439, (141, 1) = 1.051777421482412, (141, 2) = 7.2638668653095015, (142, 1) = 1.0542786729648241, (142, 2) = 7.273020652105207, (143, 1) = 1.0568365638693467, (143, 2) = 7.2825269531033054, (144, 1) = 1.0593732741457287, (144, 2) = 7.292100837581093, (145, 1) = 1.0617042474371858, (145, 2) = 7.30102779559251, (146, 1) = 1.0643758058793968, (146, 2) = 7.311413041880533, (147, 1) = 1.0667652795979898, (147, 2) = 7.3208422528656305, (148, 1) = 1.069312956959799, (148, 2) = 7.331043253784885, (149, 1) = 1.0717514092713567, (149, 2) = 7.340950763734938, (150, 1) = 1.0744589971859295, (150, 2) = 7.352118190395084, (151, 1) = 1.0768035693718592, (151, 2) = 7.361931149744626, (152, 1) = 1.0794646797738694, (152, 2) = 7.373231080549695, (153, 1) = 1.0818899930150754, (153, 2) = 7.383681312304917, (154, 1) = 1.0845429045477386, (154, 2) = 7.395279401315079, (155, 1) = 1.0868319185427135, (155, 2) = 7.4054283114400725, (156, 1) = 1.0894388382914573, (156, 2) = 7.41714822551444, (157, 1) = 1.0919569940703517, (157, 2) = 7.428633987283371, (158, 1) = 1.0944735047989949, (158, 2) = 7.4402757983695516, (159, 1) = 1.0969807577386934, (159, 2) = 7.452039047096512, (160, 1) = 1.0993894428894473, (160, 2) = 7.463495844673933, (161, 1) = 1.1019932953266331, (161, 2) = 7.476054694351653, (162, 1) = 1.1044749555025124, (162, 2) = 7.488193961431011, (163, 1) = 1.1070867859798994, (163, 2) = 7.501150880843798, (164, 1) = 1.1094511215075378, (164, 2) = 7.513041720314657, (165, 1) = 1.1120641548743717, (165, 2) = 7.526364048980445, (166, 1) = 1.1145669855025124, (166, 2) = 7.5393043856804685, (167, 1) = 1.1170637241708543, (167, 2) = 7.552390549348601, (168, 1) = 1.1196715773869346, (168, 2) = 7.566250353430385, (169, 1) = 1.12207350540201, (169, 2) = 7.5791905782058695, (170, 1) = 1.124533408241206, (170, 2) = 7.592618887426738, (171, 1) = 1.1272494332663316, (171, 2) = 7.607654330653424, (172, 1) = 1.1297085714572863, (172, 2) = 7.621459138094682, (173, 1) = 1.1322235008793968, (173, 2) = 7.635767592479609, (174, 1) = 1.134781119321608, (174, 2) = 7.650518802083269, (175, 1) = 1.1371320683668342, (175, 2) = 7.664257936597521, (176, 1) = 1.139638103919598, (176, 2) = 7.679095438431945, (177, 1) = 1.142125063366834, (177, 2) = 7.6940182484820285, (178, 1) = 1.1447853369346732, (178, 2) = 7.710202393789084, (179, 1) = 1.1471329131155779, (179, 2) = 7.724676636542349, (180, 1) = 1.1498415286934673, (180, 2) = 7.741603988852991, (181, 1) = 1.1522858454271356, (181, 2) = 7.7570911203870985, (182, 1) = 1.1547043690703518, (182, 2) = 7.772614875916924, (183, 1) = 1.1573050589447236, (183, 2) = 7.789532798882021, (184, 1) = 1.1599162691457285, (184, 2) = 7.806756758666831, (185, 1) = 1.1622920837939699, (185, 2) = 7.822637630367265, (186, 1) = 1.1648150934170853, (186, 2) = 7.8397239996654, (187, 1) = 1.1672773042211055, (187, 2) = 7.856621596485886, (188, 1) = 1.1699463667085426, (188, 2) = 7.87519100381409, (189, 1) = 1.172255847839196, (189, 2) = 7.891473341191428, (190, 1) = 1.1749083708793968, (190, 2) = 7.910423358201784, (191, 1) = 1.1774018819849246, (191, 2) = 7.928483655417103, (192, 1) = 1.1798713084924624, (192, 2) = 7.946608105818416, (193, 1) = 1.1823426994472361, (193, 2) = 7.964988049243617, (194, 1) = 1.1848633617839195, (194, 2) = 7.983986408772449, (195, 1) = 1.1875352216331658, (195, 2) = 8.004406289391483, (196, 1) = 1.189985055477387, (196, 2) = 8.023388105534064, (197, 1) = 1.1924033560552765, (197, 2) = 8.042372007258015, (198, 1) = 1.1949884795728642, (198, 2) = 8.062940226305495, (199, 1) = 1.1975679755025124, (199, 2) = 8.083750948761814, (200, 1) = 1.2, (200, 2) = 8.103638775551486}, datatype = float[8]), COLOUR(RGB, .47058824, 0., 0.54901961e-1, _ATTRIBUTE("source" = "mathdefault"))), AXESLABELS(theta[0], "v_0"), VIEW(.7 .. 1.2, DEFAULT, _ATTRIBUTE("source" = "mathdefault")))

 (15)
> 

p2 := plot(v_02, theta = .7 .. 1.2, labels = [theta[0], "v_0"]);

PLOT(CURVES(Matrix(200, 2, {(1, 1) = .7, (1, 2) = 6.942132283602075, (2, 1) = .7026288025125628, (2, 2) = 6.935599964485186, (3, 1) = .7049161095226131, (3, 2) = 6.930021361509954, (4, 1) = .7074884254773869, (4, 2) = 6.923863801289227, (5, 1) = .7100777924120603, (5, 2) = 6.917788885117302, (6, 1) = .7126548525376883, (6, 2) = 6.911865080207576, (7, 1) = .715044117160804, (7, 2) = 6.906481260033881, (8, 1) = .7175180622864321, (8, 2) = 6.901015821602973, (9, 1) = .7200766198743718, (9, 2) = 6.895479672589205, (10, 1) = .7226269721356784, (10, 2) = 6.890078227267823, (11, 1) = .7252503229145728, (11, 2) = 6.884643323439315, (12, 1) = .7275609717085427, (12, 2) = 6.879957483467325, (13, 1) = .7301622149748743, (13, 2) = 6.874795194048593, (14, 1) = .7327741391959799, (14, 2) = 6.8697313667323465, (15, 1) = .735291212160804, (15, 2) = 6.864964301904168, (16, 1) = .7375769555527638, (16, 2) = 6.860730868239887, (17, 1) = .7402949255276381, (17, 2) = 6.8558146724373055, (18, 1) = .7425974026130653, (18, 2) = 6.851749652650527, (19, 1) = .7452757308291457, (19, 2) = 6.847135523785445, (20, 1) = .7476465051256281, (20, 2) = 6.843153491499653, (21, 1) = .7502476202763819, (21, 2) = 6.8388945536769175, (22, 1) = .7527244970100502, (22, 2) = 6.834945551318883, (23, 1) = .755308858040201, (23, 2) = 6.830935482088395, (24, 1) = .7576821082160804, (24, 2) = 6.827351805968071, (25, 1) = .7602419791457286, (25, 2) = 6.82359197218415, (26, 1) = .762900965603015, (26, 2) = 6.819802203140825, (27, 1) = .7652156211306532, (27, 2) = 6.816598775216102, (28, 1) = .7677155125125628, (28, 2) = 6.813238548450864, (29, 1) = .7702981449246231, (29, 2) = 6.80987531199177, (30, 1) = .772824746884422, (30, 2) = 6.806691087670617, (31, 1) = .7752693641959798, (31, 2) = 6.803709687415179, (32, 1) = .777983694924623, (32, 2) = 6.8005136243009146, (33, 1) = .7804226418090452, (33, 2) = 6.797744064083564, (34, 1) = .7830267381909547, (34, 2) = 6.794893469007214, (35, 1) = .785386436557789, (35, 2) = 6.792405124759677, (36, 1) = .7879662101507537, (36, 2) = 6.789787463215729, (37, 1) = .7903935760552763, (37, 2) = 6.787422199071113, (38, 1) = .7929308728391959, (38, 2) = 6.785050864862013, (39, 1) = .7954115442211055, (39, 2) = 6.782832060499897, (40, 1) = .7980085772613065, (40, 2) = 6.780614445606164, (41, 1) = .8005098287437186, (41, 2) = 6.7785801816274205, (42, 1) = .8030677196482412, (42, 2) = 6.776602690377113, (43, 1) = .8056044299246231, (43, 2) = 6.774744060429203, (44, 1) = .8079354032160804, (44, 2) = 6.773125978377488, (45, 1) = .8106069616582914, (45, 2) = 6.771377056053265, (46, 1) = .8129964353768844, (46, 2) = 6.769908173017654, (47, 1) = .8155441127386934, (47, 2) = 6.768441071416018, (48, 1) = .8179825650502512, (48, 2) = 6.767132451741528, (49, 1) = .8206901529648241, (49, 2) = 6.765788773992562, (50, 1) = .8230347251507537, (50, 2) = 6.76471810831007, (51, 1) = .8256958355527637, (51, 2) = 6.763607189739656, (52, 1) = .8281211487939698, (52, 2) = 6.762691189343749, (53, 1) = .8307740603266331, (53, 2) = 6.761794484053006, (54, 1) = .833063074321608, (54, 2) = 6.761109080130931, (55, 1) = .8356699940703517, (55, 2) = 6.760428033228043, (56, 1) = .8381881498492462, (56, 2) = 6.759870765101907, (57, 1) = .8407046605778894, (57, 2) = 6.759412551727436, (58, 1) = .843211913517588, (58, 2) = 6.759054090502415, (59, 1) = .8456205986683416, (59, 2) = 6.758801875418855, (60, 1) = .8482244511055276, (60, 2) = 6.758630774115479, (61, 1) = .8507061112814069, (61, 2) = 6.758565878360301, (62, 1) = .8533179417587939, (62, 2) = 6.7586010590976935, (63, 1) = .8556822772864321, (63, 2) = 6.758724426330995, (64, 1) = .8582953106532663, (64, 2) = 6.758961955967586, (65, 1) = .860798141281407, (65, 2) = 6.759289107437526, (66, 1) = .8632948799497487, (66, 2) = 6.759712634546257, (67, 1) = .8659027331658291, (67, 2) = 6.760258686790011, (68, 1) = .8683046611809044, (68, 2) = 6.760855389776452, (69, 1) = .8707645640201005, (69, 2) = 6.761559753189205, (70, 1) = .8734805890452261, (70, 2) = 6.76244715963408, (71, 1) = .8759397272361809, (71, 2) = 6.763350036843756, (72, 1) = .8784546566582914, (72, 2) = 6.764371204707689, (73, 1) = .8810122751005025, (73, 2) = 6.76551125347139, (74, 1) = .8833632241457287, (74, 2) = 6.766649611125347, (75, 1) = .8858692596984924, (75, 2) = 6.7679585693308555, (76, 1) = .8883562191457286, (76, 2) = 6.769355130182244, (77, 1) = .8910164927135678, (77, 2) = 6.770956771226523, (78, 1) = .8933640688944723, (78, 2) = 6.772462813066257, (79, 1) = .8960726844723618, (79, 2) = 6.774308609230965, (80, 1) = .8985170012060301, (80, 2) = 6.776073931165635, (81, 1) = .9009355248492462, (81, 2) = 6.777913837836013, (82, 1) = .903536214723618, (82, 2) = 6.7799959947675275, (83, 1) = .9061474249246231, (83, 2) = 6.782194890809081, (84, 1) = .9085232395728643, (84, 2) = 6.784290074141016, (85, 1) = .9110462491959799, (85, 2) = 6.786613891502963, (86, 1) = .91350846, (86, 2) = 6.788980091373149, (87, 1) = .9161775224874371, (87, 2) = 6.791655134046972, (88, 1) = .9184870036180904, (88, 2) = 6.79406242895589, (89, 1) = .9211395266582914, (89, 2) = 6.796933639067131, (90, 1) = .9236330377638191, (90, 2) = 6.799736700290775, (91, 1) = .9261024642713567, (91, 2) = 6.802612291720638, (92, 1) = .9285738552261307, (92, 2) = 6.80558971321238, (93, 1) = .931094517562814, (93, 2) = 6.808729399318469, (94, 1) = .9337663774120603, (94, 2) = 6.812171252691092, (95, 1) = .9362162112562813, (95, 2) = 6.815430406339947, (96, 1) = .9386345118341708, (96, 2) = 6.818744882927905, (97, 1) = .9412196353517588, (97, 2) = 6.822395260047759, (98, 1) = .943799131281407, (98, 2) = 6.826148575402209, (99, 1) = .9461143820603015, (99, 2) = 6.82961208232409, (100, 1) = .9488569635678392, (100, 2) = 6.833831214742636, (101, 1) = .9511518285929648, (101, 2) = 6.83745894240009, (102, 1) = .9538359310050251, (102, 2) = 6.841814999053395, (103, 1) = .9563976467336683, (103, 2) = 6.846086566156441, (104, 1) = .9586849537437185, (104, 2) = 6.849995175660073, (105, 1) = .9612572696984925, (105, 2) = 6.8544979142980695, (106, 1) = .9638466366331657, (106, 2) = 6.859145526060855, (107, 1) = .9664236967587939, (107, 2) = 6.863886182507, (108, 1) = .9688129613819094, (108, 2) = 6.868384478653184, (109, 1) = .9712869065075377, (109, 2) = 6.873147245656275, (110, 1) = .9738454640954773, (110, 2) = 6.878185873969457, (111, 1) = .9763958163567839, (111, 2) = 6.883323243776347, (112, 1) = .9790191671356783, (112, 2) = 6.888727986117258, (113, 1) = .9813298159296482, (113, 2) = 6.893590090869581, (114, 1) = .9839310591959798, (114, 2) = 6.899178154885861, (115, 1) = .9865429834170854, (115, 2) = 6.904911841848765, (116, 1) = .9890600563819095, (116, 2) = 6.910554295585678, (117, 1) = .9913457997738693, (117, 2) = 6.915778220515233, (118, 1) = .9940637697487437, (118, 2) = 6.922114621539503, (119, 1) = .9963662468341707, (119, 2) = 6.92758894031003, (120, 1) = .9990445750502512, (120, 2) = 6.934080603378074, (121, 1) = 1.0014153493467337, (121, 2) = 6.93993851256679, (122, 1) = 1.0040164644974874, (122, 2) = 6.946486996670979, (123, 1) = 1.0064933412311556, (123, 2) = 6.952841539883481, (124, 1) = 1.0090777022613064, (124, 2) = 6.9595962353827, (125, 1) = 1.011450952437186, (125, 2) = 6.965911773809532, (126, 1) = 1.0140108233668341, (126, 2) = 6.972845613419468, (127, 1) = 1.0166698098241205, (127, 2) = 6.980182545873701, (128, 1) = 1.0189844653517588, (128, 2) = 6.986681816582038, (129, 1) = 1.0214843567336682, (129, 2) = 6.993819583857852, (130, 1) = 1.0240669891457286, (130, 2) = 7.00132359501038, (131, 1) = 1.0265935911055277, (131, 2) = 7.0087935806458646, (132, 1) = 1.0290382084170853, (132, 2) = 7.016143292223476, (133, 1) = 1.0317525391457285, (133, 2) = 7.024445665367218, (134, 1) = 1.0341914860301507, (134, 2) = 7.032033927773503, (135, 1) = 1.0367955824120603, (135, 2) = 7.040271031594629, (136, 1) = 1.0391552807788944, (136, 2) = 7.047856405152691, (137, 1) = 1.041735054371859, (137, 2) = 7.056282255109335, (138, 1) = 1.044162420276382, (138, 2) = 7.064338195357917, (139, 1) = 1.0466997170603014, (139, 2) = 7.0728925693503415, (140, 1) = 1.049180388442211, (140, 2) = 7.081389111348779, (141, 1) = 1.051777421482412, (141, 2) = 7.090426356950298, (142, 1) = 1.0542786729648241, (142, 2) = 7.099268919209009, (143, 1) = 1.0568365638693467, (143, 2) = 7.108453596928703, (144, 1) = 1.0593732741457287, (144, 2) = 7.117705136917428, (145, 1) = 1.0617042474371858, (145, 2) = 7.126332889572715, (146, 1) = 1.0643758058793968, (146, 2) = 7.136371634212564, (147, 1) = 1.0667652795979898, (147, 2) = 7.1454876558226905, (148, 1) = 1.069312956959799, (148, 2) = 7.155351286792931, (149, 1) = 1.0717514092713567, (149, 2) = 7.1649325234565175, (150, 1) = 1.0744589971859295, (150, 2) = 7.17573376129319, (151, 1) = 1.0768035693718592, (151, 2) = 7.18522627055439, (152, 1) = 1.0794646797738694, (152, 2) = 7.196158666744724, (153, 1) = 1.0818899930150754, (153, 2) = 7.206270351048991, (154, 1) = 1.0845429045477386, (154, 2) = 7.21749416567485, (155, 1) = 1.0868319185427135, (155, 2) = 7.227316779319352, (156, 1) = 1.0894388382914573, (156, 2) = 7.238661242134445, (157, 1) = 1.0919569940703517, (157, 2) = 7.249780410017507, (158, 1) = 1.0944735047989949, (158, 2) = 7.2610519645743175, (159, 1) = 1.0969807577386934, (159, 2) = 7.272442392136895, (160, 1) = 1.0993894428894473, (160, 2) = 7.283537289182961, (161, 1) = 1.1019932953266331, (161, 2) = 7.295700745820897, (162, 1) = 1.1044749555025124, (162, 2) = 7.30745909362369, (163, 1) = 1.1070867859798994, (163, 2) = 7.320010756595832, (164, 1) = 1.1094511215075378, (164, 2) = 7.331530840236331, (165, 1) = 1.1120641548743717, (165, 2) = 7.344439046691716, (166, 1) = 1.1145669855025124, (166, 2) = 7.356978372213392, (167, 1) = 1.1170637241708543, (167, 2) = 7.369660200793305, (168, 1) = 1.1196715773869346, (168, 2) = 7.383093029778976, (169, 1) = 1.12207350540201, (169, 2) = 7.395635741266005, (170, 1) = 1.124533408241206, (170, 2) = 7.408652659993416, (171, 1) = 1.1272494332663316, (171, 2) = 7.423228778629825, (172, 1) = 1.1297085714572863, (172, 2) = 7.436613025712899, (173, 1) = 1.1322235008793968, (173, 2) = 7.450486715897328, (174, 1) = 1.134781119321608, (174, 2) = 7.46479088104633, (175, 1) = 1.1371320683668342, (175, 2) = 7.478114677749691, (176, 1) = 1.139638103919598, (176, 2) = 7.492504721622233, (177, 1) = 1.142125063366834, (177, 2) = 7.506978598851826, (178, 1) = 1.1447853369346732, (178, 2) = 7.5226770677311325, (179, 1) = 1.1471329131155779, (179, 2) = 7.5367179714040615, (180, 1) = 1.1498415286934673, (180, 2) = 7.553139726838979, (181, 1) = 1.1522858454271356, (181, 2) = 7.568165361044856, (182, 1) = 1.1547043690703518, (182, 2) = 7.583227531131254, (183, 1) = 1.1573050589447236, (183, 2) = 7.599643520742495, (184, 1) = 1.1599162691457285, (184, 2) = 7.6163576135631414, (185, 1) = 1.1622920837939699, (185, 2) = 7.631769367565881, (186, 1) = 1.1648150934170853, (186, 2) = 7.648352036243793, (187, 1) = 1.1672773042211055, (187, 2) = 7.664752511381576, (188, 1) = 1.1699463667085426, (188, 2) = 7.682776737641126, (189, 1) = 1.172255847839196, (189, 2) = 7.6985819784897105, (190, 1) = 1.1749083708793968, (190, 2) = 7.716977799963304, (191, 1) = 1.1774018819849246, (191, 2) = 7.734510956868662, (192, 1) = 1.1798713084924624, (192, 2) = 7.752107377450128, (193, 1) = 1.1823426994472361, (193, 2) = 7.769952821670149, (194, 1) = 1.1848633617839195, (194, 2) = 7.788399696590104, (195, 1) = 1.1875352216331658, (195, 2) = 7.808227923993352, (196, 1) = 1.189985055477387, (196, 2) = 7.826660739103762, (197, 1) = 1.1924033560552765, (197, 2) = 7.845096498925117, (198, 1) = 1.1949884795728642, (198, 2) = 7.8650718359838585, (199, 1) = 1.1975679755025124, (199, 2) = 7.885283717088314, (200, 1) = 1.2, (200, 2) = 7.904600197804245}, datatype = float[8]), COLOUR(RGB, .47058824, 0., 0.54901961e-1, _ATTRIBUTE("source" = "mathdefault"))), AXESLABELS(theta[0], "v_0"), VIEW(.7 .. 1.2, DEFAULT, _ATTRIBUTE("source" = "mathdefault")))

 (16)
> 

with(plots):
> 

with(plottools):
> 

p0 := plot(v_0, theta = .7 .. 1.2, labels = [theta[0], "v_0"]);

PLOT(CURVES(Matrix(200, 2, {(1, 1) = .7, (1, 2) = 7.017935300079557, (2, 1) = .7026288025125628, (2, 2) = 7.0114391613656055, (3, 1) = .7049161095226131, (3, 2) = 7.005892316392008, (4, 1) = .7074884254773869, (4, 2) = 6.999770789691838, (5, 1) = .7100777924120603, (5, 2) = 6.993732496392962, (6, 1) = .7126548525376883, (6, 2) = 6.987845499783898, (7, 1) = .715044117160804, (7, 2) = 6.982496134856235, (8, 1) = .7175180622864321, (8, 2) = 6.977066715377018, (9, 1) = .7200766198743718, (9, 2) = 6.971568192965258, (10, 1) = .7226269721356784, (10, 2) = 6.966204643148839, (11, 1) = .7252503229145728, (11, 2) = 6.960809135090325, (12, 1) = .7275609717085427, (12, 2) = 6.956158351866538, (13, 1) = .7301622149748743, (13, 2) = 6.95103593679786, (14, 1) = .7327741391959799, (14, 2) = 6.946012592339679, (15, 1) = .735291212160804, (15, 2) = 6.941284970777959, (16, 1) = .7375769555527638, (16, 2) = 6.937087728588589, (17, 1) = .7402949255276381, (17, 2) = 6.932215039124193, (18, 1) = .7425974026130653, (18, 2) = 6.9281872826015585, (19, 1) = .7452757308291457, (19, 2) = 6.923616978934793, (20, 1) = .7476465051256281, (20, 2) = 6.919674176680513, (21, 1) = .7502476202763819, (21, 2) = 6.915458761052757, (22, 1) = .7527244970100502, (22, 2) = 6.911551677224963, (23, 1) = .755308858040201, (23, 2) = 6.907585847795354, (24, 1) = .7576821082160804, (24, 2) = 6.90404325639041, (25, 1) = .7602419791457286, (25, 2) = 6.900328237976243, (26, 1) = .762900965603015, (26, 2) = 6.896585577210766, (27, 1) = .7652156211306532, (27, 2) = 6.893423626640469, (28, 1) = .7677155125125628, (28, 2) = 6.890108694351694, (29, 1) = .7702981449246231, (29, 2) = 6.886792801902612, (30, 1) = .772824746884422, (30, 2) = 6.883655443252484, (31, 1) = .7752693641959798, (31, 2) = 6.880719911568692, (32, 1) = .777983694924623, (32, 2) = 6.877575389168496, (33, 1) = .7804226418090452, (33, 2) = 6.874852696593076, (34, 1) = .7830267381909547, (34, 2) = 6.872052731308583, (35, 1) = .785386436557789, (35, 2) = 6.869610796583147, (36, 1) = .7879662101507537, (36, 2) = 6.867044458137142, (37, 1) = .7903935760552763, (37, 2) = 6.864728049825279, (38, 1) = .7929308728391959, (38, 2) = 6.862408376379773, (39, 1) = .7954115442211055, (39, 2) = 6.860240671972715, (40, 1) = .7980085772613065, (40, 2) = 6.858077188584339, (41, 1) = .8005098287437186, (41, 2) = 6.8560956803627, (42, 1) = .8030677196482412, (42, 2) = 6.85417277654032, (43, 1) = .8056044299246231, (43, 2) = 6.852368925307781, (44, 1) = .8079354032160804, (44, 2) = 6.8508017500845195, (45, 1) = .8106069616582914, (45, 2) = 6.8491118524102514, (46, 1) = .8129964353768844, (46, 2) = 6.8476963831848465, (47, 1) = .8155441127386934, (47, 2) = 6.846286885118505, (48, 1) = .8179825650502512, (48, 2) = 6.845034037295592, (49, 1) = .8206901529648241, (49, 2) = 6.843753025772839, (50, 1) = .8230347251507537, (50, 2) = 6.842737258855545, (51, 1) = .8256958355527637, (51, 2) = 6.841689371715931, (52, 1) = .8281211487939698, (52, 2) = 6.8408314917964, (53, 1) = .8307740603266331, (53, 2) = 6.839999104941457, (54, 1) = .833063074321608, (54, 2) = 6.839369827495453, (55, 1) = .8356699940703517, (55, 2) = 6.838753420503889, (56, 1) = .8381881498492462, (56, 2) = 6.838259324706181, (57, 1) = .8407046605778894, (57, 2) = 6.837864969390061, (58, 1) = .843211913517588, (58, 2) = 6.83757086098544, (59, 1) = .8456205986683416, (59, 2) = 6.837381161207046, (60, 1) = .8482244511055276, (60, 2) = 6.837278411010335, (61, 1) = .8507061112814069, (61, 2) = 6.837279410727167, (62, 1) = .8533179417587939, (62, 2) = 6.837384743513784, (63, 1) = .8556822772864321, (63, 2) = 6.837572329423336, (64, 1) = .8582953106532663, (64, 2) = 6.837881629577609, (65, 1) = .860798141281407, (65, 2) = 6.838278316368982, (66, 1) = .8632948799497487, (66, 2) = 6.838771988503198, (67, 1) = .8659027331658291, (67, 2) = 6.8393921458856575, (68, 1) = .8683046611809044, (68, 2) = 6.840057867137677, (69, 1) = .8707645640201005, (69, 2) = 6.840833681599748, (70, 1) = .8734805890452261, (70, 2) = 6.841800888168315, (71, 1) = .8759397272361809, (71, 2) = 6.842776848911353, (72, 1) = .8784546566582914, (72, 2) = 6.843873582781845, (73, 1) = .8810122751005025, (73, 2) = 6.845091342914899, (74, 1) = .8833632241457287, (74, 2) = 6.84630190657111, (75, 1) = .8858692596984924, (75, 2) = 6.847688657768348, (76, 1) = .8883562191457286, (76, 2) = 6.849163267132463, (77, 1) = .8910164927135678, (77, 2) = 6.85084933908952, (78, 1) = .8933640688944723, (78, 2) = 6.852430704599613, (79, 1) = .8960726844723618, (79, 2) = 6.854364369151563, (80, 1) = .8985170012060301, (80, 2) = 6.856209876748323, (81, 1) = .9009355248492462, (81, 2) = 6.858129962570282, (82, 1) = .903536214723618, (82, 2) = 6.860299277988799, (83, 1) = .9061474249246231, (83, 2) = 6.862586674131481, (84, 1) = .9085232395728643, (84, 2) = 6.8647632482438885, (85, 1) = .9110462491959799, (85, 2) = 6.867174413367163, (86, 1) = .91350846, (86, 2) = 6.869626772113117, (87, 1) = .9161775224874371, (87, 2) = 6.872396243245862, (88, 1) = .9184870036180904, (88, 2) = 6.874886118504247, (89, 1) = .9211395266582914, (89, 2) = 6.8778531841155655, (90, 1) = .9236330377638191, (90, 2) = 6.880747346943408, (91, 1) = .9261024642713567, (91, 2) = 6.883714116487603, (92, 1) = .9285738552261307, (92, 2) = 6.8867837500387665, (93, 1) = .931094517562814, (93, 2) = 6.89001848620621, (94, 1) = .9337663774120603, (94, 2) = 6.893562203290553, (95, 1) = .9362162112562813, (95, 2) = 6.89691577113274, (96, 1) = .9386345118341708, (96, 2) = 6.900324407772268, (97, 1) = .9412196353517588, (97, 2) = 6.904076505915479, (98, 1) = .943799131281407, (98, 2) = 6.907932428340583, (99, 1) = .9461143820603015, (99, 2) = 6.911488981844593, (100, 1) = .9488569635678392, (100, 2) = 6.915819509092273, (101, 1) = .9511518285929648, (101, 2) = 6.919541434317876, (102, 1) = .9538359310050251, (102, 2) = 6.924008818030792, (103, 1) = .9563976467336683, (103, 2) = 6.928387805583633, (104, 1) = .9586849537437185, (104, 2) = 6.932393302994991, (105, 1) = .9612572696984925, (105, 2) = 6.937006110320125, (106, 1) = .9638466366331657, (106, 2) = 6.941765716100977, (107, 1) = .9664236967587939, (107, 2) = 6.946619036883938, (108, 1) = .9688129613819094, (108, 2) = 6.951222869191335, (109, 1) = .9712869065075377, (109, 2) = 6.956096019990014, (110, 1) = .9738454640954773, (110, 2) = 6.96125000338977, (111, 1) = .9763958163567839, (111, 2) = 6.966503580200813, (112, 1) = .9790191671356783, (112, 2) = 6.972029140985137, (113, 1) = .9813298159296482, (113, 2) = 6.976998752578135, (114, 1) = .9839310591959798, (114, 2) = 6.982709077059412, (115, 1) = .9865429834170854, (115, 2) = 6.9885668534350005, (116, 1) = .9890600563819095, (116, 2) = 6.994330160953184, (117, 1) = .9913457997738693, (117, 2) = 6.9996649235455255, (118, 1) = .9940637697487437, (118, 2) = 7.006134485873334, (119, 1) = .9963662468341707, (119, 2) = 7.011722780663232, (120, 1) = .9990445750502512, (120, 2) = 7.01834838989952, (121, 1) = 1.0014153493467337, (121, 2) = 7.024326100798762, (122, 1) = 1.0040164644974874, (122, 2) = 7.031007375957764, (123, 1) = 1.0064933412311556, (123, 2) = 7.037489693216733, (124, 1) = 1.0090777022613064, (124, 2) = 7.044379100167075, (125, 1) = 1.011450952437186, (125, 2) = 7.050819610956384, (126, 1) = 1.0140108233668341, (126, 2) = 7.057889621863668, (127, 1) = 1.0166698098241205, (127, 2) = 7.06536952091043, (128, 1) = 1.0189844653517588, (128, 2) = 7.071994520815318, (129, 1) = 1.0214843567336682, (129, 2) = 7.0792694271326315, (130, 1) = 1.0240669891457286, (130, 2) = 7.086916601505518, (131, 1) = 1.0265935911055277, (131, 2) = 7.0945281203871415, (132, 1) = 1.0290382084170853, (132, 2) = 7.102016176751909, (133, 1) = 1.0317525391457285, (133, 2) = 7.1104737934644335, (134, 1) = 1.0341914860301507, (134, 2) = 7.118203032546655, (135, 1) = 1.0367955824120603, (135, 2) = 7.126592226047456, (136, 1) = 1.0391552807788944, (136, 2) = 7.134316827769939, (137, 1) = 1.041735054371859, (137, 2) = 7.142896443904818, (138, 1) = 1.044162420276382, (138, 2) = 7.151098563104719, (139, 1) = 1.0466997170603014, (139, 2) = 7.159807304604897, (140, 1) = 1.049180388442211, (140, 2) = 7.168456335658456, (141, 1) = 1.051777421482412, (141, 2) = 7.177654901232928, (142, 1) = 1.0542786729648241, (142, 2) = 7.186654474583964, (143, 1) = 1.0568365638693467, (143, 2) = 7.196001402706952, (144, 1) = 1.0593732741457287, (144, 2) = 7.205415550201034, (145, 1) = 1.0617042474371858, (145, 2) = 7.214194231910059, (146, 1) = 1.0643758058793968, (146, 2) = 7.224407756572141, (147, 1) = 1.0667652795979898, (147, 2) = 7.233681748913955, (148, 1) = 1.069312956959799, (148, 2) = 7.243715540812992, (149, 1) = 1.0717514092713567, (149, 2) = 7.253461335458038, (150, 1) = 1.0744589971859295, (150, 2) = 7.264447256029058, (151, 1) = 1.0768035693718592, (151, 2) = 7.274101374452579, (152, 1) = 1.0794646797738694, (152, 2) = 7.28521911895371, (153, 1) = 1.0818899930150754, (153, 2) = 7.2955015273355395, (154, 1) = 1.0845429045477386, (154, 2) = 7.306914076106225, (155, 1) = 1.0868319185427135, (155, 2) = 7.31690122485534, (156, 1) = 1.0894388382914573, (156, 2) = 7.328435003068486, (157, 1) = 1.0919569940703517, (157, 2) = 7.339739014117614, (158, 1) = 1.0944735047989949, (158, 2) = 7.351197252727186, (159, 1) = 1.0969807577386934, (159, 2) = 7.362775651632231, (160, 1) = 1.0993894428894473, (160, 2) = 7.374053008571918, (161, 1) = 1.1019932953266331, (161, 2) = 7.386415805143011, (162, 1) = 1.1044749555025124, (162, 2) = 7.398366190152026, (163, 1) = 1.1070867859798994, (163, 2) = 7.4111221537545955, (164, 1) = 1.1094511215075378, (164, 2) = 7.422829140121075, (165, 1) = 1.1120641548743717, (165, 2) = 7.435946105113712, (166, 1) = 1.1145669855025124, (166, 2) = 7.448687574313183, (167, 1) = 1.1170637241708543, (167, 2) = 7.461573216680927, (168, 1) = 1.1196715773869346, (168, 2) = 7.47522126589387, (169, 1) = 1.12207350540201, (169, 2) = 7.487964341993207, (170, 1) = 1.124533408241206, (170, 2) = 7.501188614982278, (171, 1) = 1.1272494332663316, (171, 2) = 7.515996242291184, (172, 1) = 1.1297085714572863, (172, 2) = 7.529592454766557, (173, 1) = 1.1322235008793968, (173, 2) = 7.5436852639664895, (174, 1) = 1.134781119321608, (174, 2) = 7.558214731946497, (175, 1) = 1.1371320683668342, (175, 2) = 7.571747847123184, (176, 1) = 1.139638103919598, (176, 2) = 7.586363392138899, (177, 1) = 1.142125063366834, (177, 2) = 7.601063508737872, (178, 1) = 1.1447853369346732, (178, 2) = 7.617006728372529, (179, 1) = 1.1471329131155779, (179, 2) = 7.631266003312858, (180, 1) = 1.1498415286934673, (180, 2) = 7.6479425372098016, (181, 1) = 1.1522858454271356, (181, 2) = 7.66320072241007, (182, 1) = 1.1547043690703518, (182, 2) = 7.678495483261652, (183, 1) = 1.1573050589447236, (183, 2) = 7.695164389652054, (184, 1) = 1.1599162691457285, (184, 2) = 7.712135391582492, (185, 1) = 1.1622920837939699, (185, 2) = 7.727783517582799, (186, 1) = 1.1648150934170853, (186, 2) = 7.744619978628026, (187, 1) = 1.1672773042211055, (187, 2) = 7.761270926602097, (188, 1) = 1.1699463667085426, (188, 2) = 7.7795698350212, (189, 1) = 1.172255847839196, (189, 2) = 7.795615450197592, (190, 1) = 1.1749083708793968, (190, 2) = 7.8142904856411155, (191, 1) = 1.1774018819849246, (191, 2) = 7.8320892207872115, (192, 1) = 1.1798713084924624, (192, 2) = 7.849951663188304, (193, 1) = 1.1823426994472361, (193, 2) = 7.868066383984342, (194, 1) = 1.1848633617839195, (194, 2) = 7.886791087955675, (195, 1) = 1.1875352216331658, (195, 2) = 7.906917375615144, (196, 1) = 1.189985055477387, (196, 2) = 7.9256267592856835, (197, 1) = 1.1924033560552765, (197, 2) = 7.944338650589504, (198, 1) = 1.1949884795728642, (198, 2) = 7.964612652679151, (199, 1) = 1.1975679755025124, (199, 2) = 7.985126196054563, (200, 1) = 1.2, (200, 2) = 8.004730484114345}, datatype = float[8]), COLOUR(RGB, .47058824, 0., 0.54901961e-1, _ATTRIBUTE("source" = "mathdefault"))), AXESLABELS(theta[0], "v_0"), VIEW(.7 .. 1.2, DEFAULT, _ATTRIBUTE("source" = "mathdefault")))

 (17)
> 

theta_0L <= theta and theta < (1/2)*Pi;

arctan(tan((8/45)*Pi)+.2575757576) <= theta and theta < (1/2)*Pi

 (18)
> 

theta_0L := arctan(tan(32*Pi*(1/180))+2*h/l);

arctan(tan((8/45)*Pi)+.2575757576)

 (19)
> 

``


Download graph_1.mw

Page 1 of 1