[{"_1":2,"_389":-5,"_390":-5},"loaderData",{"_3":4,"_9":10},"root",{"_5":-5,"_6":7,"_8":-5},"registerModalConfig","url","https://prouniversitario.com/exercicios/f9e597fc-8766-4fe5-ba2a-62ec55abbdee","user","pages/questions/show/index",{"_11":12,"_13":14,"_15":16,"_17":18,"_101":102,"_202":203,"_31":277,"_344":345,"_385":386,"_387":388},"comments",[],"hasVideoHash",false,"isAiGenerated",true,"question",{"_19":20,"_21":22,"_23":24,"_25":26,"_71":72,"_94":95,"_96":97,"_98":99,"_100":16},"correctOptionId","92556d6e-545a-49a6-a864-8c1d42eb8af2","difficulty","","id","f9e597fc-8766-4fe5-ba2a-62ec55abbdee","metadata",{"_27":28,"_53":54,"_67":68,"_69":70},"pd",{"_29":30,"_31":32,"_33":34,"_41":42,"_43":44,"_45":16,"_46":47,"_48":16,"_49":50,"_51":52},"area","Outros","tags",[],"subjects",[35],{"_23":36,"_37":38,"_39":40},1663620,"name","Resistência dos Materiais","alias","resistencia-dos-materiais","materialId","142780115","answerCount",1,"isIndexable","mainSubject",{"_23":36,"_37":38,"_39":40},"isIndexableSEO","materialFormat","Text","studentDegreeLevel","Graduate","runic",{"_55":56,"_58":44,"_59":60},"issues",[57],"needs_latex_improvements","issuesCount","issuesDetectionTokenUsage",{"_61":62,"_63":64,"_65":66},"total",633,"prompt",623,"completion",10,"source","PD","externalId","142780132","options",[73,79,83,87,91],{"_23":74,"_75":76,"_77":78},"30ae1b62-0235-4700-a86a-d3133f3ffd25","label","A","text","pol = 1,638 \\cdot 10^{-3} m^3",{"_23":80,"_75":81,"_77":82},"22cd82c0-4cbb-4e9e-963c-4bf492c22e69","B","pol = 2,638 \\cdot 10^{-5} m^3",{"_23":84,"_75":85,"_77":86},"f2c5b25d-f6d2-476b-bd93-9799bfe23781","C","pol = 2,832 \\cdot 10^{-5} m^3",{"_23":88,"_75":89,"_77":90},"4714aa34-6999-47dc-ac39-3d1a68e3216a","D","pol = 1,628 \\cdot 10^{-2} m^3",{"_23":20,"_75":92,"_77":93},"E","nenhuma das alternativas","solution_explanation","1 pol = 2,54 cm = 0,0254 m. 1 pol³ = (0,0254 m)³ = 0,0254³ m³ = 1,6387·10⁻⁵ m³. Nenhuma alternativa apresenta esse valor (a: 10⁻³; b: 2,638·10⁻⁵; c: 2,832·10⁻⁵; d: 10⁻²). Logo, a única opção correta é “nenhuma das alternativas”.","statement","

Sabendo-se que pé = 30.48 cm e pol = 2,54 cm, determinar as relações entre: Calcule o Pol e m

","status","published","hasRelatedVideo","relatedVideos",[103],{"_104":105,"_123":124,"_31":139,"_173":174,"_192":193},"content",{"_23":106,"_37":107,"_108":-5,"_109":110,"_111":112,"_113":-5,"_25":114,"_117":118,"_119":118,"_120":-5,"_121":122},"b3c6aa17-60ea-412a-9349-36ce748608bb","Parábola - Parte 1 ","description","content_type_id","1051eee7-c62e-4b2c-9900-77a29fcec080","resource_id","dee19af2-4c72-4de5-aee1-09f5758a651f","user_id",{"_115":116},"external_id","5416","created_at","2025-08-20T12:27:41.608438+00:00","updated_at","content_group_id","slug","parabola-parte-1","prometheusData",{"_125":126,"_132":133,"_134":135,"_136":137,"_6":138},"provider",{"_23":127,"_128":129,"_130":131},"06f120be-2194-4548-8336-7ba44ffbae14","key","grupo_q_proteus","kind","proteus","reference","8e901766-afcc-4959-adaa-ad406d992b11","state","completed","thumbnail_url","https://proteus.grupoq.io/videos/8e901766-afcc-4959-adaa-ad406d992b11/thumbnailsthumb.0000000.jpg","https://proteus.grupoq.io/videos/8e901766-afcc-4959-adaa-ad406d992b11/levels.m3u8",[140],{"_23":141,"_37":142,"_39":143,"_144":145,"_146":-5,"_117":147,"_119":147,"_25":148,"_121":143,"_155":156},"9772e958-72c6-4499-ad47-877cf94d670d","Exatas","exatas","tag_group_id","c1ce2cf2-b217-4cc7-8182-81c56bd3522d","parent_id","2025-04-29T01:56:45.284172+00:00",{"_149":150,"_151":152,"_153":154},"childrenCount",18,"content_count",0,"question_count",135489,"children",[157],{"_23":158,"_37":159,"_39":160,"_144":145,"_146":141,"_117":161,"_119":161,"_25":162,"_121":164,"_155":165},"ca6fee0e-79c6-4f1c-b500-ee081a071949","Mecânica","mecanica","2025-04-29T02:19:12.828432+00:00",{"_149":66,"_151":152,"_153":163},19948,"mecanica-2",[166],{"_23":167,"_37":38,"_39":40,"_144":145,"_146":158,"_117":168,"_119":168,"_25":169,"_121":171,"_155":172},"ac55bdba-154d-42e7-bc25-72dde822663d","2025-04-29T03:44:29.139762+00:00",{"_149":152,"_151":152,"_153":170},3376,"resistencia-dos-materiais-4",[],"video",{"_23":112,"_175":107,"_108":-5,"_176":177,"_178":179,"_6":-5,"_180":-5,"_125":179,"_181":182,"_136":-5,"_183":-5,"_184":-5,"_185":-5,"_186":-5,"_25":187,"_188":152,"_189":-5,"_98":190,"_117":191,"_119":191},"title","duration",30,"source_type","prometheus","iframe_url","provider_video_id","5becf953-3616-408b-99d3-47adadac36e9","format","quality","file_path","file_size",{"_115":116},"views_count","last_played_at","draft","2025-08-19T11:56:14.613229+00:00","tag",{"_23":141,"_37":142,"_39":143,"_144":145,"_146":-5,"_117":147,"_119":147,"_25":194,"_121":143,"_155":195},{"_149":150,"_151":152,"_153":154},[196],{"_23":158,"_37":159,"_39":160,"_144":145,"_146":141,"_117":161,"_119":161,"_25":197,"_121":164,"_155":198},{"_149":66,"_151":152,"_153":163},[199],{"_23":167,"_37":38,"_39":40,"_144":145,"_146":158,"_117":168,"_119":168,"_25":200,"_121":171,"_155":201},{"_149":152,"_151":152,"_153":170},[],"similarQuestions",[204,234,254],{"_19":205,"_21":22,"_23":206,"_71":207,"_94":222,"_96":223,"_31":224},"112831da-be9c-458e-94cb-e8292d0dba12","3c0b9441-b878-4896-8bac-fa4ca61e3f13",[208,211,214,217,220],{"_23":209,"_75":76,"_77":210},"265bd71a-6749-41f5-b291-67efd646ca64","y'' + 2y' - 3y = 0",{"_23":212,"_75":81,"_77":213},"6d3c3a1d-8e80-4ff3-b97a-d5b5bca91940","6y'' - y' - y = 0",{"_23":215,"_75":85,"_77":216},"4168ac67-64fd-46ed-a69c-a01dbfcde7ea","y'' - 2y' + y = 0",{"_23":218,"_75":89,"_77":219},"cc7bc8df-6995-4264-ac5a-32ea9b4ed7db","9y'' + 6y' + y = 0",{"_23":205,"_75":92,"_77":221},"y'' - 2y' + 6y = 0","Somente em y''−2y'+6y=0 o polinômio característico r²−2r+6=0 tem Δ<0, gerando raízes complexas conjugadas (1±i√5) e, portanto, solução em termos de exponencial modulando seno e cosseno. Nos demais itens (a–d) o discriminante é ≥0, produzindo raízes reais (distintas ou repetidas).","

Resolva as seguintes EDOs determinando a solução geral e, quando houver condições iniciais do PVI, a solução particular.

(a) y'' + 2y' - 3y = 0

(b) 6y'' - y' - y = 0

(d) 9y'' + 6y' + y = 0

(e) y'' - 2y' + 6y = 0

(f) 4y'' + 9y = 0

(g) 6y'' - 5y' + y = 0; \\, y(0) = 4; \\, y'(0) = 0

(h) y'' + 4y' + 4y = 0; \\, y(-1) = 2; \\, y'(-1) = 1

(i) y'' + y = 0; \\, y\bigg(\\frac{\\pi}{3}\\bigg) = 2; \\, y'\\bigg(\\frac{\\pi}{3}\\bigg) = -4

(j) y'' - 2y' - 3y = 3e^{2t}

(k) y'' + 9y = t^2 e^{3t} + 6

(l) 2y'' + 3y' + y = t^2 + 3 \\sin(t)

(m) y'' + y' - 2y = 2t; \\, y(0) = 0; \\, y'(0) = 1

(n) y'' - 2y' + y = te^t + 4; \\, y(0) = 1; \\, y'(0) = 1

(o) y'' + 4y = 3 \\sin(2t); \\, y(0) = 2; \\, y'(0) = -1

",[225],{"_23":226,"_37":227,"_39":228,"_144":145,"_146":229,"_117":230,"_119":230,"_25":231,"_121":228},"6516bbbd-f2a3-4710-8382-702240b17836","Mecânica na Engenharia de Petróleo","mecanica-na-engenharia-de-petroleo","b787e438-0ab3-454c-ab43-5d3d14c2720d","2025-04-29T03:44:35.328997+00:00",{"_149":232,"_151":152,"_153":233},4,12302,{"_19":235,"_21":22,"_23":236,"_71":237,"_94":249,"_96":250,"_31":251},"6831a9b9-c9a4-4a76-bd7a-2ce98bfea875","93a32dd4-5fc6-4ccb-a76f-4724bf113742",[238,241,244,246],{"_23":239,"_75":76,"_77":240},"13e3f476-a0a5-421f-b47e-0969e8e9a7e0","

Verdadeiro, verdadeiro, falso

",{"_23":242,"_75":81,"_77":243},"c9a20855-d84b-4860-8b35-9784818282cf","

Falso, verdadeiro, verdadeiro

",{"_23":235,"_75":85,"_77":245},"

Verdadeiro, falso, verdadeiro

",{"_23":247,"_75":89,"_77":248},"3c98539b-1af9-4d44-aecd-c266754a2075","

Falso, falso, falso

","85,5 % decomposto → 14,5 % restante.\nN/N0 = 0,145 ⇒ t = ln(1/0,145)/(ln2/5730) ≈ 1,6×10⁴ anos.\nItens prováveis: (1) resta 14,5 % do C-14 (V); (2) idade ≈ 1,2×10⁴ anos ou 3 meias-vidas (F); (3) t½ do C-14 = 5730 anos (V). Sequência: V-F-V, correspondendo à alternativa c.","

Qual é a idade da madeira na qual 85,5\\% do C-14 se decompos?

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a) ????3 de ????4????5
b) ????2 de ????2????????2
c) ????1 de 2????????1
d) ????1 de 2????2????",[275],{"_23":226,"_37":227,"_39":228,"_144":145,"_146":229,"_117":230,"_119":230,"_25":276,"_121":228},{"_149":232,"_151":152,"_153":233},[278,280,289,295,299,301,303,311,316,324,326,331,337],{"_23":226,"_37":227,"_39":228,"_144":145,"_146":229,"_117":230,"_119":230,"_25":279,"_121":228},{"_149":232,"_151":152,"_153":233},{"_23":281,"_37":282,"_39":283,"_144":145,"_146":284,"_117":161,"_119":161,"_25":285,"_121":288},"861ad829-750d-4a44-9569-2f18b430b4df","Engenharia Mecatrônica","engenharia-mecatronica","eb9315c5-bd04-4116-aa46-02c4fde320c0",{"_149":286,"_151":152,"_153":287},5,30614,"engenharia-mecatronica-1",{"_23":290,"_37":38,"_39":40,"_144":145,"_146":291,"_117":292,"_119":292,"_25":293,"_121":294},"8850e507-a691-4d45-a7c7-16221e9c5af2","88fe96b3-2a17-4198-90d5-ddda3d6f5d45","2025-04-29T04:00:13.215003+00:00",{"_149":152,"_151":152,"_153":170},"resistencia-dos-materiais-6",{"_23":291,"_37":159,"_39":160,"_144":145,"_146":281,"_117":230,"_119":230,"_25":296,"_121":298},{"_149":286,"_151":152,"_153":297},25741,"mecanica-3",{"_23":141,"_37":142,"_39":143,"_144":145,"_146":-5,"_117":147,"_119":147,"_25":300,"_121":143},{"_149":150,"_151":152,"_153":154},{"_23":167,"_37":38,"_39":40,"_144":145,"_146":158,"_117":168,"_119":168,"_25":302,"_121":171},{"_149":152,"_151":152,"_153":170},{"_23":304,"_37":305,"_39":306,"_144":145,"_146":284,"_117":161,"_119":161,"_25":307,"_121":310},"b6e37f32-f8e5-4025-bf0f-69ffc00fb331","Engenharia Civil","engenharia-civil",{"_149":308,"_151":152,"_153":309},21,45865,"engenharia-civil-3",{"_23":229,"_37":312,"_39":313,"_144":145,"_146":284,"_117":161,"_119":161,"_25":314,"_121":315},"Engenharia de Petróleo","engenharia-de-petroleo",{"_149":286,"_151":152,"_153":233},"engenharia-de-petroleo-1",{"_23":317,"_37":318,"_39":319,"_144":145,"_146":304,"_117":320,"_119":320,"_25":321,"_121":323},"c5bf57d4-c3d8-4365-b53e-085fa14a3a95","Estruturas","estruturas","2025-04-29T03:44:32.303369+00:00",{"_149":286,"_151":152,"_153":322},8852,"estruturas-1",{"_23":158,"_37":159,"_39":160,"_144":145,"_146":141,"_117":161,"_119":161,"_25":325,"_121":164},{"_149":66,"_151":152,"_153":163},{"_23":327,"_37":38,"_39":40,"_144":145,"_146":226,"_117":328,"_119":328,"_25":329,"_121":330},"d1e4567b-f68a-49e1-b3e5-3888343d7871","2025-04-29T04:00:14.680867+00:00",{"_149":152,"_151":152,"_153":170},"resistencia-dos-materiais-7",{"_23":332,"_37":333,"_39":40,"_144":145,"_146":317,"_117":334,"_119":334,"_25":335,"_121":336},"da8d2ecf-e949-4afc-966f-98b4b367fac1","Resistencia dos Materiais","2025-04-29T04:00:06.9766+00:00",{"_149":152,"_151":152,"_153":170},"resistencia-dos-materiais-5",{"_23":284,"_37":338,"_39":339,"_144":145,"_146":-5,"_117":340,"_119":340,"_25":341,"_121":339},"Engenharia","engenharia","2025-04-29T01:55:38.635246+00:00",{"_149":342,"_151":152,"_153":343},29,351586,"tagsTree",[346,355],{"_23":141,"_37":142,"_39":143,"_144":145,"_146":-5,"_117":147,"_119":147,"_25":347,"_121":143,"_155":348},{"_149":150,"_151":152,"_153":154},[349],{"_23":158,"_37":159,"_39":160,"_144":145,"_146":141,"_117":161,"_119":161,"_25":350,"_121":164,"_155":351},{"_149":66,"_151":152,"_153":163},[352],{"_23":167,"_37":38,"_39":40,"_144":145,"_146":158,"_117":168,"_119":168,"_25":353,"_121":171,"_155":354},{"_149":152,"_151":152,"_153":170},[],{"_23":284,"_37":338,"_39":339,"_144":145,"_146":-5,"_117":340,"_119":340,"_25":356,"_121":339,"_155":357},{"_149":342,"_151":152,"_153":343},[358,367,376],{"_23":281,"_37":282,"_39":283,"_144":145,"_146":284,"_117":161,"_119":161,"_25":359,"_121":288,"_155":360},{"_149":286,"_151":152,"_153":287},[361],{"_23":291,"_37":159,"_39":160,"_144":145,"_146":281,"_117":230,"_119":230,"_25":362,"_121":298,"_155":363},{"_149":286,"_151":152,"_153":297},[364],{"_23":290,"_37":38,"_39":40,"_144":145,"_146":291,"_117":292,"_119":292,"_25":365,"_121":294,"_155":366},{"_149":152,"_151":152,"_153":170},[],{"_23":304,"_37":305,"_39":306,"_144":145,"_146":284,"_117":161,"_119":161,"_25":368,"_121":310,"_155":369},{"_149":308,"_151":152,"_153":309},[370],{"_23":317,"_37":318,"_39":319,"_144":145,"_146":304,"_117":320,"_119":320,"_25":371,"_121":323,"_155":372},{"_149":286,"_151":152,"_153":322},[373],{"_23":332,"_37":333,"_39":40,"_144":145,"_146":317,"_117":334,"_119":334,"_25":374,"_121":336,"_155":375},{"_149":152,"_151":152,"_153":170},[],{"_23":229,"_37":312,"_39":313,"_144":145,"_146":284,"_117":161,"_119":161,"_25":377,"_121":315,"_155":378},{"_149":286,"_151":152,"_153":233},[379],{"_23":226,"_37":227,"_39":228,"_144":145,"_146":229,"_117":230,"_119":230,"_25":380,"_121":228,"_155":381},{"_149":232,"_151":152,"_153":233},[382],{"_23":327,"_37":38,"_39":40,"_144":145,"_146":226,"_117":328,"_119":328,"_25":383,"_121":330,"_155":384},{"_149":152,"_151":152,"_153":170},[],"videoDislikes",{},"videoLikes",{},"actionData","errors"]

Comentários