[{"_1":2,"_357":-5,"_358":-5},"loaderData",{"_3":4,"_31":32},"root",{"_5":6,"_28":29,"_30":-5},"registerModalConfig",{"_7":8,"_15":16},"blockedConfig",{"_9":10,"_15":16,"_17":18,"_21":22,"_24":25},"answerQuestion",{"_11":12,"_13":14},"subtitle","Crie sua conta gratuita e utilize todos os nossos recursos de questões disponiveis","title","Para responder, cadastre-se gratuitamente","customBlockedUI",true,"defaultRegister",{"_11":19,"_13":20},"Crie sua conta gratuita e utilize todos os nossos recursos disponíveis","Cadastre-se gratuitamente","imageSearch",{"_11":19,"_13":23},"Para buscar por imagem, cadastre-se gratuitamente","questionAnswer",{"_11":26,"_13":27},"Crie sua conta gratuita e utilize todos os nossos recursos disponíveis para responder","Para ver a resposta, cadastre-se gratuitamente","url","https://prouniversitario.com/exercicios/b29d697d-e8ad-4a9f-a191-1132a2c98d7a","user","pages/questions/show/index",{"_33":34,"_35":36,"_37":36,"_38":39,"_105":106,"_197":198,"_50":269,"_331":332,"_353":354,"_355":356},"comments",[],"hasVideoHash",false,"isAiGenerated","question",{"_40":41,"_42":41,"_43":44,"_45":46,"_79":80,"_99":41,"_100":101,"_102":103,"_104":16},"correctOptionId","","difficulty","id","b29d697d-e8ad-4a9f-a191-1132a2c98d7a","metadata",{"_47":48,"_75":76,"_77":78},"pd",{"_49":-5,"_50":51,"_57":58,"_63":64,"_65":66,"_67":16,"_68":69,"_70":16,"_71":72,"_73":74},"area","tags",[52],{"_43":53,"_54":55,"_56":55},38584,"name","x","alias","subjects",[59],{"_43":60,"_54":61,"_56":62},1663620,"Resistência dos Materiais","resistencia-dos-materiais","materialId","122702018","answerCount",1,"isIndexable","mainSubject",{"_43":60,"_54":61,"_56":62},"isIndexableSEO","materialFormat","Text","studentDegreeLevel","High School","source","PD","externalId","122788254","options",[81,87,91,95],{"_43":82,"_83":84,"_85":86},"f59f7475-d059-46ce-a357-15c97ab39b0f","label","A","text","

Escolher o material da viga.

",{"_43":88,"_83":89,"_85":90},"d8728248-3ca6-4113-8bde-27292d224e59","B","

Determinar as dimensões da seção transversal.

",{"_43":92,"_83":93,"_85":94},"6d2684cd-b3db-43be-a638-c7dd922a99f7","C","

Construir o diagrama de força cortante e momento fletor.

",{"_43":96,"_83":97,"_85":98},"2c862381-db3d-4493-98e3-e6ce192fbf14","D","

Verificar se a tensão de cisalhamento máxima permitida não foi extrapolada.

","solution_explanation","statement","

No texto apresentado, qual é o primeiro passo para se projetar uma viga?

","status","pending_classification","hasRelatedVideo","relatedVideos",[107],{"_108":109,"_127":128,"_50":143,"_178":179,"_196":144},"content",{"_43":110,"_54":111,"_112":-5,"_113":114,"_115":116,"_117":-5,"_45":118,"_121":122,"_123":122,"_124":-5,"_125":126},"468e3e62-35e0-47be-a15f-68dd43bb32bb","Óptica Geométrica - Parte 1","description","content_type_id","1051eee7-c62e-4b2c-9900-77a29fcec080","resource_id","fa6aaf42-4cc4-4d76-8915-7a67081f7e9a","user_id",{"_119":120},"external_id","4963","created_at","2025-08-20T12:27:41.608438+00:00","updated_at","content_group_id","slug","optica-geometrica-parte-1","prometheusData",{"_129":130,"_136":137,"_138":139,"_140":141,"_28":142},"provider",{"_43":131,"_132":133,"_134":135},"06f120be-2194-4548-8336-7ba44ffbae14","key","grupo_q_proteus","kind","proteus","reference","d80487a0-0f98-42c8-99bb-551165ba3068","state","completed","thumbnail_url","https://proteus.grupoq.io/videos/d80487a0-0f98-42c8-99bb-551165ba3068/thumbnailsthumb.0000000.jpg","https://proteus.grupoq.io/videos/d80487a0-0f98-42c8-99bb-551165ba3068/levels.m3u8",[144],{"_43":145,"_54":146,"_56":147,"_148":149,"_150":-5,"_121":151,"_123":151,"_45":152,"_125":147,"_159":160},"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",{"_153":154,"_155":156,"_157":158},"childrenCount",18,"content_count",0,"question_count",135489,"children",[161],{"_43":162,"_54":163,"_56":164,"_148":149,"_150":145,"_121":165,"_123":165,"_45":166,"_125":169,"_159":170},"ca6fee0e-79c6-4f1c-b500-ee081a071949","Mecânica","mecanica","2025-04-29T02:19:12.828432+00:00",{"_153":167,"_155":156,"_157":168},10,19948,"mecanica-2",[171],{"_43":172,"_54":61,"_56":62,"_148":149,"_150":162,"_121":173,"_123":173,"_45":174,"_125":176,"_159":177},"ac55bdba-154d-42e7-bc25-72dde822663d","2025-04-29T03:44:29.139762+00:00",{"_153":156,"_155":156,"_157":175},3376,"resistencia-dos-materiais-4",[],"video",{"_43":116,"_13":111,"_112":-5,"_180":181,"_182":183,"_28":-5,"_184":-5,"_129":183,"_185":186,"_140":-5,"_187":-5,"_188":-5,"_189":-5,"_190":-5,"_45":191,"_192":156,"_193":-5,"_102":194,"_121":195,"_123":195},"duration",20,"source_type","prometheus","iframe_url","provider_video_id","1cd3d633-d690-4f4b-9995-9b0e44994e35","format","quality","file_path","file_size",{"_119":120},"views_count","last_played_at","draft","2025-08-19T11:56:20.758718+00:00","tag","similarQuestions",[199,230,248],{"_40":200,"_42":41,"_43":201,"_79":202,"_99":218,"_100":219,"_50":220},"112831da-be9c-458e-94cb-e8292d0dba12","3c0b9441-b878-4896-8bac-fa4ca61e3f13",[203,206,209,212,215],{"_43":204,"_83":84,"_85":205},"265bd71a-6749-41f5-b291-67efd646ca64","y'' + 2y' - 3y = 0",{"_43":207,"_83":89,"_85":208},"6d3c3a1d-8e80-4ff3-b97a-d5b5bca91940","6y'' - y' - y = 0",{"_43":210,"_83":93,"_85":211},"4168ac67-64fd-46ed-a69c-a01dbfcde7ea","y'' - 2y' + y = 0",{"_43":213,"_83":97,"_85":214},"cc7bc8df-6995-4264-ac5a-32ea9b4ed7db","9y'' + 6y' + y = 0",{"_43":200,"_83":216,"_85":217},"E","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

",[221],{"_43":222,"_54":223,"_56":224,"_148":149,"_150":225,"_121":226,"_123":226,"_45":227,"_125":224},"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",{"_153":228,"_155":156,"_157":229},4,12302,{"_40":231,"_42":41,"_43":232,"_79":233,"_99":245,"_100":246,"_50":247},"6831a9b9-c9a4-4a76-bd7a-2ce98bfea875","93a32dd4-5fc6-4ccb-a76f-4724bf113742",[234,237,240,242],{"_43":235,"_83":84,"_85":236},"13e3f476-a0a5-421f-b47e-0969e8e9a7e0","

Verdadeiro, verdadeiro, falso

",{"_43":238,"_83":89,"_85":239},"c9a20855-d84b-4860-8b35-9784818282cf","

Falso, verdadeiro, verdadeiro

",{"_43":231,"_83":93,"_85":241},"

Verdadeiro, falso, verdadeiro

",{"_43":243,"_83":97,"_85":244},"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?

",[221],{"_40":249,"_42":41,"_43":250,"_79":251,"_99":266,"_100":267,"_50":268},"3ce109b1-6cdb-4b4d-8816-a6af4d74bed0","c478a46c-46a8-4942-ae14-2e79def3dda2",[252,255,258,260,263],{"_43":253,"_83":84,"_85":254},"a5a16a42-3e58-4c76-80f2-c291aa2d8e49","Sim",{"_43":256,"_83":89,"_85":257},"5e6d0254-696c-4da0-b572-82e3a19f433e","Não",{"_43":249,"_83":93,"_85":259},"Indeterminado",{"_43":261,"_83":97,"_85":262},"35403f68-a880-429d-97f4-db507c58de38","Todos",{"_43":264,"_83":216,"_85":265},"2e06d948-d37e-4350-afc7-ced04941bcaf","Nenhum","Os polinômios e números fornecidos estão corrompidos (símbolos “????”), impossibilitando aplicar Ruffini e concluir se são raízes. Sem dados completos, o problema é indeterminado.","Emplea la regla de Ruffini para dictaminar si los siguientes números son o no raíces de los polinomios citados:
a) ????3 de ????4????5
b) ????2 de ????2????????2
c) ????1 de 2????????1
d) ????1 de 2????2????",[221],[221,270,279,285,289,290,291,299,304,312,313,318,324],{"_43":271,"_54":272,"_56":273,"_148":149,"_150":274,"_121":165,"_123":165,"_45":275,"_125":278},"861ad829-750d-4a44-9569-2f18b430b4df","Engenharia Mecatrônica","engenharia-mecatronica","eb9315c5-bd04-4116-aa46-02c4fde320c0",{"_153":276,"_155":156,"_157":277},5,30614,"engenharia-mecatronica-1",{"_43":280,"_54":61,"_56":62,"_148":149,"_150":281,"_121":282,"_123":282,"_45":283,"_125":284},"8850e507-a691-4d45-a7c7-16221e9c5af2","88fe96b3-2a17-4198-90d5-ddda3d6f5d45","2025-04-29T04:00:13.215003+00:00",{"_153":156,"_155":156,"_157":175},"resistencia-dos-materiais-6",{"_43":281,"_54":163,"_56":164,"_148":149,"_150":271,"_121":226,"_123":226,"_45":286,"_125":288},{"_153":276,"_155":156,"_157":287},25741,"mecanica-3",{"_43":145,"_54":146,"_56":147,"_148":149,"_150":-5,"_121":151,"_123":151,"_45":152,"_125":147},{"_43":172,"_54":61,"_56":62,"_148":149,"_150":162,"_121":173,"_123":173,"_45":174,"_125":176},{"_43":292,"_54":293,"_56":294,"_148":149,"_150":274,"_121":165,"_123":165,"_45":295,"_125":298},"b6e37f32-f8e5-4025-bf0f-69ffc00fb331","Engenharia Civil","engenharia-civil",{"_153":296,"_155":156,"_157":297},21,45865,"engenharia-civil-3",{"_43":225,"_54":300,"_56":301,"_148":149,"_150":274,"_121":165,"_123":165,"_45":302,"_125":303},"Engenharia de Petróleo","engenharia-de-petroleo",{"_153":276,"_155":156,"_157":229},"engenharia-de-petroleo-1",{"_43":305,"_54":306,"_56":307,"_148":149,"_150":292,"_121":308,"_123":308,"_45":309,"_125":311},"c5bf57d4-c3d8-4365-b53e-085fa14a3a95","Estruturas","estruturas","2025-04-29T03:44:32.303369+00:00",{"_153":276,"_155":156,"_157":310},8852,"estruturas-1",{"_43":162,"_54":163,"_56":164,"_148":149,"_150":145,"_121":165,"_123":165,"_45":166,"_125":169},{"_43":314,"_54":61,"_56":62,"_148":149,"_150":222,"_121":315,"_123":315,"_45":316,"_125":317},"d1e4567b-f68a-49e1-b3e5-3888343d7871","2025-04-29T04:00:14.680867+00:00",{"_153":156,"_155":156,"_157":175},"resistencia-dos-materiais-7",{"_43":319,"_54":320,"_56":62,"_148":149,"_150":305,"_121":321,"_123":321,"_45":322,"_125":323},"da8d2ecf-e949-4afc-966f-98b4b367fac1","Resistencia dos Materiais","2025-04-29T04:00:06.9766+00:00",{"_153":156,"_155":156,"_157":175},"resistencia-dos-materiais-5",{"_43":274,"_54":325,"_56":326,"_148":149,"_150":-5,"_121":327,"_123":327,"_45":328,"_125":326},"Engenharia","engenharia","2025-04-29T01:55:38.635246+00:00",{"_153":329,"_155":156,"_157":330},29,351586,"tagsTree",[144,333],{"_43":274,"_54":325,"_56":326,"_148":149,"_150":-5,"_121":327,"_123":327,"_45":328,"_125":326,"_159":334},[335,341,347],{"_43":271,"_54":272,"_56":273,"_148":149,"_150":274,"_121":165,"_123":165,"_45":275,"_125":278,"_159":336},[337],{"_43":281,"_54":163,"_56":164,"_148":149,"_150":271,"_121":226,"_123":226,"_45":286,"_125":288,"_159":338},[339],{"_43":280,"_54":61,"_56":62,"_148":149,"_150":281,"_121":282,"_123":282,"_45":283,"_125":284,"_159":340},[],{"_43":292,"_54":293,"_56":294,"_148":149,"_150":274,"_121":165,"_123":165,"_45":295,"_125":298,"_159":342},[343],{"_43":305,"_54":306,"_56":307,"_148":149,"_150":292,"_121":308,"_123":308,"_45":309,"_125":311,"_159":344},[345],{"_43":319,"_54":320,"_56":62,"_148":149,"_150":305,"_121":321,"_123":321,"_45":322,"_125":323,"_159":346},[],{"_43":225,"_54":300,"_56":301,"_148":149,"_150":274,"_121":165,"_123":165,"_45":302,"_125":303,"_159":348},[349],{"_43":222,"_54":223,"_56":224,"_148":149,"_150":225,"_121":226,"_123":226,"_45":227,"_125":224,"_159":350},[351],{"_43":314,"_54":61,"_56":62,"_148":149,"_150":222,"_121":315,"_123":315,"_45":316,"_125":317,"_159":352},[],"videoDislikes",{},"videoLikes",{},"actionData","errors"]

Comentários