[{"_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/a8a12aae-48f9-41c9-a6d2-621b44acf8e2?video=true","user","pages/questions/show/index",{"_33":34,"_35":36,"_37":36,"_38":39,"_106":107,"_198":199,"_50":269,"_331":332,"_353":354,"_355":356},"comments",[],"hasVideoHash",false,"isAiGenerated","question",{"_40":41,"_42":41,"_43":44,"_45":46,"_76":77,"_100":41,"_101":102,"_103":104,"_105":16},"correctOptionId","","difficulty","id","a8a12aae-48f9-41c9-a6d2-621b44acf8e2","metadata",{"_47":48,"_72":73,"_74":75},"pd",{"_49":-5,"_50":51,"_52":53,"_60":61,"_62":63,"_64":16,"_65":66,"_67":36,"_68":69,"_70":71},"area","tags",[],"subjects",[54],{"_43":55,"_56":57,"_58":59},1663620,"name","Resistência dos Materiais","alias","resistencia-dos-materiais","materialId","122678749","answerCount",1,"isIndexable","mainSubject",{"_43":55,"_56":57,"_58":59},"isIndexableSEO","materialFormat","Text","studentDegreeLevel","High School","source","PD","externalId","122783425","options",[78,84,88,92,96],{"_43":79,"_80":81,"_82":83},"dd8cc83e-ab57-4ce2-b1ed-f3e79eb43cf5","label","A","text","

400MPa

",{"_43":85,"_80":86,"_82":87},"3adb280a-924a-464c-b6ff-80f5b55545bf","B","

300MPa

",{"_43":89,"_80":90,"_82":91},"d7abd651-6a7c-4d71-9090-76865e5a39c8","C","

200MPa

",{"_43":93,"_80":94,"_82":95},"ed25f689-9db3-403b-8b05-6e00733064b6","D","

1000MPa

",{"_43":97,"_80":98,"_82":99},"d2badab1-244a-4f50-a0d2-4750757ea596","E","

375MPa

","solution_explanation","statement","

Qual é a tensão de torção em uma barra retangular de dimensões 60 \text{ mm} e 25 \text{ mm} respectivamente, considerando o coeficiente de torção em 0,250 e a tensão admissível máxima de 40 \text{ MPa}?

","status","pending_classification","hasRelatedVideo","relatedVideos",[108],{"_109":110,"_128":129,"_50":144,"_179":180,"_197":145},"content",{"_43":111,"_56":112,"_113":-5,"_114":115,"_116":117,"_118":-5,"_45":119,"_122":123,"_124":123,"_125":-5,"_126":127},"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",{"_120":121},"external_id","4963","created_at","2025-08-20T12:27:41.608438+00:00","updated_at","content_group_id","slug","optica-geometrica-parte-1","prometheusData",{"_130":131,"_137":138,"_139":140,"_141":142,"_28":143},"provider",{"_43":132,"_133":134,"_135":136},"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",[145],{"_43":146,"_56":147,"_58":148,"_149":150,"_151":-5,"_122":152,"_124":152,"_45":153,"_126":148,"_160":161},"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",{"_154":155,"_156":157,"_158":159},"childrenCount",18,"content_count",0,"question_count",135489,"children",[162],{"_43":163,"_56":164,"_58":165,"_149":150,"_151":146,"_122":166,"_124":166,"_45":167,"_126":170,"_160":171},"ca6fee0e-79c6-4f1c-b500-ee081a071949","Mecânica","mecanica","2025-04-29T02:19:12.828432+00:00",{"_154":168,"_156":157,"_158":169},10,19948,"mecanica-2",[172],{"_43":173,"_56":57,"_58":59,"_149":150,"_151":163,"_122":174,"_124":174,"_45":175,"_126":177,"_160":178},"ac55bdba-154d-42e7-bc25-72dde822663d","2025-04-29T03:44:29.139762+00:00",{"_154":157,"_156":157,"_158":176},3376,"resistencia-dos-materiais-4",[],"video",{"_43":117,"_13":112,"_113":-5,"_181":182,"_183":184,"_28":-5,"_185":-5,"_130":184,"_186":187,"_141":-5,"_188":-5,"_189":-5,"_190":-5,"_191":-5,"_45":192,"_193":157,"_194":-5,"_103":195,"_122":196,"_124":196},"duration",20,"source_type","prometheus","iframe_url","provider_video_id","1cd3d633-d690-4f4b-9995-9b0e44994e35","format","quality","file_path","file_size",{"_120":121},"views_count","last_played_at","draft","2025-08-19T11:56:20.758718+00:00","tag","similarQuestions",[200,230,248],{"_40":201,"_42":41,"_43":202,"_76":203,"_100":218,"_101":219,"_50":220},"112831da-be9c-458e-94cb-e8292d0dba12","3c0b9441-b878-4896-8bac-fa4ca61e3f13",[204,207,210,213,216],{"_43":205,"_80":81,"_82":206},"265bd71a-6749-41f5-b291-67efd646ca64","y'' + 2y' - 3y = 0",{"_43":208,"_80":86,"_82":209},"6d3c3a1d-8e80-4ff3-b97a-d5b5bca91940","6y'' - y' - y = 0",{"_43":211,"_80":90,"_82":212},"4168ac67-64fd-46ed-a69c-a01dbfcde7ea","y'' - 2y' + y = 0",{"_43":214,"_80":94,"_82":215},"cc7bc8df-6995-4264-ac5a-32ea9b4ed7db","9y'' + 6y' + y = 0",{"_43":201,"_80":98,"_82":217},"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,"_56":223,"_58":224,"_149":150,"_151":225,"_122":226,"_124":226,"_45":227,"_126":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",{"_154":228,"_156":157,"_158":229},4,12302,{"_40":231,"_42":41,"_43":232,"_76":233,"_100":245,"_101":246,"_50":247},"6831a9b9-c9a4-4a76-bd7a-2ce98bfea875","93a32dd4-5fc6-4ccb-a76f-4724bf113742",[234,237,240,242],{"_43":235,"_80":81,"_82":236},"13e3f476-a0a5-421f-b47e-0969e8e9a7e0","

Verdadeiro, verdadeiro, falso

",{"_43":238,"_80":86,"_82":239},"c9a20855-d84b-4860-8b35-9784818282cf","

Falso, verdadeiro, verdadeiro

",{"_43":231,"_80":90,"_82":241},"

Verdadeiro, falso, verdadeiro

",{"_43":243,"_80":94,"_82":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,"_76":251,"_100":266,"_101":267,"_50":268},"3ce109b1-6cdb-4b4d-8816-a6af4d74bed0","c478a46c-46a8-4942-ae14-2e79def3dda2",[252,255,258,260,263],{"_43":253,"_80":81,"_82":254},"a5a16a42-3e58-4c76-80f2-c291aa2d8e49","Sim",{"_43":256,"_80":86,"_82":257},"5e6d0254-696c-4da0-b572-82e3a19f433e","Não",{"_43":249,"_80":90,"_82":259},"Indeterminado",{"_43":261,"_80":94,"_82":262},"35403f68-a880-429d-97f4-db507c58de38","Todos",{"_43":264,"_80":98,"_82":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,"_56":272,"_58":273,"_149":150,"_151":274,"_122":166,"_124":166,"_45":275,"_126":278},"861ad829-750d-4a44-9569-2f18b430b4df","Engenharia Mecatrônica","engenharia-mecatronica","eb9315c5-bd04-4116-aa46-02c4fde320c0",{"_154":276,"_156":157,"_158":277},5,30614,"engenharia-mecatronica-1",{"_43":280,"_56":57,"_58":59,"_149":150,"_151":281,"_122":282,"_124":282,"_45":283,"_126":284},"8850e507-a691-4d45-a7c7-16221e9c5af2","88fe96b3-2a17-4198-90d5-ddda3d6f5d45","2025-04-29T04:00:13.215003+00:00",{"_154":157,"_156":157,"_158":176},"resistencia-dos-materiais-6",{"_43":281,"_56":164,"_58":165,"_149":150,"_151":271,"_122":226,"_124":226,"_45":286,"_126":288},{"_154":276,"_156":157,"_158":287},25741,"mecanica-3",{"_43":146,"_56":147,"_58":148,"_149":150,"_151":-5,"_122":152,"_124":152,"_45":153,"_126":148},{"_43":173,"_56":57,"_58":59,"_149":150,"_151":163,"_122":174,"_124":174,"_45":175,"_126":177},{"_43":292,"_56":293,"_58":294,"_149":150,"_151":274,"_122":166,"_124":166,"_45":295,"_126":298},"b6e37f32-f8e5-4025-bf0f-69ffc00fb331","Engenharia Civil","engenharia-civil",{"_154":296,"_156":157,"_158":297},21,45865,"engenharia-civil-3",{"_43":225,"_56":300,"_58":301,"_149":150,"_151":274,"_122":166,"_124":166,"_45":302,"_126":303},"Engenharia de Petróleo","engenharia-de-petroleo",{"_154":276,"_156":157,"_158":229},"engenharia-de-petroleo-1",{"_43":305,"_56":306,"_58":307,"_149":150,"_151":292,"_122":308,"_124":308,"_45":309,"_126":311},"c5bf57d4-c3d8-4365-b53e-085fa14a3a95","Estruturas","estruturas","2025-04-29T03:44:32.303369+00:00",{"_154":276,"_156":157,"_158":310},8852,"estruturas-1",{"_43":163,"_56":164,"_58":165,"_149":150,"_151":146,"_122":166,"_124":166,"_45":167,"_126":170},{"_43":314,"_56":57,"_58":59,"_149":150,"_151":222,"_122":315,"_124":315,"_45":316,"_126":317},"d1e4567b-f68a-49e1-b3e5-3888343d7871","2025-04-29T04:00:14.680867+00:00",{"_154":157,"_156":157,"_158":176},"resistencia-dos-materiais-7",{"_43":319,"_56":320,"_58":59,"_149":150,"_151":305,"_122":321,"_124":321,"_45":322,"_126":323},"da8d2ecf-e949-4afc-966f-98b4b367fac1","Resistencia dos Materiais","2025-04-29T04:00:06.9766+00:00",{"_154":157,"_156":157,"_158":176},"resistencia-dos-materiais-5",{"_43":274,"_56":325,"_58":326,"_149":150,"_151":-5,"_122":327,"_124":327,"_45":328,"_126":326},"Engenharia","engenharia","2025-04-29T01:55:38.635246+00:00",{"_154":329,"_156":157,"_158":330},29,351586,"tagsTree",[145,333],{"_43":274,"_56":325,"_58":326,"_149":150,"_151":-5,"_122":327,"_124":327,"_45":328,"_126":326,"_160":334},[335,341,347],{"_43":271,"_56":272,"_58":273,"_149":150,"_151":274,"_122":166,"_124":166,"_45":275,"_126":278,"_160":336},[337],{"_43":281,"_56":164,"_58":165,"_149":150,"_151":271,"_122":226,"_124":226,"_45":286,"_126":288,"_160":338},[339],{"_43":280,"_56":57,"_58":59,"_149":150,"_151":281,"_122":282,"_124":282,"_45":283,"_126":284,"_160":340},[],{"_43":292,"_56":293,"_58":294,"_149":150,"_151":274,"_122":166,"_124":166,"_45":295,"_126":298,"_160":342},[343],{"_43":305,"_56":306,"_58":307,"_149":150,"_151":292,"_122":308,"_124":308,"_45":309,"_126":311,"_160":344},[345],{"_43":319,"_56":320,"_58":59,"_149":150,"_151":305,"_122":321,"_124":321,"_45":322,"_126":323,"_160":346},[],{"_43":225,"_56":300,"_58":301,"_149":150,"_151":274,"_122":166,"_124":166,"_45":302,"_126":303,"_160":348},[349],{"_43":222,"_56":223,"_58":224,"_149":150,"_151":225,"_122":226,"_124":226,"_45":227,"_126":224,"_160":350},[351],{"_43":314,"_56":57,"_58":59,"_149":150,"_151":222,"_122":315,"_124":315,"_45":316,"_126":317,"_160":352},[],"videoDislikes",{},"videoLikes",{},"actionData","errors"]

Comentários