[{"_1":2,"_373":-5,"_374":-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/974ef02b-e08b-4798-8272-8c8266e14874","user","pages/questions/show/index",{"_33":34,"_35":36,"_37":36,"_38":39,"_123":124,"_213":214,"_52":285,"_347":348,"_369":370,"_371":372},"comments",[],"hasVideoHash",false,"isAiGenerated","question",{"_40":41,"_42":43,"_44":45,"_46":47,"_98":99,"_117":43,"_118":119,"_120":121,"_122":16},"correctOptionId","fbd489c5-589c-4ec8-95ed-16208fa67a32","difficulty","","id","974ef02b-e08b-4798-8272-8c8266e14874","metadata",{"_48":49,"_94":95,"_96":97},"pd",{"_50":51,"_52":53,"_60":61,"_82":83,"_84":85,"_86":16,"_87":88,"_89":16,"_90":91,"_92":93},"area","Outros","tags",[54],{"_44":55,"_56":57,"_58":59},417,"name","Cinemática","alias","cinematica","subjects",[62,66,70,74,78],{"_44":63,"_56":64,"_58":65},669766,"Estatisticas","estatisticas",{"_44":67,"_56":68,"_58":69},672071,"Mecânica","mecanica",{"_44":71,"_56":72,"_58":73},674824,"Mecânica dos Solos","mecanica-dos-solos",{"_44":75,"_56":76,"_58":77},678528,"Estática","estatica",{"_44":79,"_56":80,"_58":81},1663620,"Resistência dos Materiais","resistencia-dos-materiais","materialId","79996527","answerCount",1,"isIndexable","mainSubject",{"_44":79,"_56":80,"_58":81},"isIndexableSEO","materialFormat","Text","studentDegreeLevel","Graduate","source","PD","externalId","129690416","options",[100,106,109,113],{"_44":101,"_102":103,"_104":105},"f67ccb8f-dc1f-415e-ab61-90312410d6b8","label","A","text","

A lei da inércia

",{"_44":41,"_102":107,"_104":108},"B","

A lei da ação e reação

",{"_44":110,"_102":111,"_104":112},"349bcf92-a65b-49c5-9be4-946e123b81e9","C","

A lei da conservação da energia

",{"_44":114,"_102":115,"_104":116},"5d220a0d-2ec9-4d62-b44d-1730f53b7593","D","

A lei da gravitação universal

","solution_explanation","statement","

Qual é a lei da física que estabelece que as forças de ação e reação entre corpos interagindo têm as mesmas intensidades, mesmas linhas de ação e sentidos opostos?

","status","pending_classification","hasRelatedVideo","relatedVideos",[125],{"_126":127,"_145":146,"_52":161,"_194":195,"_212":162},"content",{"_44":128,"_56":129,"_130":-5,"_131":132,"_133":134,"_135":-5,"_46":136,"_139":140,"_141":140,"_142":-5,"_143":144},"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",{"_137":138},"external_id","4963","created_at","2025-08-20T12:27:41.608438+00:00","updated_at","content_group_id","slug","optica-geometrica-parte-1","prometheusData",{"_147":148,"_154":155,"_156":157,"_158":159,"_28":160},"provider",{"_44":149,"_150":151,"_152":153},"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",[162],{"_44":163,"_56":164,"_58":165,"_166":167,"_168":-5,"_139":169,"_141":169,"_46":170,"_143":165,"_177":178},"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",{"_171":172,"_173":174,"_175":176},"childrenCount",18,"content_count",0,"question_count",135489,"children",[179],{"_44":180,"_56":68,"_58":69,"_166":167,"_168":163,"_139":181,"_141":181,"_46":182,"_143":185,"_177":186},"ca6fee0e-79c6-4f1c-b500-ee081a071949","2025-04-29T02:19:12.828432+00:00",{"_171":183,"_173":174,"_175":184},10,19948,"mecanica-2",[187],{"_44":188,"_56":80,"_58":81,"_166":167,"_168":180,"_139":189,"_141":189,"_46":190,"_143":192,"_177":193},"ac55bdba-154d-42e7-bc25-72dde822663d","2025-04-29T03:44:29.139762+00:00",{"_171":174,"_173":174,"_175":191},3376,"resistencia-dos-materiais-4",[],"video",{"_44":134,"_13":129,"_130":-5,"_196":197,"_198":199,"_28":-5,"_200":-5,"_147":199,"_201":202,"_158":-5,"_203":-5,"_204":-5,"_205":-5,"_206":-5,"_46":207,"_208":174,"_209":-5,"_120":210,"_139":211,"_141":211},"duration",20,"source_type","prometheus","iframe_url","provider_video_id","1cd3d633-d690-4f4b-9995-9b0e44994e35","format","quality","file_path","file_size",{"_137":138},"views_count","last_played_at","draft","2025-08-19T11:56:20.758718+00:00","tag","similarQuestions",[215,246,264],{"_40":216,"_42":43,"_44":217,"_98":218,"_117":234,"_118":235,"_52":236},"112831da-be9c-458e-94cb-e8292d0dba12","3c0b9441-b878-4896-8bac-fa4ca61e3f13",[219,222,225,228,231],{"_44":220,"_102":103,"_104":221},"265bd71a-6749-41f5-b291-67efd646ca64","y'' + 2y' - 3y = 0",{"_44":223,"_102":107,"_104":224},"6d3c3a1d-8e80-4ff3-b97a-d5b5bca91940","6y'' - y' - y = 0",{"_44":226,"_102":111,"_104":227},"4168ac67-64fd-46ed-a69c-a01dbfcde7ea","y'' - 2y' + y = 0",{"_44":229,"_102":115,"_104":230},"cc7bc8df-6995-4264-ac5a-32ea9b4ed7db","9y'' + 6y' + y = 0",{"_44":216,"_102":232,"_104":233},"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

",[237],{"_44":238,"_56":239,"_58":240,"_166":167,"_168":241,"_139":242,"_141":242,"_46":243,"_143":240},"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",{"_171":244,"_173":174,"_175":245},4,12302,{"_40":247,"_42":43,"_44":248,"_98":249,"_117":261,"_118":262,"_52":263},"6831a9b9-c9a4-4a76-bd7a-2ce98bfea875","93a32dd4-5fc6-4ccb-a76f-4724bf113742",[250,253,256,258],{"_44":251,"_102":103,"_104":252},"13e3f476-a0a5-421f-b47e-0969e8e9a7e0","

Verdadeiro, verdadeiro, falso

",{"_44":254,"_102":107,"_104":255},"c9a20855-d84b-4860-8b35-9784818282cf","

Falso, verdadeiro, verdadeiro

",{"_44":247,"_102":111,"_104":257},"

Verdadeiro, falso, verdadeiro

",{"_44":259,"_102":115,"_104":260},"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?

",[237],{"_40":265,"_42":43,"_44":266,"_98":267,"_117":282,"_118":283,"_52":284},"3ce109b1-6cdb-4b4d-8816-a6af4d74bed0","c478a46c-46a8-4942-ae14-2e79def3dda2",[268,271,274,276,279],{"_44":269,"_102":103,"_104":270},"a5a16a42-3e58-4c76-80f2-c291aa2d8e49","Sim",{"_44":272,"_102":107,"_104":273},"5e6d0254-696c-4da0-b572-82e3a19f433e","Não",{"_44":265,"_102":111,"_104":275},"Indeterminado",{"_44":277,"_102":115,"_104":278},"35403f68-a880-429d-97f4-db507c58de38","Todos",{"_44":280,"_102":232,"_104":281},"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????",[237],[237,286,295,301,305,306,307,315,320,328,329,334,340],{"_44":287,"_56":288,"_58":289,"_166":167,"_168":290,"_139":181,"_141":181,"_46":291,"_143":294},"861ad829-750d-4a44-9569-2f18b430b4df","Engenharia Mecatrônica","engenharia-mecatronica","eb9315c5-bd04-4116-aa46-02c4fde320c0",{"_171":292,"_173":174,"_175":293},5,30614,"engenharia-mecatronica-1",{"_44":296,"_56":80,"_58":81,"_166":167,"_168":297,"_139":298,"_141":298,"_46":299,"_143":300},"8850e507-a691-4d45-a7c7-16221e9c5af2","88fe96b3-2a17-4198-90d5-ddda3d6f5d45","2025-04-29T04:00:13.215003+00:00",{"_171":174,"_173":174,"_175":191},"resistencia-dos-materiais-6",{"_44":297,"_56":68,"_58":69,"_166":167,"_168":287,"_139":242,"_141":242,"_46":302,"_143":304},{"_171":292,"_173":174,"_175":303},25741,"mecanica-3",{"_44":163,"_56":164,"_58":165,"_166":167,"_168":-5,"_139":169,"_141":169,"_46":170,"_143":165},{"_44":188,"_56":80,"_58":81,"_166":167,"_168":180,"_139":189,"_141":189,"_46":190,"_143":192},{"_44":308,"_56":309,"_58":310,"_166":167,"_168":290,"_139":181,"_141":181,"_46":311,"_143":314},"b6e37f32-f8e5-4025-bf0f-69ffc00fb331","Engenharia Civil","engenharia-civil",{"_171":312,"_173":174,"_175":313},21,45865,"engenharia-civil-3",{"_44":241,"_56":316,"_58":317,"_166":167,"_168":290,"_139":181,"_141":181,"_46":318,"_143":319},"Engenharia de Petróleo","engenharia-de-petroleo",{"_171":292,"_173":174,"_175":245},"engenharia-de-petroleo-1",{"_44":321,"_56":322,"_58":323,"_166":167,"_168":308,"_139":324,"_141":324,"_46":325,"_143":327},"c5bf57d4-c3d8-4365-b53e-085fa14a3a95","Estruturas","estruturas","2025-04-29T03:44:32.303369+00:00",{"_171":292,"_173":174,"_175":326},8852,"estruturas-1",{"_44":180,"_56":68,"_58":69,"_166":167,"_168":163,"_139":181,"_141":181,"_46":182,"_143":185},{"_44":330,"_56":80,"_58":81,"_166":167,"_168":238,"_139":331,"_141":331,"_46":332,"_143":333},"d1e4567b-f68a-49e1-b3e5-3888343d7871","2025-04-29T04:00:14.680867+00:00",{"_171":174,"_173":174,"_175":191},"resistencia-dos-materiais-7",{"_44":335,"_56":336,"_58":81,"_166":167,"_168":321,"_139":337,"_141":337,"_46":338,"_143":339},"da8d2ecf-e949-4afc-966f-98b4b367fac1","Resistencia dos Materiais","2025-04-29T04:00:06.9766+00:00",{"_171":174,"_173":174,"_175":191},"resistencia-dos-materiais-5",{"_44":290,"_56":341,"_58":342,"_166":167,"_168":-5,"_139":343,"_141":343,"_46":344,"_143":342},"Engenharia","engenharia","2025-04-29T01:55:38.635246+00:00",{"_171":345,"_173":174,"_175":346},29,351586,"tagsTree",[162,349],{"_44":290,"_56":341,"_58":342,"_166":167,"_168":-5,"_139":343,"_141":343,"_46":344,"_143":342,"_177":350},[351,357,363],{"_44":287,"_56":288,"_58":289,"_166":167,"_168":290,"_139":181,"_141":181,"_46":291,"_143":294,"_177":352},[353],{"_44":297,"_56":68,"_58":69,"_166":167,"_168":287,"_139":242,"_141":242,"_46":302,"_143":304,"_177":354},[355],{"_44":296,"_56":80,"_58":81,"_166":167,"_168":297,"_139":298,"_141":298,"_46":299,"_143":300,"_177":356},[],{"_44":308,"_56":309,"_58":310,"_166":167,"_168":290,"_139":181,"_141":181,"_46":311,"_143":314,"_177":358},[359],{"_44":321,"_56":322,"_58":323,"_166":167,"_168":308,"_139":324,"_141":324,"_46":325,"_143":327,"_177":360},[361],{"_44":335,"_56":336,"_58":81,"_166":167,"_168":321,"_139":337,"_141":337,"_46":338,"_143":339,"_177":362},[],{"_44":241,"_56":316,"_58":317,"_166":167,"_168":290,"_139":181,"_141":181,"_46":318,"_143":319,"_177":364},[365],{"_44":238,"_56":239,"_58":240,"_166":167,"_168":241,"_139":242,"_141":242,"_46":243,"_143":240,"_177":366},[367],{"_44":330,"_56":80,"_58":81,"_166":167,"_168":238,"_139":331,"_141":331,"_46":332,"_143":333,"_177":368},[],"videoDislikes",{},"videoLikes",{},"actionData","errors"]

Comentários