[{"_1":2,"_391":-5,"_392":-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/41b7434f-78ca-487d-8a25-62a9a2d5916f?video=true","user","pages/questions/show/index",{"_33":34,"_35":36,"_37":36,"_38":39,"_102":103,"_203":204,"_51":279,"_346":347,"_387":388,"_389":390},"comments",[],"hasVideoHash",false,"isAiGenerated","question",{"_40":41,"_42":43,"_44":45,"_46":47,"_77":78,"_96":43,"_97":98,"_99":100,"_101":16},"correctOptionId","5555a467-fb55-48bb-8a0c-6b31b0b68a17","difficulty","","id","41b7434f-78ca-487d-8a25-62a9a2d5916f","metadata",{"_48":49,"_73":74,"_75":76},"pd",{"_50":-5,"_51":52,"_53":54,"_61":62,"_63":64,"_65":16,"_66":67,"_68":16,"_69":70,"_71":72},"area","tags",[],"subjects",[55],{"_44":56,"_57":58,"_59":60},1663620,"name","Resistência dos Materiais","alias","resistencia-dos-materiais","materialId","122319311","answerCount",1,"isIndexable","mainSubject",{"_44":56,"_57":58,"_59":60},"isIndexableSEO","materialFormat","Text","studentDegreeLevel","High School","source","PD","externalId","122381856","options",[79,84,88,92],{"_44":41,"_80":81,"_82":83},"label","A","text","

Calcular a tensão de cisalhamento, esmagamento e fator de segurança.

",{"_44":85,"_80":86,"_82":87},"c3626d06-fcec-46f7-8c10-547b82310cac","B","

Calcular a tensão de compressão, tração e cisalhamento.

",{"_44":89,"_80":90,"_82":91},"8bda0998-9b98-4113-b5ac-e3fcf166264f","C","

Calcular a tensão de cisalhamento, esmagamento e deformação.

",{"_44":93,"_80":94,"_82":95},"1e8560eb-25b6-41c0-b67e-34bb5eda344b","D","

Calcular a tensão de compressão, tração e deformação.

","solution_explanation","statement","

Qual é o objetivo da 5ª atividade de Mecânica dos Sólidos?

","status","pending_classification","hasRelatedVideo","relatedVideos",[104],{"_105":106,"_124":125,"_51":140,"_175":176,"_193":194},"content",{"_44":107,"_57":108,"_109":-5,"_110":111,"_112":113,"_114":-5,"_46":115,"_118":119,"_120":119,"_121":-5,"_122":123},"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",{"_116":117},"external_id","4963","created_at","2025-08-20T12:27:41.608438+00:00","updated_at","content_group_id","slug","optica-geometrica-parte-1","prometheusData",{"_126":127,"_133":134,"_135":136,"_137":138,"_28":139},"provider",{"_44":128,"_129":130,"_131":132},"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",[141],{"_44":142,"_57":143,"_59":144,"_145":146,"_147":-5,"_118":148,"_120":148,"_46":149,"_122":144,"_156":157},"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",{"_150":151,"_152":153,"_154":155},"childrenCount",18,"content_count",0,"question_count",135489,"children",[158],{"_44":159,"_57":160,"_59":161,"_145":146,"_147":142,"_118":162,"_120":162,"_46":163,"_122":166,"_156":167},"ca6fee0e-79c6-4f1c-b500-ee081a071949","Mecânica","mecanica","2025-04-29T02:19:12.828432+00:00",{"_150":164,"_152":153,"_154":165},10,19948,"mecanica-2",[168],{"_44":169,"_57":58,"_59":60,"_145":146,"_147":159,"_118":170,"_120":170,"_46":171,"_122":173,"_156":174},"ac55bdba-154d-42e7-bc25-72dde822663d","2025-04-29T03:44:29.139762+00:00",{"_150":153,"_152":153,"_154":172},3376,"resistencia-dos-materiais-4",[],"video",{"_44":113,"_13":108,"_109":-5,"_177":178,"_179":180,"_28":-5,"_181":-5,"_126":180,"_182":183,"_137":-5,"_184":-5,"_185":-5,"_186":-5,"_187":-5,"_46":188,"_189":153,"_190":-5,"_99":191,"_118":192,"_120":192},"duration",20,"source_type","prometheus","iframe_url","provider_video_id","1cd3d633-d690-4f4b-9995-9b0e44994e35","format","quality","file_path","file_size",{"_116":117},"views_count","last_played_at","draft","2025-08-19T11:56:20.758718+00:00","tag",{"_44":142,"_57":143,"_59":144,"_145":146,"_147":-5,"_118":148,"_120":148,"_46":195,"_122":144,"_156":196},{"_150":151,"_152":153,"_154":155},[197],{"_44":159,"_57":160,"_59":161,"_145":146,"_147":142,"_118":162,"_120":162,"_46":198,"_122":166,"_156":199},{"_150":164,"_152":153,"_154":165},[200],{"_44":169,"_57":58,"_59":60,"_145":146,"_147":159,"_118":170,"_120":170,"_46":201,"_122":173,"_156":202},{"_150":153,"_152":153,"_154":172},[],"similarQuestions",[205,236,256],{"_40":206,"_42":43,"_44":207,"_77":208,"_96":224,"_97":225,"_51":226},"112831da-be9c-458e-94cb-e8292d0dba12","3c0b9441-b878-4896-8bac-fa4ca61e3f13",[209,212,215,218,221],{"_44":210,"_80":81,"_82":211},"265bd71a-6749-41f5-b291-67efd646ca64","y'' + 2y' - 3y = 0",{"_44":213,"_80":86,"_82":214},"6d3c3a1d-8e80-4ff3-b97a-d5b5bca91940","6y'' - y' - y = 0",{"_44":216,"_80":90,"_82":217},"4168ac67-64fd-46ed-a69c-a01dbfcde7ea","y'' - 2y' + y = 0",{"_44":219,"_80":94,"_82":220},"cc7bc8df-6995-4264-ac5a-32ea9b4ed7db","9y'' + 6y' + y = 0",{"_44":206,"_80":222,"_82":223},"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

",[227],{"_44":228,"_57":229,"_59":230,"_145":146,"_147":231,"_118":232,"_120":232,"_46":233,"_122":230},"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",{"_150":234,"_152":153,"_154":235},4,12302,{"_40":237,"_42":43,"_44":238,"_77":239,"_96":251,"_97":252,"_51":253},"6831a9b9-c9a4-4a76-bd7a-2ce98bfea875","93a32dd4-5fc6-4ccb-a76f-4724bf113742",[240,243,246,248],{"_44":241,"_80":81,"_82":242},"13e3f476-a0a5-421f-b47e-0969e8e9a7e0","

Verdadeiro, verdadeiro, falso

",{"_44":244,"_80":86,"_82":245},"c9a20855-d84b-4860-8b35-9784818282cf","

Falso, verdadeiro, verdadeiro

",{"_44":237,"_80":90,"_82":247},"

Verdadeiro, falso, verdadeiro

",{"_44":249,"_80":94,"_82":250},"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?

",[254],{"_44":228,"_57":229,"_59":230,"_145":146,"_147":231,"_118":232,"_120":232,"_46":255,"_122":230},{"_150":234,"_152":153,"_154":235},{"_40":257,"_42":43,"_44":258,"_77":259,"_96":274,"_97":275,"_51":276},"3ce109b1-6cdb-4b4d-8816-a6af4d74bed0","c478a46c-46a8-4942-ae14-2e79def3dda2",[260,263,266,268,271],{"_44":261,"_80":81,"_82":262},"a5a16a42-3e58-4c76-80f2-c291aa2d8e49","Sim",{"_44":264,"_80":86,"_82":265},"5e6d0254-696c-4da0-b572-82e3a19f433e","Não",{"_44":257,"_80":90,"_82":267},"Indeterminado",{"_44":269,"_80":94,"_82":270},"35403f68-a880-429d-97f4-db507c58de38","Todos",{"_44":272,"_80":222,"_82":273},"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????",[277],{"_44":228,"_57":229,"_59":230,"_145":146,"_147":231,"_118":232,"_120":232,"_46":278,"_122":230},{"_150":234,"_152":153,"_154":235},[280,282,291,297,301,303,305,313,318,326,328,333,339],{"_44":228,"_57":229,"_59":230,"_145":146,"_147":231,"_118":232,"_120":232,"_46":281,"_122":230},{"_150":234,"_152":153,"_154":235},{"_44":283,"_57":284,"_59":285,"_145":146,"_147":286,"_118":162,"_120":162,"_46":287,"_122":290},"861ad829-750d-4a44-9569-2f18b430b4df","Engenharia Mecatrônica","engenharia-mecatronica","eb9315c5-bd04-4116-aa46-02c4fde320c0",{"_150":288,"_152":153,"_154":289},5,30614,"engenharia-mecatronica-1",{"_44":292,"_57":58,"_59":60,"_145":146,"_147":293,"_118":294,"_120":294,"_46":295,"_122":296},"8850e507-a691-4d45-a7c7-16221e9c5af2","88fe96b3-2a17-4198-90d5-ddda3d6f5d45","2025-04-29T04:00:13.215003+00:00",{"_150":153,"_152":153,"_154":172},"resistencia-dos-materiais-6",{"_44":293,"_57":160,"_59":161,"_145":146,"_147":283,"_118":232,"_120":232,"_46":298,"_122":300},{"_150":288,"_152":153,"_154":299},25741,"mecanica-3",{"_44":142,"_57":143,"_59":144,"_145":146,"_147":-5,"_118":148,"_120":148,"_46":302,"_122":144},{"_150":151,"_152":153,"_154":155},{"_44":169,"_57":58,"_59":60,"_145":146,"_147":159,"_118":170,"_120":170,"_46":304,"_122":173},{"_150":153,"_152":153,"_154":172},{"_44":306,"_57":307,"_59":308,"_145":146,"_147":286,"_118":162,"_120":162,"_46":309,"_122":312},"b6e37f32-f8e5-4025-bf0f-69ffc00fb331","Engenharia Civil","engenharia-civil",{"_150":310,"_152":153,"_154":311},21,45865,"engenharia-civil-3",{"_44":231,"_57":314,"_59":315,"_145":146,"_147":286,"_118":162,"_120":162,"_46":316,"_122":317},"Engenharia de Petróleo","engenharia-de-petroleo",{"_150":288,"_152":153,"_154":235},"engenharia-de-petroleo-1",{"_44":319,"_57":320,"_59":321,"_145":146,"_147":306,"_118":322,"_120":322,"_46":323,"_122":325},"c5bf57d4-c3d8-4365-b53e-085fa14a3a95","Estruturas","estruturas","2025-04-29T03:44:32.303369+00:00",{"_150":288,"_152":153,"_154":324},8852,"estruturas-1",{"_44":159,"_57":160,"_59":161,"_145":146,"_147":142,"_118":162,"_120":162,"_46":327,"_122":166},{"_150":164,"_152":153,"_154":165},{"_44":329,"_57":58,"_59":60,"_145":146,"_147":228,"_118":330,"_120":330,"_46":331,"_122":332},"d1e4567b-f68a-49e1-b3e5-3888343d7871","2025-04-29T04:00:14.680867+00:00",{"_150":153,"_152":153,"_154":172},"resistencia-dos-materiais-7",{"_44":334,"_57":335,"_59":60,"_145":146,"_147":319,"_118":336,"_120":336,"_46":337,"_122":338},"da8d2ecf-e949-4afc-966f-98b4b367fac1","Resistencia dos Materiais","2025-04-29T04:00:06.9766+00:00",{"_150":153,"_152":153,"_154":172},"resistencia-dos-materiais-5",{"_44":286,"_57":340,"_59":341,"_145":146,"_147":-5,"_118":342,"_120":342,"_46":343,"_122":341},"Engenharia","engenharia","2025-04-29T01:55:38.635246+00:00",{"_150":344,"_152":153,"_154":345},29,351586,"tagsTree",[348,357],{"_44":142,"_57":143,"_59":144,"_145":146,"_147":-5,"_118":148,"_120":148,"_46":349,"_122":144,"_156":350},{"_150":151,"_152":153,"_154":155},[351],{"_44":159,"_57":160,"_59":161,"_145":146,"_147":142,"_118":162,"_120":162,"_46":352,"_122":166,"_156":353},{"_150":164,"_152":153,"_154":165},[354],{"_44":169,"_57":58,"_59":60,"_145":146,"_147":159,"_118":170,"_120":170,"_46":355,"_122":173,"_156":356},{"_150":153,"_152":153,"_154":172},[],{"_44":286,"_57":340,"_59":341,"_145":146,"_147":-5,"_118":342,"_120":342,"_46":358,"_122":341,"_156":359},{"_150":344,"_152":153,"_154":345},[360,369,378],{"_44":283,"_57":284,"_59":285,"_145":146,"_147":286,"_118":162,"_120":162,"_46":361,"_122":290,"_156":362},{"_150":288,"_152":153,"_154":289},[363],{"_44":293,"_57":160,"_59":161,"_145":146,"_147":283,"_118":232,"_120":232,"_46":364,"_122":300,"_156":365},{"_150":288,"_152":153,"_154":299},[366],{"_44":292,"_57":58,"_59":60,"_145":146,"_147":293,"_118":294,"_120":294,"_46":367,"_122":296,"_156":368},{"_150":153,"_152":153,"_154":172},[],{"_44":306,"_57":307,"_59":308,"_145":146,"_147":286,"_118":162,"_120":162,"_46":370,"_122":312,"_156":371},{"_150":310,"_152":153,"_154":311},[372],{"_44":319,"_57":320,"_59":321,"_145":146,"_147":306,"_118":322,"_120":322,"_46":373,"_122":325,"_156":374},{"_150":288,"_152":153,"_154":324},[375],{"_44":334,"_57":335,"_59":60,"_145":146,"_147":319,"_118":336,"_120":336,"_46":376,"_122":338,"_156":377},{"_150":153,"_152":153,"_154":172},[],{"_44":231,"_57":314,"_59":315,"_145":146,"_147":286,"_118":162,"_120":162,"_46":379,"_122":317,"_156":380},{"_150":288,"_152":153,"_154":235},[381],{"_44":228,"_57":229,"_59":230,"_145":146,"_147":231,"_118":232,"_120":232,"_46":382,"_122":230,"_156":383},{"_150":234,"_152":153,"_154":235},[384],{"_44":329,"_57":58,"_59":60,"_145":146,"_147":228,"_118":330,"_120":330,"_46":385,"_122":332,"_156":386},{"_150":153,"_152":153,"_154":172},[],"videoDislikes",{},"videoLikes",{},"actionData","errors"]

Comentários