[{"_1":2,"_395":-5,"_396":-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/772a5ebc-1f0b-403d-9ef3-6021ff7f7774?video=true","user","pages/questions/show/index",{"_33":34,"_35":36,"_37":36,"_38":39,"_107":108,"_208":209,"_52":283,"_350":351,"_391":392,"_393":394},"comments",[],"hasVideoHash",false,"isAiGenerated","question",{"_40":41,"_42":43,"_44":45,"_46":47,"_78":79,"_101":43,"_102":103,"_104":105,"_106":16},"correctOptionId","0031e65a-aed5-433a-8dd9-5160629ae18f","difficulty","","id","772a5ebc-1f0b-403d-9ef3-6021ff7f7774","metadata",{"_48":49,"_74":75,"_76":77},"pd",{"_50":51,"_52":53,"_54":55,"_62":63,"_64":65,"_66":16,"_67":68,"_69":16,"_70":71,"_72":73},"area","Outros","tags",[],"subjects",[56],{"_44":57,"_58":59,"_60":61},1663620,"name","Resistência dos Materiais","alias","resistencia-dos-materiais","materialId","133464178","answerCount",1,"isIndexable","mainSubject",{"_44":57,"_58":59,"_60":61},"isIndexableSEO","materialFormat","Text","studentDegreeLevel","Graduate","source","PD","externalId","133513829","options",[80,86,89,93,97],{"_44":81,"_82":83,"_84":85},"a83c0611-6e09-44d7-889b-d257c2038aa2","label","A","text","\\tau_{máx} = 50 \\, \\text{Mpa}",{"_44":41,"_82":87,"_84":88},"B","\\tau_{máx} = 87,3 \\, \\text{Mpa}",{"_44":90,"_82":91,"_84":92},"d7cb1dad-ba33-4bda-93e5-6c3e473ca018","C","\\tau_{máx} = 100 \\, \\text{Mpa}",{"_44":94,"_82":95,"_84":96},"4ca5b0b3-aa04-487f-bf2f-11953318c1a5","D","\\tau_{máx} = 75 \\, \\text{Mpa}",{"_44":98,"_82":99,"_84":100},"39118330-1f8f-47aa-b380-22e5b60d1f6f","E","\\tau_{máx} = 60 \\, \\text{Mpa}","solution_explanation","statement","

Determine a tensão de cisalhamento máxima provocada por um torque de intensidade T = 800 \\, \text{N.m}.

","status","pending_classification","hasRelatedVideo","relatedVideos",[109],{"_110":111,"_129":130,"_52":145,"_180":181,"_198":199},"content",{"_44":112,"_58":113,"_114":-5,"_115":116,"_117":118,"_119":-5,"_46":120,"_123":124,"_125":124,"_126":-5,"_127":128},"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",{"_121":122},"external_id","4963","created_at","2025-08-20T12:27:41.608438+00:00","updated_at","content_group_id","slug","optica-geometrica-parte-1","prometheusData",{"_131":132,"_138":139,"_140":141,"_142":143,"_28":144},"provider",{"_44":133,"_134":135,"_136":137},"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",[146],{"_44":147,"_58":148,"_60":149,"_150":151,"_152":-5,"_123":153,"_125":153,"_46":154,"_127":149,"_161":162},"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",{"_155":156,"_157":158,"_159":160},"childrenCount",18,"content_count",0,"question_count",135489,"children",[163],{"_44":164,"_58":165,"_60":166,"_150":151,"_152":147,"_123":167,"_125":167,"_46":168,"_127":171,"_161":172},"ca6fee0e-79c6-4f1c-b500-ee081a071949","Mecânica","mecanica","2025-04-29T02:19:12.828432+00:00",{"_155":169,"_157":158,"_159":170},10,19948,"mecanica-2",[173],{"_44":174,"_58":59,"_60":61,"_150":151,"_152":164,"_123":175,"_125":175,"_46":176,"_127":178,"_161":179},"ac55bdba-154d-42e7-bc25-72dde822663d","2025-04-29T03:44:29.139762+00:00",{"_155":158,"_157":158,"_159":177},3376,"resistencia-dos-materiais-4",[],"video",{"_44":118,"_13":113,"_114":-5,"_182":183,"_184":185,"_28":-5,"_186":-5,"_131":185,"_187":188,"_142":-5,"_189":-5,"_190":-5,"_191":-5,"_192":-5,"_46":193,"_194":158,"_195":-5,"_104":196,"_123":197,"_125":197},"duration",20,"source_type","prometheus","iframe_url","provider_video_id","1cd3d633-d690-4f4b-9995-9b0e44994e35","format","quality","file_path","file_size",{"_121":122},"views_count","last_played_at","draft","2025-08-19T11:56:20.758718+00:00","tag",{"_44":147,"_58":148,"_60":149,"_150":151,"_152":-5,"_123":153,"_125":153,"_46":200,"_127":149,"_161":201},{"_155":156,"_157":158,"_159":160},[202],{"_44":164,"_58":165,"_60":166,"_150":151,"_152":147,"_123":167,"_125":167,"_46":203,"_127":171,"_161":204},{"_155":169,"_157":158,"_159":170},[205],{"_44":174,"_58":59,"_60":61,"_150":151,"_152":164,"_123":175,"_125":175,"_46":206,"_127":178,"_161":207},{"_155":158,"_157":158,"_159":177},[],"similarQuestions",[210,240,260],{"_40":211,"_42":43,"_44":212,"_78":213,"_101":228,"_102":229,"_52":230},"112831da-be9c-458e-94cb-e8292d0dba12","3c0b9441-b878-4896-8bac-fa4ca61e3f13",[214,217,220,223,226],{"_44":215,"_82":83,"_84":216},"265bd71a-6749-41f5-b291-67efd646ca64","y'' + 2y' - 3y = 0",{"_44":218,"_82":87,"_84":219},"6d3c3a1d-8e80-4ff3-b97a-d5b5bca91940","6y'' - y' - y = 0",{"_44":221,"_82":91,"_84":222},"4168ac67-64fd-46ed-a69c-a01dbfcde7ea","y'' - 2y' + y = 0",{"_44":224,"_82":95,"_84":225},"cc7bc8df-6995-4264-ac5a-32ea9b4ed7db","9y'' + 6y' + y = 0",{"_44":211,"_82":99,"_84":227},"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

",[231],{"_44":232,"_58":233,"_60":234,"_150":151,"_152":235,"_123":236,"_125":236,"_46":237,"_127":234},"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",{"_155":238,"_157":158,"_159":239},4,12302,{"_40":241,"_42":43,"_44":242,"_78":243,"_101":255,"_102":256,"_52":257},"6831a9b9-c9a4-4a76-bd7a-2ce98bfea875","93a32dd4-5fc6-4ccb-a76f-4724bf113742",[244,247,250,252],{"_44":245,"_82":83,"_84":246},"13e3f476-a0a5-421f-b47e-0969e8e9a7e0","

Verdadeiro, verdadeiro, falso

",{"_44":248,"_82":87,"_84":249},"c9a20855-d84b-4860-8b35-9784818282cf","

Falso, verdadeiro, verdadeiro

",{"_44":241,"_82":91,"_84":251},"

Verdadeiro, falso, verdadeiro

",{"_44":253,"_82":95,"_84":254},"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????",[281],{"_44":232,"_58":233,"_60":234,"_150":151,"_152":235,"_123":236,"_125":236,"_46":282,"_127":234},{"_155":238,"_157":158,"_159":239},[284,286,295,301,305,307,309,317,322,330,332,337,343],{"_44":232,"_58":233,"_60":234,"_150":151,"_152":235,"_123":236,"_125":236,"_46":285,"_127":234},{"_155":238,"_157":158,"_159":239},{"_44":287,"_58":288,"_60":289,"_150":151,"_152":290,"_123":167,"_125":167,"_46":291,"_127":294},"861ad829-750d-4a44-9569-2f18b430b4df","Engenharia Mecatrônica","engenharia-mecatronica","eb9315c5-bd04-4116-aa46-02c4fde320c0",{"_155":292,"_157":158,"_159":293},5,30614,"engenharia-mecatronica-1",{"_44":296,"_58":59,"_60":61,"_150":151,"_152":297,"_123":298,"_125":298,"_46":299,"_127":300},"8850e507-a691-4d45-a7c7-16221e9c5af2","88fe96b3-2a17-4198-90d5-ddda3d6f5d45","2025-04-29T04:00:13.215003+00:00",{"_155":158,"_157":158,"_159":177},"resistencia-dos-materiais-6",{"_44":297,"_58":165,"_60":166,"_150":151,"_152":287,"_123":236,"_125":236,"_46":302,"_127":304},{"_155":292,"_157":158,"_159":303},25741,"mecanica-3",{"_44":147,"_58":148,"_60":149,"_150":151,"_152":-5,"_123":153,"_125":153,"_46":306,"_127":149},{"_155":156,"_157":158,"_159":160},{"_44":174,"_58":59,"_60":61,"_150":151,"_152":164,"_123":175,"_125":175,"_46":308,"_127":178},{"_155":158,"_157":158,"_159":177},{"_44":310,"_58":311,"_60":312,"_150":151,"_152":290,"_123":167,"_125":167,"_46":313,"_127":316},"b6e37f32-f8e5-4025-bf0f-69ffc00fb331","Engenharia Civil","engenharia-civil",{"_155":314,"_157":158,"_159":315},21,45865,"engenharia-civil-3",{"_44":235,"_58":318,"_60":319,"_150":151,"_152":290,"_123":167,"_125":167,"_46":320,"_127":321},"Engenharia de Petróleo","engenharia-de-petroleo",{"_155":292,"_157":158,"_159":239},"engenharia-de-petroleo-1",{"_44":323,"_58":324,"_60":325,"_150":151,"_152":310,"_123":326,"_125":326,"_46":327,"_127":329},"c5bf57d4-c3d8-4365-b53e-085fa14a3a95","Estruturas","estruturas","2025-04-29T03:44:32.303369+00:00",{"_155":292,"_157":158,"_159":328},8852,"estruturas-1",{"_44":164,"_58":165,"_60":166,"_150":151,"_152":147,"_123":167,"_125":167,"_46":331,"_127":171},{"_155":169,"_157":158,"_159":170},{"_44":333,"_58":59,"_60":61,"_150":151,"_152":232,"_123":334,"_125":334,"_46":335,"_127":336},"d1e4567b-f68a-49e1-b3e5-3888343d7871","2025-04-29T04:00:14.680867+00:00",{"_155":158,"_157":158,"_159":177},"resistencia-dos-materiais-7",{"_44":338,"_58":339,"_60":61,"_150":151,"_152":323,"_123":340,"_125":340,"_46":341,"_127":342},"da8d2ecf-e949-4afc-966f-98b4b367fac1","Resistencia dos Materiais","2025-04-29T04:00:06.9766+00:00",{"_155":158,"_157":158,"_159":177},"resistencia-dos-materiais-5",{"_44":290,"_58":344,"_60":345,"_150":151,"_152":-5,"_123":346,"_125":346,"_46":347,"_127":345},"Engenharia","engenharia","2025-04-29T01:55:38.635246+00:00",{"_155":348,"_157":158,"_159":349},29,351586,"tagsTree",[352,361],{"_44":147,"_58":148,"_60":149,"_150":151,"_152":-5,"_123":153,"_125":153,"_46":353,"_127":149,"_161":354},{"_155":156,"_157":158,"_159":160},[355],{"_44":164,"_58":165,"_60":166,"_150":151,"_152":147,"_123":167,"_125":167,"_46":356,"_127":171,"_161":357},{"_155":169,"_157":158,"_159":170},[358],{"_44":174,"_58":59,"_60":61,"_150":151,"_152":164,"_123":175,"_125":175,"_46":359,"_127":178,"_161":360},{"_155":158,"_157":158,"_159":177},[],{"_44":290,"_58":344,"_60":345,"_150":151,"_152":-5,"_123":346,"_125":346,"_46":362,"_127":345,"_161":363},{"_155":348,"_157":158,"_159":349},[364,373,382],{"_44":287,"_58":288,"_60":289,"_150":151,"_152":290,"_123":167,"_125":167,"_46":365,"_127":294,"_161":366},{"_155":292,"_157":158,"_159":293},[367],{"_44":297,"_58":165,"_60":166,"_150":151,"_152":287,"_123":236,"_125":236,"_46":368,"_127":304,"_161":369},{"_155":292,"_157":158,"_159":303},[370],{"_44":296,"_58":59,"_60":61,"_150":151,"_152":297,"_123":298,"_125":298,"_46":371,"_127":300,"_161":372},{"_155":158,"_157":158,"_159":177},[],{"_44":310,"_58":311,"_60":312,"_150":151,"_152":290,"_123":167,"_125":167,"_46":374,"_127":316,"_161":375},{"_155":314,"_157":158,"_159":315},[376],{"_44":323,"_58":324,"_60":325,"_150":151,"_152":310,"_123":326,"_125":326,"_46":377,"_127":329,"_161":378},{"_155":292,"_157":158,"_159":328},[379],{"_44":338,"_58":339,"_60":61,"_150":151,"_152":323,"_123":340,"_125":340,"_46":380,"_127":342,"_161":381},{"_155":158,"_157":158,"_159":177},[],{"_44":235,"_58":318,"_60":319,"_150":151,"_152":290,"_123":167,"_125":167,"_46":383,"_127":321,"_161":384},{"_155":292,"_157":158,"_159":239},[385],{"_44":232,"_58":233,"_60":234,"_150":151,"_152":235,"_123":236,"_125":236,"_46":386,"_127":234,"_161":387},{"_155":238,"_157":158,"_159":239},[388],{"_44":333,"_58":59,"_60":61,"_150":151,"_152":232,"_123":334,"_125":334,"_46":389,"_127":336,"_161":390},{"_155":158,"_157":158,"_159":177},[],"videoDislikes",{},"videoLikes",{},"actionData","errors"]

Comentários