[{"_1":2,"_389":-5,"_390":-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/7f3c3e80-9c0e-4f34-9841-eebb3075b553?video=true","user","pages/questions/show/index",{"_33":34,"_35":36,"_37":36,"_38":39,"_99":100,"_200":201,"_52":277,"_344":345,"_385":386,"_387":388},"comments",[],"hasVideoHash",false,"isAiGenerated","question",{"_40":41,"_42":43,"_44":45,"_46":47,"_78":79,"_93":43,"_94":95,"_96":97,"_98":16},"correctOptionId","cbe1cd74-2365-49c5-a7aa-d1d346856428","difficulty","","id","7f3c3e80-9c0e-4f34-9841-eebb3075b553","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","128819815","answerCount",1,"isIndexable","mainSubject",{"_44":57,"_58":59,"_60":61},"isIndexableSEO","materialFormat","Text","studentDegreeLevel","Graduate","source","PD","externalId","142612633","options",[80,85,89],{"_44":41,"_81":82,"_83":84},"label","A","text","\\sigma_A=-231 \\text{ MPa} e \\sigma_B=132,6 \\text{ MPa}",{"_44":86,"_81":87,"_83":88},"e0f6b6b1-ae8d-4f7c-b13e-e62354c3f755","B","\\sigma_A=38,5 \\text{ MPa} e \\sigma_B=-22,1 \\text{ MPa}",{"_44":90,"_81":91,"_83":92},"1b18677b-13ec-467a-a6c8-c5ec7712326c","C","\\sigma_A=-38,5 \\text{ MPa} e \\sigma_B=22,1 \\text{ MPa}","solution_explanation","statement","

Para a barra curva e o carregamento mostrado, determine a máxima tensão nos pontos A e B para r1=8 mm.

","status","pending_classification","hasRelatedVideo","relatedVideos",[101],{"_102":103,"_121":122,"_52":137,"_172":173,"_190":191},"content",{"_44":104,"_58":105,"_106":-5,"_107":108,"_109":110,"_111":-5,"_46":112,"_115":116,"_117":116,"_118":-5,"_119":120},"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",{"_113":114},"external_id","4963","created_at","2025-08-20T12:27:41.608438+00:00","updated_at","content_group_id","slug","optica-geometrica-parte-1","prometheusData",{"_123":124,"_130":131,"_132":133,"_134":135,"_28":136},"provider",{"_44":125,"_126":127,"_128":129},"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",[138],{"_44":139,"_58":140,"_60":141,"_142":143,"_144":-5,"_115":145,"_117":145,"_46":146,"_119":141,"_153":154},"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",{"_147":148,"_149":150,"_151":152},"childrenCount",18,"content_count",0,"question_count",135489,"children",[155],{"_44":156,"_58":157,"_60":158,"_142":143,"_144":139,"_115":159,"_117":159,"_46":160,"_119":163,"_153":164},"ca6fee0e-79c6-4f1c-b500-ee081a071949","Mecânica","mecanica","2025-04-29T02:19:12.828432+00:00",{"_147":161,"_149":150,"_151":162},10,19948,"mecanica-2",[165],{"_44":166,"_58":59,"_60":61,"_142":143,"_144":156,"_115":167,"_117":167,"_46":168,"_119":170,"_153":171},"ac55bdba-154d-42e7-bc25-72dde822663d","2025-04-29T03:44:29.139762+00:00",{"_147":150,"_149":150,"_151":169},3376,"resistencia-dos-materiais-4",[],"video",{"_44":110,"_13":105,"_106":-5,"_174":175,"_176":177,"_28":-5,"_178":-5,"_123":177,"_179":180,"_134":-5,"_181":-5,"_182":-5,"_183":-5,"_184":-5,"_46":185,"_186":150,"_187":-5,"_96":188,"_115":189,"_117":189},"duration",20,"source_type","prometheus","iframe_url","provider_video_id","1cd3d633-d690-4f4b-9995-9b0e44994e35","format","quality","file_path","file_size",{"_113":114},"views_count","last_played_at","draft","2025-08-19T11:56:20.758718+00:00","tag",{"_44":139,"_58":140,"_60":141,"_142":143,"_144":-5,"_115":145,"_117":145,"_46":192,"_119":141,"_153":193},{"_147":148,"_149":150,"_151":152},[194],{"_44":156,"_58":157,"_60":158,"_142":143,"_144":139,"_115":159,"_117":159,"_46":195,"_119":163,"_153":196},{"_147":161,"_149":150,"_151":162},[197],{"_44":166,"_58":59,"_60":61,"_142":143,"_144":156,"_115":167,"_117":167,"_46":198,"_119":170,"_153":199},{"_147":150,"_149":150,"_151":169},[],"similarQuestions",[202,234,254],{"_40":203,"_42":43,"_44":204,"_78":205,"_93":222,"_94":223,"_52":224},"112831da-be9c-458e-94cb-e8292d0dba12","3c0b9441-b878-4896-8bac-fa4ca61e3f13",[206,209,212,215,219],{"_44":207,"_81":82,"_83":208},"265bd71a-6749-41f5-b291-67efd646ca64","y'' + 2y' - 3y = 0",{"_44":210,"_81":87,"_83":211},"6d3c3a1d-8e80-4ff3-b97a-d5b5bca91940","6y'' - y' - y = 0",{"_44":213,"_81":91,"_83":214},"4168ac67-64fd-46ed-a69c-a01dbfcde7ea","y'' - 2y' + y = 0",{"_44":216,"_81":217,"_83":218},"cc7bc8df-6995-4264-ac5a-32ea9b4ed7db","D","9y'' + 6y' + y = 0",{"_44":203,"_81":220,"_83":221},"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

",[225],{"_44":226,"_58":227,"_60":228,"_142":143,"_144":229,"_115":230,"_117":230,"_46":231,"_119":228},"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",{"_147":232,"_149":150,"_151":233},4,12302,{"_40":235,"_42":43,"_44":236,"_78":237,"_93":249,"_94":250,"_52":251},"6831a9b9-c9a4-4a76-bd7a-2ce98bfea875","93a32dd4-5fc6-4ccb-a76f-4724bf113742",[238,241,244,246],{"_44":239,"_81":82,"_83":240},"13e3f476-a0a5-421f-b47e-0969e8e9a7e0","

Verdadeiro, verdadeiro, falso

",{"_44":242,"_81":87,"_83":243},"c9a20855-d84b-4860-8b35-9784818282cf","

Falso, verdadeiro, verdadeiro

",{"_44":235,"_81":91,"_83":245},"

Verdadeiro, falso, verdadeiro

",{"_44":247,"_81":217,"_83":248},"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????",[275],{"_44":226,"_58":227,"_60":228,"_142":143,"_144":229,"_115":230,"_117":230,"_46":276,"_119":228},{"_147":232,"_149":150,"_151":233},[278,280,289,295,299,301,303,311,316,324,326,331,337],{"_44":226,"_58":227,"_60":228,"_142":143,"_144":229,"_115":230,"_117":230,"_46":279,"_119":228},{"_147":232,"_149":150,"_151":233},{"_44":281,"_58":282,"_60":283,"_142":143,"_144":284,"_115":159,"_117":159,"_46":285,"_119":288},"861ad829-750d-4a44-9569-2f18b430b4df","Engenharia Mecatrônica","engenharia-mecatronica","eb9315c5-bd04-4116-aa46-02c4fde320c0",{"_147":286,"_149":150,"_151":287},5,30614,"engenharia-mecatronica-1",{"_44":290,"_58":59,"_60":61,"_142":143,"_144":291,"_115":292,"_117":292,"_46":293,"_119":294},"8850e507-a691-4d45-a7c7-16221e9c5af2","88fe96b3-2a17-4198-90d5-ddda3d6f5d45","2025-04-29T04:00:13.215003+00:00",{"_147":150,"_149":150,"_151":169},"resistencia-dos-materiais-6",{"_44":291,"_58":157,"_60":158,"_142":143,"_144":281,"_115":230,"_117":230,"_46":296,"_119":298},{"_147":286,"_149":150,"_151":297},25741,"mecanica-3",{"_44":139,"_58":140,"_60":141,"_142":143,"_144":-5,"_115":145,"_117":145,"_46":300,"_119":141},{"_147":148,"_149":150,"_151":152},{"_44":166,"_58":59,"_60":61,"_142":143,"_144":156,"_115":167,"_117":167,"_46":302,"_119":170},{"_147":150,"_149":150,"_151":169},{"_44":304,"_58":305,"_60":306,"_142":143,"_144":284,"_115":159,"_117":159,"_46":307,"_119":310},"b6e37f32-f8e5-4025-bf0f-69ffc00fb331","Engenharia Civil","engenharia-civil",{"_147":308,"_149":150,"_151":309},21,45865,"engenharia-civil-3",{"_44":229,"_58":312,"_60":313,"_142":143,"_144":284,"_115":159,"_117":159,"_46":314,"_119":315},"Engenharia de Petróleo","engenharia-de-petroleo",{"_147":286,"_149":150,"_151":233},"engenharia-de-petroleo-1",{"_44":317,"_58":318,"_60":319,"_142":143,"_144":304,"_115":320,"_117":320,"_46":321,"_119":323},"c5bf57d4-c3d8-4365-b53e-085fa14a3a95","Estruturas","estruturas","2025-04-29T03:44:32.303369+00:00",{"_147":286,"_149":150,"_151":322},8852,"estruturas-1",{"_44":156,"_58":157,"_60":158,"_142":143,"_144":139,"_115":159,"_117":159,"_46":325,"_119":163},{"_147":161,"_149":150,"_151":162},{"_44":327,"_58":59,"_60":61,"_142":143,"_144":226,"_115":328,"_117":328,"_46":329,"_119":330},"d1e4567b-f68a-49e1-b3e5-3888343d7871","2025-04-29T04:00:14.680867+00:00",{"_147":150,"_149":150,"_151":169},"resistencia-dos-materiais-7",{"_44":332,"_58":333,"_60":61,"_142":143,"_144":317,"_115":334,"_117":334,"_46":335,"_119":336},"da8d2ecf-e949-4afc-966f-98b4b367fac1","Resistencia dos Materiais","2025-04-29T04:00:06.9766+00:00",{"_147":150,"_149":150,"_151":169},"resistencia-dos-materiais-5",{"_44":284,"_58":338,"_60":339,"_142":143,"_144":-5,"_115":340,"_117":340,"_46":341,"_119":339},"Engenharia","engenharia","2025-04-29T01:55:38.635246+00:00",{"_147":342,"_149":150,"_151":343},29,351586,"tagsTree",[346,355],{"_44":139,"_58":140,"_60":141,"_142":143,"_144":-5,"_115":145,"_117":145,"_46":347,"_119":141,"_153":348},{"_147":148,"_149":150,"_151":152},[349],{"_44":156,"_58":157,"_60":158,"_142":143,"_144":139,"_115":159,"_117":159,"_46":350,"_119":163,"_153":351},{"_147":161,"_149":150,"_151":162},[352],{"_44":166,"_58":59,"_60":61,"_142":143,"_144":156,"_115":167,"_117":167,"_46":353,"_119":170,"_153":354},{"_147":150,"_149":150,"_151":169},[],{"_44":284,"_58":338,"_60":339,"_142":143,"_144":-5,"_115":340,"_117":340,"_46":356,"_119":339,"_153":357},{"_147":342,"_149":150,"_151":343},[358,367,376],{"_44":281,"_58":282,"_60":283,"_142":143,"_144":284,"_115":159,"_117":159,"_46":359,"_119":288,"_153":360},{"_147":286,"_149":150,"_151":287},[361],{"_44":291,"_58":157,"_60":158,"_142":143,"_144":281,"_115":230,"_117":230,"_46":362,"_119":298,"_153":363},{"_147":286,"_149":150,"_151":297},[364],{"_44":290,"_58":59,"_60":61,"_142":143,"_144":291,"_115":292,"_117":292,"_46":365,"_119":294,"_153":366},{"_147":150,"_149":150,"_151":169},[],{"_44":304,"_58":305,"_60":306,"_142":143,"_144":284,"_115":159,"_117":159,"_46":368,"_119":310,"_153":369},{"_147":308,"_149":150,"_151":309},[370],{"_44":317,"_58":318,"_60":319,"_142":143,"_144":304,"_115":320,"_117":320,"_46":371,"_119":323,"_153":372},{"_147":286,"_149":150,"_151":322},[373],{"_44":332,"_58":333,"_60":61,"_142":143,"_144":317,"_115":334,"_117":334,"_46":374,"_119":336,"_153":375},{"_147":150,"_149":150,"_151":169},[],{"_44":229,"_58":312,"_60":313,"_142":143,"_144":284,"_115":159,"_117":159,"_46":377,"_119":315,"_153":378},{"_147":286,"_149":150,"_151":233},[379],{"_44":226,"_58":227,"_60":228,"_142":143,"_144":229,"_115":230,"_117":230,"_46":380,"_119":228,"_153":381},{"_147":232,"_149":150,"_151":233},[382],{"_44":327,"_58":59,"_60":61,"_142":143,"_144":226,"_115":328,"_117":328,"_46":383,"_119":330,"_153":384},{"_147":150,"_149":150,"_151":169},[],"videoDislikes",{},"videoLikes",{},"actionData","errors"]

Comentários