[{"_1":2,"_358":-5,"_359":-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/73964036-e820-4283-88e2-5cba94642bd1?video=true","user","pages/questions/show/index",{"_33":34,"_35":36,"_37":36,"_38":39,"_107":108,"_199":200,"_51":270,"_332":333,"_354":355,"_356":357},"comments",[],"hasVideoHash",false,"isAiGenerated","question",{"_40":41,"_42":41,"_43":44,"_45":46,"_77":78,"_101":41,"_102":103,"_104":105,"_106":16},"correctOptionId","","difficulty","id","73964036-e820-4283-88e2-5cba94642bd1","metadata",{"_47":48,"_73":74,"_75":76},"pd",{"_49":50,"_51":52,"_53":54,"_61":62,"_63":64,"_65":16,"_66":67,"_68":16,"_69":70,"_71":72},"area","Outros","tags",[],"subjects",[55],{"_43":56,"_57":58,"_59":60},1663620,"name","Resistência dos Materiais","alias","resistencia-dos-materiais","materialId","135934037","answerCount",1,"isIndexable","mainSubject",{"_43":56,"_57":58,"_59":60},"isIndexableSEO","materialFormat","Text","studentDegreeLevel","Graduate","source","PD","externalId","135934125","options",[79,85,89,93,97],{"_43":80,"_81":82,"_83":84},"0c9530d6-7f48-4b5b-80ae-f0f916e5471f","label","A","text","XC = 350,00 \\, mm e YC = 357,50 \\, mm",{"_43":86,"_81":87,"_83":88},"9bced9b8-4f8d-4c45-af9e-eeb24785b4a3","B","XC = 450,00 \\, mm e YC = 357,50 \\, mm",{"_43":90,"_81":91,"_83":92},"0d19f04b-e61a-4ad4-8bbb-5261858c8794","C","XC = 450,00 \\, mm e YC = 258,50 \\, mm",{"_43":94,"_81":95,"_83":96},"5be296c6-dfd7-4944-acfd-1631c588bc26","D","XC = 350,00 \\, mm e YC = 295,50 \\, mm",{"_43":98,"_81":99,"_83":100},"10882f75-2a5d-4ca4-bd6a-f644d9ca371c","E","XC = 450,00 \\, mm e YC = 295,50 \\, mm","solution_explanation","statement","Encontre o centro de gravidade da seção transversal de uma viga, mostrada abaixo","status","pending_classification","hasRelatedVideo","relatedVideos",[109],{"_110":111,"_129":130,"_51":145,"_180":181,"_198":146},"content",{"_43":112,"_57":113,"_114":-5,"_115":116,"_117":118,"_119":-5,"_45":120,"_123":124,"_125":124,"_126":-5,"_127":128},"468e3e62-35e0-47be-a15f-68dd43bb32bb","Óptica Geométrica - 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3y = 0",{"_43":209,"_81":87,"_83":210},"6d3c3a1d-8e80-4ff3-b97a-d5b5bca91940","6y'' - y' - y = 0",{"_43":212,"_81":91,"_83":213},"4168ac67-64fd-46ed-a69c-a01dbfcde7ea","y'' - 2y' + y = 0",{"_43":215,"_81":95,"_83":216},"cc7bc8df-6995-4264-ac5a-32ea9b4ed7db","9y'' + 6y' + y = 0",{"_43":202,"_81":99,"_83":218},"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

",[222],{"_43":223,"_57":224,"_59":225,"_150":151,"_152":226,"_123":227,"_125":227,"_45":228,"_127":225},"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":229,"_157":158,"_159":230},4,12302,{"_40":232,"_42":41,"_43":233,"_77":234,"_101":246,"_102":247,"_51":248},"6831a9b9-c9a4-4a76-bd7a-2ce98bfea875","93a32dd4-5fc6-4ccb-a76f-4724bf113742",[235,238,241,243],{"_43":236,"_81":82,"_83":237},"13e3f476-a0a5-421f-b47e-0969e8e9a7e0","

Verdadeiro, verdadeiro, falso

",{"_43":239,"_81":87,"_83":240},"c9a20855-d84b-4860-8b35-9784818282cf","

Falso, verdadeiro, verdadeiro

",{"_43":232,"_81":91,"_83":242},"

Verdadeiro, falso, verdadeiro

",{"_43":244,"_81":95,"_83":245},"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?

",[222],{"_40":250,"_42":41,"_43":251,"_77":252,"_101":267,"_102":268,"_51":269},"3ce109b1-6cdb-4b4d-8816-a6af4d74bed0","c478a46c-46a8-4942-ae14-2e79def3dda2",[253,256,259,261,264],{"_43":254,"_81":82,"_83":255},"a5a16a42-3e58-4c76-80f2-c291aa2d8e49","Sim",{"_43":257,"_81":87,"_83":258},"5e6d0254-696c-4da0-b572-82e3a19f433e","Não",{"_43":250,"_81":91,"_83":260},"Indeterminado",{"_43":262,"_81":95,"_83":263},"35403f68-a880-429d-97f4-db507c58de38","Todos",{"_43":265,"_81":99,"_83":266},"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????",[222],[222,271,280,286,290,291,292,300,305,313,314,319,325],{"_43":272,"_57":273,"_59":274,"_150":151,"_152":275,"_123":167,"_125":167,"_45":276,"_127":279},"861ad829-750d-4a44-9569-2f18b430b4df","Engenharia Mecatrônica","engenharia-mecatronica","eb9315c5-bd04-4116-aa46-02c4fde320c0",{"_155":277,"_157":158,"_159":278},5,30614,"engenharia-mecatronica-1",{"_43":281,"_57":58,"_59":60,"_150":151,"_152":282,"_123":283,"_125":283,"_45":284,"_127":285},"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",{"_43":282,"_57":165,"_59":166,"_150":151,"_152":272,"_123":227,"_125":227,"_45":287,"_127":289},{"_155":277,"_157":158,"_159":288},25741,"mecanica-3",{"_43":147,"_57":148,"_59":149,"_150":151,"_152":-5,"_123":153,"_125":153,"_45":154,"_127":149},{"_43":174,"_57":58,"_59":60,"_150":151,"_152":164,"_123":175,"_125":175,"_45":176,"_127":178},{"_43":293,"_57":294,"_59":295,"_150":151,"_152":275,"_123":167,"_125":167,"_45":296,"_127":299},"b6e37f32-f8e5-4025-bf0f-69ffc00fb331","Engenharia Civil","engenharia-civil",{"_155":297,"_157":158,"_159":298},21,45865,"engenharia-civil-3",{"_43":226,"_57":301,"_59":302,"_150":151,"_152":275,"_123":167,"_125":167,"_45":303,"_127":304},"Engenharia de Petróleo","engenharia-de-petroleo",{"_155":277,"_157":158,"_159":230},"engenharia-de-petroleo-1",{"_43":306,"_57":307,"_59":308,"_150":151,"_152":293,"_123":309,"_125":309,"_45":310,"_127":312},"c5bf57d4-c3d8-4365-b53e-085fa14a3a95","Estruturas","estruturas","2025-04-29T03:44:32.303369+00:00",{"_155":277,"_157":158,"_159":311},8852,"estruturas-1",{"_43":164,"_57":165,"_59":166,"_150":151,"_152":147,"_123":167,"_125":167,"_45":168,"_127":171},{"_43":315,"_57":58,"_59":60,"_150":151,"_152":223,"_123":316,"_125":316,"_45":317,"_127":318},"d1e4567b-f68a-49e1-b3e5-3888343d7871","2025-04-29T04:00:14.680867+00:00",{"_155":158,"_157":158,"_159":177},"resistencia-dos-materiais-7",{"_43":320,"_57":321,"_59":60,"_150":151,"_152":306,"_123":322,"_125":322,"_45":323,"_127":324},"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",{"_43":275,"_57":326,"_59":327,"_150":151,"_152":-5,"_123":328,"_125":328,"_45":329,"_127":327},"Engenharia","engenharia","2025-04-29T01:55:38.635246+00:00",{"_155":330,"_157":158,"_159":331},29,351586,"tagsTree",[146,334],{"_43":275,"_57":326,"_59":327,"_150":151,"_152":-5,"_123":328,"_125":328,"_45":329,"_127":327,"_161":335},[336,342,348],{"_43":272,"_57":273,"_59":274,"_150":151,"_152":275,"_123":167,"_125":167,"_45":276,"_127":279,"_161":337},[338],{"_43":282,"_57":165,"_59":166,"_150":151,"_152":272,"_123":227,"_125":227,"_45":287,"_127":289,"_161":339},[340],{"_43":281,"_57":58,"_59":60,"_150":151,"_152":282,"_123":283,"_125":283,"_45":284,"_127":285,"_161":341},[],{"_43":293,"_57":294,"_59":295,"_150":151,"_152":275,"_123":167,"_125":167,"_45":296,"_127":299,"_161":343},[344],{"_43":306,"_57":307,"_59":308,"_150":151,"_152":293,"_123":309,"_125":309,"_45":310,"_127":312,"_161":345},[346],{"_43":320,"_57":321,"_59":60,"_150":151,"_152":306,"_123":322,"_125":322,"_45":323,"_127":324,"_161":347},[],{"_43":226,"_57":301,"_59":302,"_150":151,"_152":275,"_123":167,"_125":167,"_45":303,"_127":304,"_161":349},[350],{"_43":223,"_57":224,"_59":225,"_150":151,"_152":226,"_123":227,"_125":227,"_45":228,"_127":225,"_161":351},[352],{"_43":315,"_57":58,"_59":60,"_150":151,"_152":223,"_123":316,"_125":316,"_45":317,"_127":318,"_161":353},[],"videoDislikes",{},"videoLikes",{},"actionData","errors"]

Comentários