[{"_1":2,"_228":-5,"_229":-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/b51c3ecf-2ae0-4427-8785-980e50d9c3de","user","pages/questions/show/index",{"_33":34,"_35":36,"_37":36,"_38":39,"_106":107,"_108":109,"_50":191,"_213":214,"_224":225,"_226":227},"comments",[],"hasVideoHash",false,"isAiGenerated","question",{"_40":41,"_42":41,"_43":44,"_45":46,"_80":81,"_100":41,"_101":102,"_103":104,"_105":36},"correctOptionId","","difficulty","id","b51c3ecf-2ae0-4427-8785-980e50d9c3de","metadata",{"_47":48,"_76":77,"_78":79},"pd",{"_49":-5,"_50":51,"_58":59,"_64":65,"_66":67,"_68":16,"_69":70,"_71":16,"_72":73,"_74":75},"area","tags",[52],{"_43":53,"_54":55,"_56":57},156051,"name","Cursos-online","alias","cursos-online","subjects",[60],{"_43":61,"_54":62,"_56":63},678643,"Análise Estrutural","analise-estrutural","materialId","143928180","answerCount",1,"isIndexable","mainSubject",{"_43":61,"_54":62,"_56":63},"isIndexableSEO","materialFormat","Text","studentDegreeLevel","High School","source","PD","externalId","123767339","options",[82,88,92,96],{"_43":83,"_84":85,"_86":87},"1a0c36b9-1e84-48eb-a7e3-d42b33f7718a","label","A","text","

To explain the advantages of empotramiento in wooden posts.

",{"_43":89,"_84":90,"_86":91},"2e1bd543-6ee8-4a4b-9ffb-c9f9ed9a2edd","B","

To present a table with the load capacity of wooden posts.

",{"_43":93,"_84":94,"_86":95},"1d3c9f67-df08-460d-96e7-b16a167a79ad","C","

To discuss the economic distribution of wooden floors.

",{"_43":97,"_84":98,"_86":99},"73d0e3fb-bfd1-4685-9768-4c0ff9263041","D","

To provide a numerical example of the load capacity of wooden floors.

","solution_explanation","statement","

What is the purpose of this text?

","status","pending_classification","hasRelatedVideo","relatedVideos",[],"similarQuestions",[110,152,170],{"_40":111,"_42":41,"_43":112,"_80":113,"_100":129,"_101":130,"_50":131},"112831da-be9c-458e-94cb-e8292d0dba12","3c0b9441-b878-4896-8bac-fa4ca61e3f13",[114,117,120,123,126],{"_43":115,"_84":85,"_86":116},"265bd71a-6749-41f5-b291-67efd646ca64","y'' + 2y' - 3y = 0",{"_43":118,"_84":90,"_86":119},"6d3c3a1d-8e80-4ff3-b97a-d5b5bca91940","6y'' - y' - y = 0",{"_43":121,"_84":94,"_86":122},"4168ac67-64fd-46ed-a69c-a01dbfcde7ea","y'' - 2y' + y = 0",{"_43":124,"_84":98,"_86":125},"cc7bc8df-6995-4264-ac5a-32ea9b4ed7db","9y'' + 6y' + y = 0",{"_43":111,"_84":127,"_86":128},"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

",[132],{"_43":133,"_54":134,"_56":135,"_136":137,"_138":139,"_140":141,"_142":141,"_45":143,"_150":151},"b6e37f32-f8e5-4025-bf0f-69ffc00fb331","Engenharia Civil","engenharia-civil","tag_group_id","c1ce2cf2-b217-4cc7-8182-81c56bd3522d","parent_id","eb9315c5-bd04-4116-aa46-02c4fde320c0","created_at","2025-04-29T02:19:12.828432+00:00","updated_at",{"_144":145,"_146":147,"_148":149},"childrenCount",21,"content_count",0,"question_count",45865,"slug","engenharia-civil-3",{"_40":153,"_42":41,"_43":154,"_80":155,"_100":167,"_101":168,"_50":169},"6831a9b9-c9a4-4a76-bd7a-2ce98bfea875","93a32dd4-5fc6-4ccb-a76f-4724bf113742",[156,159,162,164],{"_43":157,"_84":85,"_86":158},"13e3f476-a0a5-421f-b47e-0969e8e9a7e0","

Verdadeiro, verdadeiro, falso

",{"_43":160,"_84":90,"_86":161},"c9a20855-d84b-4860-8b35-9784818282cf","

Falso, verdadeiro, verdadeiro

",{"_43":153,"_84":94,"_86":163},"

Verdadeiro, falso, verdadeiro

",{"_43":165,"_84":98,"_86":166},"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?

",[132],{"_40":171,"_42":41,"_43":172,"_80":173,"_100":188,"_101":189,"_50":190},"3ce109b1-6cdb-4b4d-8816-a6af4d74bed0","c478a46c-46a8-4942-ae14-2e79def3dda2",[174,177,180,182,185],{"_43":175,"_84":85,"_86":176},"a5a16a42-3e58-4c76-80f2-c291aa2d8e49","Sim",{"_43":178,"_84":90,"_86":179},"5e6d0254-696c-4da0-b572-82e3a19f433e","Não",{"_43":171,"_84":94,"_86":181},"Indeterminado",{"_43":183,"_84":98,"_86":184},"35403f68-a880-429d-97f4-db507c58de38","Todos",{"_43":186,"_84":127,"_86":187},"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????",[132],[132,192,201,206],{"_43":193,"_54":194,"_56":195,"_136":137,"_138":133,"_140":196,"_142":196,"_45":197,"_150":200},"c5bf57d4-c3d8-4365-b53e-085fa14a3a95","Estruturas","estruturas","2025-04-29T03:44:32.303369+00:00",{"_144":198,"_146":147,"_148":199},5,8852,"estruturas-1",{"_43":202,"_54":62,"_56":63,"_136":137,"_138":193,"_140":203,"_142":203,"_45":204,"_150":63},"e9d666f5-dcb8-4aa3-abc7-27cfb929e3b6","2025-04-29T04:00:06.9766+00:00",{"_144":147,"_146":147,"_148":205},4694,{"_43":139,"_54":207,"_56":208,"_136":137,"_138":-5,"_140":209,"_142":209,"_45":210,"_150":208},"Engenharia","engenharia","2025-04-29T01:55:38.635246+00:00",{"_144":211,"_146":147,"_148":212},29,351586,"tagsTree",[215],{"_43":139,"_54":207,"_56":208,"_136":137,"_138":-5,"_140":209,"_142":209,"_45":210,"_150":208,"_216":217},"children",[218],{"_43":133,"_54":134,"_56":135,"_136":137,"_138":139,"_140":141,"_142":141,"_45":143,"_150":151,"_216":219},[220],{"_43":193,"_54":194,"_56":195,"_136":137,"_138":133,"_140":196,"_142":196,"_45":197,"_150":200,"_216":221},[222],{"_43":202,"_54":62,"_56":63,"_136":137,"_138":193,"_140":203,"_142":203,"_45":204,"_150":63,"_216":223},[],"videoDislikes",{},"videoLikes",{},"actionData","errors"]

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