[{"_1":2,"_340":-5,"_341":-5},"loaderData",{"_3":4,"_8":9},"root",{"_5":6,"_7":-5},"url","https://prouniversitario.com/exercicios/ff40b2cd-90d7-4ceb-9251-743d89b746c7?video=true","user","pages/questions/show/index",{"_10":11,"_12":13,"_14":13,"_15":16,"_49":50,"_147":148,"_87":253,"_314":315,"_336":337,"_338":339},"comments",[],"hasVideoHash",false,"isAiGenerated","question",{"_17":18,"_19":18,"_20":21,"_22":23,"_42":18,"_43":44,"_45":46,"_47":48},"correctOptionId","","difficulty","id","ff40b2cd-90d7-4ceb-9251-743d89b746c7","options",[24,30,34,38],{"_20":25,"_26":27,"_28":29},"86386057-ce94-4b65-b095-7ed9fd29545a","label","A","text","712 kJ/m³",{"_20":31,"_26":32,"_28":33},"964b20ae-0125-476a-9133-e0f2f4b0e293","B","21,607 kJ/m³",{"_20":35,"_26":36,"_28":37},"32d02591-ddc1-4c22-bbb5-73d698d8f830","C","160,325 kJ/m³",{"_20":39,"_26":40,"_28":41},"4b077d04-4b96-4ee9-b3cd-672c0cca9ae2","D","39,286 kJ/m³","solution_explanation","statement","

Para o a liga de alumínio 1000-HI-4 que tem E = 70 \text{ GPa} e \text{tensão de escoamento} = 55 \text{ MPa}. Determine seu \text{módulo de resiliência}.

","status","has_issues","hasRelatedVideo",true,"relatedVideos",[51],{"_52":53,"_71":72,"_87":88,"_127":128,"_146":89},"content",{"_20":54,"_55":56,"_57":-5,"_58":59,"_60":61,"_62":-5,"_63":64,"_67":68,"_69":68,"_70":-5},"fea1149f-ed42-488e-b8d0-46e5016f329f","name","Relações Trigonométricas no Triângulo Retângulo, Leis dos Senos e Cossenos - 06 - Revisando e Praticando - Parte 06","description","content_type_id","1051eee7-c62e-4b2c-9900-77a29fcec080","resource_id","d7fcad9c-530e-4eec-824f-930373662cdc","user_id","metadata",{"_65":66},"external_id","12593","created_at","2025-08-20T12:27:41.608438+00:00","updated_at","content_group_id","prometheusData",{"_73":74,"_80":81,"_82":83,"_84":85,"_5":86},"provider",{"_20":75,"_76":77,"_78":79},"06f120be-2194-4548-8336-7ba44ffbae14","key","grupo_q_proteus","kind","proteus","reference","c3d18e75-a612-4049-bb1b-05fa8436e75a","state","completed","thumbnail_url","https://proteus.grupoq.io/videos/c3d18e75-a612-4049-bb1b-05fa8436e75a/thumbnailsthumb.0000000.jpg","https://proteus.grupoq.io/videos/c3d18e75-a612-4049-bb1b-05fa8436e75a/levels.m3u8","tags",[89],{"_20":90,"_55":91,"_92":93,"_94":95,"_96":-5,"_67":97,"_69":97,"_63":98,"_105":93,"_106":107},"9772e958-72c6-4499-ad47-877cf94d670d","Exatas","alias","exatas","tag_group_id","c1ce2cf2-b217-4cc7-8182-81c56bd3522d","parent_id","2025-04-29T01:56:45.284172+00:00",{"_99":100,"_101":102,"_103":104},"childrenCount",18,"content_count",0,"question_count",135489,"slug","children",[108],{"_20":109,"_55":110,"_92":111,"_94":95,"_96":90,"_67":112,"_69":112,"_63":113,"_105":116,"_106":117},"ca6fee0e-79c6-4f1c-b500-ee081a071949","Mecânica","mecanica","2025-04-29T02:19:12.828432+00:00",{"_99":114,"_101":102,"_103":115},10,19948,"mecanica-2",[118],{"_20":119,"_55":120,"_92":121,"_94":95,"_96":109,"_67":122,"_69":122,"_63":123,"_105":125,"_106":126},"ac55bdba-154d-42e7-bc25-72dde822663d","Resistência dos Materiais","resistencia-dos-materiais","2025-04-29T03:44:29.139762+00:00",{"_99":102,"_101":102,"_103":124},3376,"resistencia-dos-materiais-4",[],"video",{"_20":61,"_129":56,"_57":-5,"_130":131,"_132":133,"_5":-5,"_134":-5,"_73":133,"_135":136,"_84":-5,"_137":-5,"_138":-5,"_139":-5,"_140":-5,"_63":141,"_142":102,"_143":-5,"_45":144,"_67":145,"_69":145},"title","duration",21,"source_type","prometheus","iframe_url","provider_video_id","8335867d-4f35-401e-a9c3-13c4a0db8c56","format","quality","file_path","file_size",{"_65":66},"views_count","last_played_at","draft","2025-08-19T11:56:14.613229+00:00","tag","similarQuestions",[149,179,196,213,233],{"_17":18,"_19":18,"_20":150,"_22":151,"_42":18,"_43":168,"_87":169},"3c0b9441-b878-4896-8bac-fa4ca61e3f13",[152,155,158,161,164],{"_20":153,"_26":27,"_28":154},"265bd71a-6749-41f5-b291-67efd646ca64","y'' + 2y' - 3y = 0",{"_20":156,"_26":32,"_28":157},"6d3c3a1d-8e80-4ff3-b97a-d5b5bca91940","6y'' - y' - y = 0",{"_20":159,"_26":36,"_28":160},"4168ac67-64fd-46ed-a69c-a01dbfcde7ea","y'' - 2y' + y = 0",{"_20":162,"_26":40,"_28":163},"cc7bc8df-6995-4264-ac5a-32ea9b4ed7db","9y'' + 6y' + y = 0",{"_20":165,"_26":166,"_28":167},"112831da-be9c-458e-94cb-e8292d0dba12","E","y'' - 2y' + 6y = 0","

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

",[170],{"_20":171,"_55":172,"_92":173,"_94":95,"_96":174,"_67":175,"_69":175,"_63":176,"_105":173},"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",{"_99":177,"_101":102,"_103":178},4,12302,{"_17":18,"_19":18,"_20":180,"_22":181,"_42":18,"_43":194,"_87":195},"4a3f20e5-655d-4a84-bbdf-aa3b0de4581a",[182,185,188,191],{"_20":183,"_26":27,"_28":184},"8dee6a5e-57a3-4743-8b5a-da9b8c54fb32","Verdadero, verdadero, verdadero, verdadero.",{"_20":186,"_26":32,"_28":187},"ca0a9b0d-3004-478e-9ca9-bafa5243aca9","Verdadero, verdadero, falso, verdadero.",{"_20":189,"_26":36,"_28":190},"68712800-8b4b-46af-9cdf-3f83e4032c30","Verdadero, falso, verdadero, falso.",{"_20":192,"_26":40,"_28":193},"1f5e395b-c362-4503-8261-dcfcae96b1ce","Falso, verdadero, verdadeiro, verdadeiro.","

Divide el polinomio p(x) = 3x^4 + 4x^3 + x^2 entre el polinomio q(x) = 2+x. Como el polinomio divisor, q(x), es de grado 2, debemos encontrar dos polinomios, un polinomio cociente (c(x)) y un polinomio resto (r(x)) de grado 1 o 0, tales que p(x) = q(x) * c(x) + r(x).

El polinomio p(x) es de grado 4.

El polinomio q(x) es de grado 1.

El polinomio cociente c(x) es de grado 2.

El polinomio resto r(x) es de grado 1 o 0.

",[170],{"_17":18,"_19":18,"_20":197,"_22":198,"_42":18,"_43":211,"_87":212},"93a32dd4-5fc6-4ccb-a76f-4724bf113742",[199,202,205,208],{"_20":200,"_26":27,"_28":201},"13e3f476-a0a5-421f-b47e-0969e8e9a7e0","

Verdadeiro, verdadeiro, falso

",{"_20":203,"_26":32,"_28":204},"c9a20855-d84b-4860-8b35-9784818282cf","

Falso, verdadeiro, verdadeiro

",{"_20":206,"_26":36,"_28":207},"6831a9b9-c9a4-4a76-bd7a-2ce98bfea875","

Verdadeiro, falso, verdadeiro

",{"_20":209,"_26":40,"_28":210},"3c98539b-1af9-4d44-aecd-c266754a2075","

Falso, falso, falso

","

Qual é a idade da madeira na qual 85,5\\% do C-14 se decompos?

",[170],{"_17":18,"_19":18,"_20":214,"_22":215,"_42":18,"_43":231,"_87":232},"996628fc-4ac3-4821-86bd-839f86a97a6d",[216,219,222,225,228],{"_20":217,"_26":27,"_28":218},"5ad09994-6dcb-4c66-87ae-ec00e9b439b7","5 + 3x < 2x + 4",{"_20":220,"_26":32,"_28":221},"b3ae9948-890b-4807-b801-1e1888cb0c10","3 + 4x \\leq 8x + 6",{"_20":223,"_26":36,"_28":224},"d2964603-f26c-4be6-99ae-d174678f104c","5 + 4x > 3x + 2",{"_20":226,"_26":40,"_28":227},"88c48b1a-ce37-4eae-a900-a4fb4bd581d9","1 + 3x \\geq 5x + 7",{"_20":229,"_26":166,"_28":230},"155e0bb0-6c7f-4d9c-96e5-d1cdb97c632b","4(3 + 2x) < -(6x + 8)","Resolver las siguientes inecuaciones y representar la solución en la recta real:",[170],{"_17":18,"_19":18,"_20":234,"_22":235,"_42":18,"_43":251,"_87":252},"c478a46c-46a8-4942-ae14-2e79def3dda2",[236,239,242,245,248],{"_20":237,"_26":27,"_28":238},"a5a16a42-3e58-4c76-80f2-c291aa2d8e49","Sim",{"_20":240,"_26":32,"_28":241},"5e6d0254-696c-4da0-b572-82e3a19f433e","Não",{"_20":243,"_26":36,"_28":244},"3ce109b1-6cdb-4b4d-8816-a6af4d74bed0","Indeterminado",{"_20":246,"_26":40,"_28":247},"35403f68-a880-429d-97f4-db507c58de38","Todos",{"_20":249,"_26":166,"_28":250},"2e06d948-d37e-4350-afc7-ced04941bcaf","Nenhum","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????",[170],[170,254,263,269,273,274,275,282,287,295,296,301,307],{"_20":255,"_55":256,"_92":257,"_94":95,"_96":258,"_67":112,"_69":112,"_63":259,"_105":262},"861ad829-750d-4a44-9569-2f18b430b4df","Engenharia Mecatrônica","engenharia-mecatronica","eb9315c5-bd04-4116-aa46-02c4fde320c0",{"_99":260,"_101":102,"_103":261},5,30614,"engenharia-mecatronica-1",{"_20":264,"_55":120,"_92":121,"_94":95,"_96":265,"_67":266,"_69":266,"_63":267,"_105":268},"8850e507-a691-4d45-a7c7-16221e9c5af2","88fe96b3-2a17-4198-90d5-ddda3d6f5d45","2025-04-29T04:00:13.215003+00:00",{"_99":102,"_101":102,"_103":124},"resistencia-dos-materiais-6",{"_20":265,"_55":110,"_92":111,"_94":95,"_96":255,"_67":175,"_69":175,"_63":270,"_105":272},{"_99":260,"_101":102,"_103":271},25741,"mecanica-3",{"_20":90,"_55":91,"_92":93,"_94":95,"_96":-5,"_67":97,"_69":97,"_63":98,"_105":93},{"_20":119,"_55":120,"_92":121,"_94":95,"_96":109,"_67":122,"_69":122,"_63":123,"_105":125},{"_20":276,"_55":277,"_92":278,"_94":95,"_96":258,"_67":112,"_69":112,"_63":279,"_105":281},"b6e37f32-f8e5-4025-bf0f-69ffc00fb331","Engenharia Civil","engenharia-civil",{"_99":131,"_101":102,"_103":280},45865,"engenharia-civil-3",{"_20":174,"_55":283,"_92":284,"_94":95,"_96":258,"_67":112,"_69":112,"_63":285,"_105":286},"Engenharia de Petróleo","engenharia-de-petroleo",{"_99":260,"_101":102,"_103":178},"engenharia-de-petroleo-1",{"_20":288,"_55":289,"_92":290,"_94":95,"_96":276,"_67":291,"_69":291,"_63":292,"_105":294},"c5bf57d4-c3d8-4365-b53e-085fa14a3a95","Estruturas","estruturas","2025-04-29T03:44:32.303369+00:00",{"_99":260,"_101":102,"_103":293},8852,"estruturas-1",{"_20":109,"_55":110,"_92":111,"_94":95,"_96":90,"_67":112,"_69":112,"_63":113,"_105":116},{"_20":297,"_55":120,"_92":121,"_94":95,"_96":171,"_67":298,"_69":298,"_63":299,"_105":300},"d1e4567b-f68a-49e1-b3e5-3888343d7871","2025-04-29T04:00:14.680867+00:00",{"_99":102,"_101":102,"_103":124},"resistencia-dos-materiais-7",{"_20":302,"_55":303,"_92":121,"_94":95,"_96":288,"_67":304,"_69":304,"_63":305,"_105":306},"da8d2ecf-e949-4afc-966f-98b4b367fac1","Resistencia dos Materiais","2025-04-29T04:00:06.9766+00:00",{"_99":102,"_101":102,"_103":124},"resistencia-dos-materiais-5",{"_20":258,"_55":308,"_92":309,"_94":95,"_96":-5,"_67":310,"_69":310,"_63":311,"_105":309},"Engenharia","engenharia","2025-04-29T01:55:38.635246+00:00",{"_99":312,"_101":102,"_103":313},29,351586,"tagsTree",[89,316],{"_20":258,"_55":308,"_92":309,"_94":95,"_96":-5,"_67":310,"_69":310,"_63":311,"_105":309,"_106":317},[318,324,330],{"_20":255,"_55":256,"_92":257,"_94":95,"_96":258,"_67":112,"_69":112,"_63":259,"_105":262,"_106":319},[320],{"_20":265,"_55":110,"_92":111,"_94":95,"_96":255,"_67":175,"_69":175,"_63":270,"_105":272,"_106":321},[322],{"_20":264,"_55":120,"_92":121,"_94":95,"_96":265,"_67":266,"_69":266,"_63":267,"_105":268,"_106":323},[],{"_20":276,"_55":277,"_92":278,"_94":95,"_96":258,"_67":112,"_69":112,"_63":279,"_105":281,"_106":325},[326],{"_20":288,"_55":289,"_92":290,"_94":95,"_96":276,"_67":291,"_69":291,"_63":292,"_105":294,"_106":327},[328],{"_20":302,"_55":303,"_92":121,"_94":95,"_96":288,"_67":304,"_69":304,"_63":305,"_105":306,"_106":329},[],{"_20":174,"_55":283,"_92":284,"_94":95,"_96":258,"_67":112,"_69":112,"_63":285,"_105":286,"_106":331},[332],{"_20":171,"_55":172,"_92":173,"_94":95,"_96":174,"_67":175,"_69":175,"_63":176,"_105":173,"_106":333},[334],{"_20":297,"_55":120,"_92":121,"_94":95,"_96":171,"_67":298,"_69":298,"_63":299,"_105":300,"_106":335},[],"videoDislikes",{},"videoLikes",{},"actionData","errors"]

Comentários