[{"_1":2,"_384":-5,"_385":-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/5fc80b8b-cff5-46c3-9783-16fe3d57526a","user","pages/questions/show/index",{"_33":34,"_35":36,"_37":36,"_38":39,"_133":134,"_225":226,"_50":296,"_358":359,"_380":381,"_382":383},"comments",[],"hasVideoHash",false,"isAiGenerated","question",{"_40":41,"_42":41,"_43":44,"_45":46,"_103":104,"_127":41,"_128":129,"_130":131,"_132":16},"correctOptionId","","difficulty","id","5fc80b8b-cff5-46c3-9783-16fe3d57526a","metadata",{"_47":48,"_99":100,"_101":102},"pd",{"_49":-5,"_50":51,"_82":83,"_87":88,"_89":90,"_91":16,"_92":93,"_94":16,"_95":96,"_97":98},"area","tags",[52,58,62,66,70,74,78],{"_43":53,"_54":55,"_56":57},98,"name","Exercício","alias","exercicio",{"_43":59,"_54":60,"_56":61},3433,"Resistência dos materiais","resistencia-dos-materiais",{"_43":63,"_54":64,"_56":65},3679,"Tensão de cisalhamento","tensao-de-cisalhamento",{"_43":67,"_54":68,"_56":69},69163,"Lei-de-Hooke","lei-de-hooke",{"_43":71,"_54":72,"_56":73},1199147,"#respostas #respostascertas","%23respostas%23respostascertas",{"_43":75,"_54":76,"_56":77},1312200,"Lei de Hooke, tração e compressão","lei-de-hooke-tracao-e-compressao",{"_43":79,"_54":80,"_56":81},1312201,"flambagem e dimensionamento de peças comprimidas.","flambagem-e-dimensionamento-de-pecas-comprimidas","subjects",[84],{"_43":85,"_54":86,"_56":61},1663620,"Resistência dos Materiais","materialId","122625747","answerCount",1,"isIndexable","mainSubject",{"_43":85,"_54":86,"_56":61},"isIndexableSEO","materialFormat","Text","studentDegreeLevel","High School","source","PD","externalId","122748122","options",[105,111,115,119,123],{"_43":106,"_107":108,"_109":110},"68341ad3-b7d4-47cc-8f47-a16ec1d35695","label","A","text","P = 22.10 \text{ kN}",{"_43":112,"_107":113,"_109":114},"c179107c-1ea9-4201-8769-6987359aab83","B","P = 14.62 \text{ kN}",{"_43":116,"_107":117,"_109":118},"f9a26d54-eb04-48bc-b145-b4ec590d49b5","C","P = 15.87 \text{ kN}",{"_43":120,"_107":121,"_109":122},"17f5ba38-cf60-4528-b87b-69953eda66b9","D","P = 4.32 \text{ kN}",{"_43":124,"_107":125,"_109":126},"80e8606c-43be-474b-ab8b-e8c45d2dee2c","E","P = 24.64 \text{ kN}","solution_explanation","statement","Determine the maximum eccentric load P that can be applied at the top without causing buckling. Consider E = 12 \text{ GPa} and f_y = 56 \text{ MPa}. A wooden column embedded at the base and top has a length of 3.60 \text{ m} and a cross section of 38 \times 88 \text{ mm}.","status","pending_classification","hasRelatedVideo","relatedVideos",[135],{"_136":137,"_155":156,"_50":171,"_206":207,"_224":172},"content",{"_43":138,"_54":139,"_140":-5,"_141":142,"_143":144,"_145":-5,"_45":146,"_149":150,"_151":150,"_152":-5,"_153":154},"f5895c2c-17bd-4165-86cc-683ff24676d3","Equação Logarítmica - Resolução de Equações Logarítmicas - Parte 02","description","content_type_id","1051eee7-c62e-4b2c-9900-77a29fcec080","resource_id","f4c15931-d540-4f99-b0bc-f92745890a8d","user_id",{"_147":148},"external_id","11503","created_at","2025-08-20T12:27:41.608438+00:00","updated_at","content_group_id","slug","equacao-logaritmica-resolucao-de-equacoes-logaritmicas-parte-02","prometheusData",{"_157":158,"_164":165,"_166":167,"_168":169,"_28":170},"provider",{"_43":159,"_160":161,"_162":163},"06f120be-2194-4548-8336-7ba44ffbae14","key","grupo_q_proteus","kind","proteus","reference","284b5e72-780d-4388-a0f3-4cfe8643c4ad","state","completed","thumbnail_url","https://proteus.grupoq.io/videos/284b5e72-780d-4388-a0f3-4cfe8643c4ad/thumbnailsthumb.0000000.jpg","https://proteus.grupoq.io/videos/284b5e72-780d-4388-a0f3-4cfe8643c4ad/levels.m3u8",[172],{"_43":173,"_54":174,"_56":175,"_176":177,"_178":-5,"_149":179,"_151":179,"_45":180,"_153":175,"_187":188},"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",{"_181":182,"_183":184,"_185":186},"childrenCount",18,"content_count",0,"question_count",135489,"children",[189],{"_43":190,"_54":191,"_56":192,"_176":177,"_178":173,"_149":193,"_151":193,"_45":194,"_153":197,"_187":198},"ca6fee0e-79c6-4f1c-b500-ee081a071949","Mecânica","mecanica","2025-04-29T02:19:12.828432+00:00",{"_181":195,"_183":184,"_185":196},10,19948,"mecanica-2",[199],{"_43":200,"_54":86,"_56":61,"_176":177,"_178":190,"_149":201,"_151":201,"_45":202,"_153":204,"_187":205},"ac55bdba-154d-42e7-bc25-72dde822663d","2025-04-29T03:44:29.139762+00:00",{"_181":184,"_183":184,"_185":203},3376,"resistencia-dos-materiais-4",[],"video",{"_43":144,"_13":139,"_140":-5,"_208":209,"_210":211,"_28":-5,"_212":-5,"_157":211,"_213":214,"_168":-5,"_215":-5,"_216":-5,"_217":-5,"_218":-5,"_45":219,"_220":184,"_221":-5,"_130":222,"_149":223,"_151":223},"duration",19,"source_type","prometheus","iframe_url","provider_video_id","ede34503-2720-4e6f-8a56-95cf27518ed0","format","quality","file_path","file_size",{"_147":148},"views_count","last_played_at","draft","2025-08-19T11:56:14.613229+00:00","tag","similarQuestions",[227,257,275],{"_40":228,"_42":41,"_43":229,"_103":230,"_127":245,"_128":246,"_50":247},"112831da-be9c-458e-94cb-e8292d0dba12","3c0b9441-b878-4896-8bac-fa4ca61e3f13",[231,234,237,240,243],{"_43":232,"_107":108,"_109":233},"265bd71a-6749-41f5-b291-67efd646ca64","y'' + 2y' - 3y = 0",{"_43":235,"_107":113,"_109":236},"6d3c3a1d-8e80-4ff3-b97a-d5b5bca91940","6y'' - y' - y = 0",{"_43":238,"_107":117,"_109":239},"4168ac67-64fd-46ed-a69c-a01dbfcde7ea","y'' - 2y' + y = 0",{"_43":241,"_107":121,"_109":242},"cc7bc8df-6995-4264-ac5a-32ea9b4ed7db","9y'' + 6y' + y = 0",{"_43":228,"_107":125,"_109":244},"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

",[248],{"_43":249,"_54":250,"_56":251,"_176":177,"_178":252,"_149":253,"_151":253,"_45":254,"_153":251},"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",{"_181":255,"_183":184,"_185":256},4,12302,{"_40":258,"_42":41,"_43":259,"_103":260,"_127":272,"_128":273,"_50":274},"6831a9b9-c9a4-4a76-bd7a-2ce98bfea875","93a32dd4-5fc6-4ccb-a76f-4724bf113742",[261,264,267,269],{"_43":262,"_107":108,"_109":263},"13e3f476-a0a5-421f-b47e-0969e8e9a7e0","

Verdadeiro, verdadeiro, falso

",{"_43":265,"_107":113,"_109":266},"c9a20855-d84b-4860-8b35-9784818282cf","

Falso, verdadeiro, verdadeiro

",{"_43":258,"_107":117,"_109":268},"

Verdadeiro, falso, verdadeiro

",{"_43":270,"_107":121,"_109":271},"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?

",[248],{"_40":276,"_42":41,"_43":277,"_103":278,"_127":293,"_128":294,"_50":295},"3ce109b1-6cdb-4b4d-8816-a6af4d74bed0","c478a46c-46a8-4942-ae14-2e79def3dda2",[279,282,285,287,290],{"_43":280,"_107":108,"_109":281},"a5a16a42-3e58-4c76-80f2-c291aa2d8e49","Sim",{"_43":283,"_107":113,"_109":284},"5e6d0254-696c-4da0-b572-82e3a19f433e","Não",{"_43":276,"_107":117,"_109":286},"Indeterminado",{"_43":288,"_107":121,"_109":289},"35403f68-a880-429d-97f4-db507c58de38","Todos",{"_43":291,"_107":125,"_109":292},"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????",[248],[248,297,306,312,316,317,318,326,331,339,340,345,351],{"_43":298,"_54":299,"_56":300,"_176":177,"_178":301,"_149":193,"_151":193,"_45":302,"_153":305},"861ad829-750d-4a44-9569-2f18b430b4df","Engenharia Mecatrônica","engenharia-mecatronica","eb9315c5-bd04-4116-aa46-02c4fde320c0",{"_181":303,"_183":184,"_185":304},5,30614,"engenharia-mecatronica-1",{"_43":307,"_54":86,"_56":61,"_176":177,"_178":308,"_149":309,"_151":309,"_45":310,"_153":311},"8850e507-a691-4d45-a7c7-16221e9c5af2","88fe96b3-2a17-4198-90d5-ddda3d6f5d45","2025-04-29T04:00:13.215003+00:00",{"_181":184,"_183":184,"_185":203},"resistencia-dos-materiais-6",{"_43":308,"_54":191,"_56":192,"_176":177,"_178":298,"_149":253,"_151":253,"_45":313,"_153":315},{"_181":303,"_183":184,"_185":314},25741,"mecanica-3",{"_43":173,"_54":174,"_56":175,"_176":177,"_178":-5,"_149":179,"_151":179,"_45":180,"_153":175},{"_43":200,"_54":86,"_56":61,"_176":177,"_178":190,"_149":201,"_151":201,"_45":202,"_153":204},{"_43":319,"_54":320,"_56":321,"_176":177,"_178":301,"_149":193,"_151":193,"_45":322,"_153":325},"b6e37f32-f8e5-4025-bf0f-69ffc00fb331","Engenharia Civil","engenharia-civil",{"_181":323,"_183":184,"_185":324},21,45865,"engenharia-civil-3",{"_43":252,"_54":327,"_56":328,"_176":177,"_178":301,"_149":193,"_151":193,"_45":329,"_153":330},"Engenharia de Petróleo","engenharia-de-petroleo",{"_181":303,"_183":184,"_185":256},"engenharia-de-petroleo-1",{"_43":332,"_54":333,"_56":334,"_176":177,"_178":319,"_149":335,"_151":335,"_45":336,"_153":338},"c5bf57d4-c3d8-4365-b53e-085fa14a3a95","Estruturas","estruturas","2025-04-29T03:44:32.303369+00:00",{"_181":303,"_183":184,"_185":337},8852,"estruturas-1",{"_43":190,"_54":191,"_56":192,"_176":177,"_178":173,"_149":193,"_151":193,"_45":194,"_153":197},{"_43":341,"_54":86,"_56":61,"_176":177,"_178":249,"_149":342,"_151":342,"_45":343,"_153":344},"d1e4567b-f68a-49e1-b3e5-3888343d7871","2025-04-29T04:00:14.680867+00:00",{"_181":184,"_183":184,"_185":203},"resistencia-dos-materiais-7",{"_43":346,"_54":347,"_56":61,"_176":177,"_178":332,"_149":348,"_151":348,"_45":349,"_153":350},"da8d2ecf-e949-4afc-966f-98b4b367fac1","Resistencia dos Materiais","2025-04-29T04:00:06.9766+00:00",{"_181":184,"_183":184,"_185":203},"resistencia-dos-materiais-5",{"_43":301,"_54":352,"_56":353,"_176":177,"_178":-5,"_149":354,"_151":354,"_45":355,"_153":353},"Engenharia","engenharia","2025-04-29T01:55:38.635246+00:00",{"_181":356,"_183":184,"_185":357},29,351586,"tagsTree",[172,360],{"_43":301,"_54":352,"_56":353,"_176":177,"_178":-5,"_149":354,"_151":354,"_45":355,"_153":353,"_187":361},[362,368,374],{"_43":298,"_54":299,"_56":300,"_176":177,"_178":301,"_149":193,"_151":193,"_45":302,"_153":305,"_187":363},[364],{"_43":308,"_54":191,"_56":192,"_176":177,"_178":298,"_149":253,"_151":253,"_45":313,"_153":315,"_187":365},[366],{"_43":307,"_54":86,"_56":61,"_176":177,"_178":308,"_149":309,"_151":309,"_45":310,"_153":311,"_187":367},[],{"_43":319,"_54":320,"_56":321,"_176":177,"_178":301,"_149":193,"_151":193,"_45":322,"_153":325,"_187":369},[370],{"_43":332,"_54":333,"_56":334,"_176":177,"_178":319,"_149":335,"_151":335,"_45":336,"_153":338,"_187":371},[372],{"_43":346,"_54":347,"_56":61,"_176":177,"_178":332,"_149":348,"_151":348,"_45":349,"_153":350,"_187":373},[],{"_43":252,"_54":327,"_56":328,"_176":177,"_178":301,"_149":193,"_151":193,"_45":329,"_153":330,"_187":375},[376],{"_43":249,"_54":250,"_56":251,"_176":177,"_178":252,"_149":253,"_151":253,"_45":254,"_153":251,"_187":377},[378],{"_43":341,"_54":86,"_56":61,"_176":177,"_178":249,"_149":342,"_151":342,"_45":343,"_153":344,"_187":379},[],"videoDislikes",{},"videoLikes",{},"actionData","errors"]

Comentários