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Os ângulos para os quais as tensões normais atingem seu valor máximo e mínimo.

",{"_21":65,"_60":66,"_62":67},"6545246b-eda9-4c6a-beae-38ed128cfa9d","B","

Os valores de tensão normal e de cisalhamento em um plano qualquer.

",{"_21":69,"_60":70,"_62":71},"c791a006-4947-4eea-8e11-4403a38df17f","C","

O ângulo que define o plano principal de tensão de cisalhamento máximo.

","solution_explanation","statement","

O que representa a direção das tensões principais?

","status","pending_classification","hasRelatedVideo","relatedVideos",[80],{"_81":82,"_100":101,"_29":116,"_151":152,"_170":171},"content",{"_21":83,"_35":84,"_85":-5,"_86":87,"_88":89,"_90":-5,"_23":91,"_94":95,"_96":95,"_97":-5,"_98":99},"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",{"_92":93},"external_id","4963","created_at","2025-08-20T12:27:41.608438+00:00","updated_at","content_group_id","slug","optica-geometrica-parte-1","prometheusData",{"_102":103,"_109":110,"_111":112,"_113":114,"_6":115},"provider",{"_21":104,"_105":106,"_107":108},"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",[117],{"_21":118,"_35":119,"_37":120,"_121":122,"_123":-5,"_94":124,"_96":124,"_23":125,"_98":120,"_132":133},"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",{"_126":127,"_128":129,"_130":131},"childrenCount",18,"content_count",0,"question_count",135489,"children",[134],{"_21":135,"_35":136,"_37":137,"_121":122,"_123":118,"_94":138,"_96":138,"_23":139,"_98":142,"_132":143},"ca6fee0e-79c6-4f1c-b500-ee081a071949","Mecânica","mecanica","2025-04-29T02:19:12.828432+00:00",{"_126":140,"_128":129,"_130":141},10,19948,"mecanica-2",[144],{"_21":145,"_35":36,"_37":38,"_121":122,"_123":135,"_94":146,"_96":146,"_23":147,"_98":149,"_132":150},"ac55bdba-154d-42e7-bc25-72dde822663d","2025-04-29T03:44:29.139762+00:00",{"_126":129,"_128":129,"_130":148},3376,"resistencia-dos-materiais-4",[],"video",{"_21":89,"_153":84,"_85":-5,"_154":155,"_156":157,"_6":-5,"_158":-5,"_102":157,"_159":160,"_113":-5,"_161":-5,"_162":-5,"_163":-5,"_164":-5,"_23":165,"_166":129,"_167":-5,"_75":168,"_94":169,"_96":169},"title","duration",20,"source_type","prometheus","iframe_url","provider_video_id","1cd3d633-d690-4f4b-9995-9b0e44994e35","format","quality","file_path","file_size",{"_92":93},"views_count","last_played_at","draft","2025-08-19T11:56:20.758718+00:00","tag",{"_21":118,"_35":119,"_37":120,"_121":122,"_123":-5,"_94":124,"_96":124,"_23":172,"_98":120,"_132":173},{"_126":127,"_128":129,"_130":131},[174],{"_21":135,"_35":136,"_37":137,"_121":122,"_123":118,"_94":138,"_96":138,"_23":175,"_98":142,"_132":176},{"_126":140,"_128":129,"_130":141},[177],{"_21":145,"_35":36,"_37":38,"_121":122,"_123":135,"_94":146,"_96":146,"_23":178,"_98":149,"_132":179},{"_126":129,"_128":129,"_130":148},[],"similarQuestions",[182,214,234],{"_18":183,"_20":19,"_21":184,"_56":185,"_72":202,"_73":203,"_29":204},"112831da-be9c-458e-94cb-e8292d0dba12","3c0b9441-b878-4896-8bac-fa4ca61e3f13",[186,189,192,195,199],{"_21":187,"_60":61,"_62":188},"265bd71a-6749-41f5-b291-67efd646ca64","y'' + 2y' - 3y = 0",{"_21":190,"_60":66,"_62":191},"6d3c3a1d-8e80-4ff3-b97a-d5b5bca91940","6y'' - y' - y = 0",{"_21":193,"_60":70,"_62":194},"4168ac67-64fd-46ed-a69c-a01dbfcde7ea","y'' - 2y' + y = 0",{"_21":196,"_60":197,"_62":198},"cc7bc8df-6995-4264-ac5a-32ea9b4ed7db","D","9y'' + 6y' + y = 0",{"_21":183,"_60":200,"_62":201},"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

",[205],{"_21":206,"_35":207,"_37":208,"_121":122,"_123":209,"_94":210,"_96":210,"_23":211,"_98":208},"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",{"_126":212,"_128":129,"_130":213},4,12302,{"_18":215,"_20":19,"_21":216,"_56":217,"_72":229,"_73":230,"_29":231},"6831a9b9-c9a4-4a76-bd7a-2ce98bfea875","93a32dd4-5fc6-4ccb-a76f-4724bf113742",[218,221,224,226],{"_21":219,"_60":61,"_62":220},"13e3f476-a0a5-421f-b47e-0969e8e9a7e0","

Verdadeiro, verdadeiro, falso

",{"_21":222,"_60":66,"_62":223},"c9a20855-d84b-4860-8b35-9784818282cf","

Falso, verdadeiro, verdadeiro

",{"_21":215,"_60":70,"_62":225},"

Verdadeiro, falso, verdadeiro

",{"_21":227,"_60":197,"_62":228},"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????",[255],{"_21":206,"_35":207,"_37":208,"_121":122,"_123":209,"_94":210,"_96":210,"_23":256,"_98":208},{"_126":212,"_128":129,"_130":213},[258,260,269,275,279,281,283,291,296,304,306,311,317],{"_21":206,"_35":207,"_37":208,"_121":122,"_123":209,"_94":210,"_96":210,"_23":259,"_98":208},{"_126":212,"_128":129,"_130":213},{"_21":261,"_35":262,"_37":263,"_121":122,"_123":264,"_94":138,"_96":138,"_23":265,"_98":268},"861ad829-750d-4a44-9569-2f18b430b4df","Engenharia Mecatrônica","engenharia-mecatronica","eb9315c5-bd04-4116-aa46-02c4fde320c0",{"_126":266,"_128":129,"_130":267},5,30614,"engenharia-mecatronica-1",{"_21":270,"_35":36,"_37":38,"_121":122,"_123":271,"_94":272,"_96":272,"_23":273,"_98":274},"8850e507-a691-4d45-a7c7-16221e9c5af2","88fe96b3-2a17-4198-90d5-ddda3d6f5d45","2025-04-29T04:00:13.215003+00:00",{"_126":129,"_128":129,"_130":148},"resistencia-dos-materiais-6",{"_21":271,"_35":136,"_37":137,"_121":122,"_123":261,"_94":210,"_96":210,"_23":276,"_98":278},{"_126":266,"_128":129,"_130":277},25741,"mecanica-3",{"_21":118,"_35":119,"_37":120,"_121":122,"_123":-5,"_94":124,"_96":124,"_23":280,"_98":120},{"_126":127,"_128":129,"_130":131},{"_21":145,"_35":36,"_37":38,"_121":122,"_123":135,"_94":146,"_96":146,"_23":282,"_98":149},{"_126":129,"_128":129,"_130":148},{"_21":284,"_35":285,"_37":286,"_121":122,"_123":264,"_94":138,"_96":138,"_23":287,"_98":290},"b6e37f32-f8e5-4025-bf0f-69ffc00fb331","Engenharia Civil","engenharia-civil",{"_126":288,"_128":129,"_130":289},21,45865,"engenharia-civil-3",{"_21":209,"_35":292,"_37":293,"_121":122,"_123":264,"_94":138,"_96":138,"_23":294,"_98":295},"Engenharia de Petróleo","engenharia-de-petroleo",{"_126":266,"_128":129,"_130":213},"engenharia-de-petroleo-1",{"_21":297,"_35":298,"_37":299,"_121":122,"_123":284,"_94":300,"_96":300,"_23":301,"_98":303},"c5bf57d4-c3d8-4365-b53e-085fa14a3a95","Estruturas","estruturas","2025-04-29T03:44:32.303369+00:00",{"_126":266,"_128":129,"_130":302},8852,"estruturas-1",{"_21":135,"_35":136,"_37":137,"_121":122,"_123":118,"_94":138,"_96":138,"_23":305,"_98":142},{"_126":140,"_128":129,"_130":141},{"_21":307,"_35":36,"_37":38,"_121":122,"_123":206,"_94":308,"_96":308,"_23":309,"_98":310},"d1e4567b-f68a-49e1-b3e5-3888343d7871","2025-04-29T04:00:14.680867+00:00",{"_126":129,"_128":129,"_130":148},"resistencia-dos-materiais-7",{"_21":312,"_35":313,"_37":38,"_121":122,"_123":297,"_94":314,"_96":314,"_23":315,"_98":316},"da8d2ecf-e949-4afc-966f-98b4b367fac1","Resistencia dos Materiais","2025-04-29T04:00:06.9766+00:00",{"_126":129,"_128":129,"_130":148},"resistencia-dos-materiais-5",{"_21":264,"_35":318,"_37":319,"_121":122,"_123":-5,"_94":320,"_96":320,"_23":321,"_98":319},"Engenharia","engenharia","2025-04-29T01:55:38.635246+00:00",{"_126":322,"_128":129,"_130":323},29,351586,"tagsTree",[326,335],{"_21":118,"_35":119,"_37":120,"_121":122,"_123":-5,"_94":124,"_96":124,"_23":327,"_98":120,"_132":328},{"_126":127,"_128":129,"_130":131},[329],{"_21":135,"_35":136,"_37":137,"_121":122,"_123":118,"_94":138,"_96":138,"_23":330,"_98":142,"_132":331},{"_126":140,"_128":129,"_130":141},[332],{"_21":145,"_35":36,"_37":38,"_121":122,"_123":135,"_94":146,"_96":146,"_23":333,"_98":149,"_132":334},{"_126":129,"_128":129,"_130":148},[],{"_21":264,"_35":318,"_37":319,"_121":122,"_123":-5,"_94":320,"_96":320,"_23":336,"_98":319,"_132":337},{"_126":322,"_128":129,"_130":323},[338,347,356],{"_21":261,"_35":262,"_37":263,"_121":122,"_123":264,"_94":138,"_96":138,"_23":339,"_98":268,"_132":340},{"_126":266,"_128":129,"_130":267},[341],{"_21":271,"_35":136,"_37":137,"_121":122,"_123":261,"_94":210,"_96":210,"_23":342,"_98":278,"_132":343},{"_126":266,"_128":129,"_130":277},[344],{"_21":270,"_35":36,"_37":38,"_121":122,"_123":271,"_94":272,"_96":272,"_23":345,"_98":274,"_132":346},{"_126":129,"_128":129,"_130":148},[],{"_21":284,"_35":285,"_37":286,"_121":122,"_123":264,"_94":138,"_96":138,"_23":348,"_98":290,"_132":349},{"_126":288,"_128":129,"_130":289},[350],{"_21":297,"_35":298,"_37":299,"_121":122,"_123":284,"_94":300,"_96":300,"_23":351,"_98":303,"_132":352},{"_126":266,"_128":129,"_130":302},[353],{"_21":312,"_35":313,"_37":38,"_121":122,"_123":297,"_94":314,"_96":314,"_23":354,"_98":316,"_132":355},{"_126":129,"_128":129,"_130":148},[],{"_21":209,"_35":292,"_37":293,"_121":122,"_123":264,"_94":138,"_96":138,"_23":357,"_98":295,"_132":358},{"_126":266,"_128":129,"_130":213},[359],{"_21":206,"_35":207,"_37":208,"_121":122,"_123":209,"_94":210,"_96":210,"_23":360,"_98":208,"_132":361},{"_126":212,"_128":129,"_130":213},[362],{"_21":307,"_35":36,"_37":38,"_121":122,"_123":206,"_94":308,"_96":308,"_23":363,"_98":310,"_132":364},{"_126":129,"_128":129,"_130":148},[],"videoDislikes",{},"videoLikes",{},"actionData","errors"]

Comentários