[{"_1":2,"_278":-5,"_279":-5},"loaderData",{"_3":4,"_6":7},"root",{"_5":-5},"user","pages/questions/show/index",{"_8":9,"_10":11,"_44":45,"_46":47,"_67":248,"_249":250},"comments",[],"question",{"_12":13,"_14":13,"_15":16,"_17":18,"_41":13,"_42":43},"correctOptionId","","difficulty","id","fc62c2d6-0140-424f-8177-3e326a9d31c8","options",[19,25,29,33,37],{"_15":20,"_21":22,"_23":24},"a570aa35-9dc8-43f2-9e7e-121285dc3b1c","label","A","text","\\theta = 45,24°",{"_15":26,"_21":27,"_23":28},"a76a0b20-fc04-4d6f-905c-642530859253","B","\\theta = 64,61°",{"_15":30,"_21":31,"_23":32},"b2eac020-852e-45b1-b66b-f93bafa2f744","C","\\theta = 70,23°",{"_15":34,"_21":35,"_23":36},"16b1cadf-43da-4b9b-b31b-250f17262ce5","D","\\theta = 74,59°",{"_15":38,"_21":39,"_23":40},"207da6d2-a9f4-4e90-8d02-942fcf1296f4","E","\\theta = 81,27°","solution_explanation","statement","

Na aula 1 tema 5 vimos como projetar um vetor em uma determinada direção utilizando o produto escalar. Considerando o problema apresentado na figura, determine o ângulo \\theta entre as duas cordas.

","relatedVideos",[],"similarQuestions",[48,174,191,208,228],{"_12":13,"_14":13,"_15":49,"_17":50,"_41":13,"_42":66,"_67":68},"3c0b9441-b878-4896-8bac-fa4ca61e3f13",[51,54,57,60,63],{"_15":52,"_21":22,"_23":53},"265bd71a-6749-41f5-b291-67efd646ca64","y'' + 2y' - 3y = 0",{"_15":55,"_21":27,"_23":56},"6d3c3a1d-8e80-4ff3-b97a-d5b5bca91940","6y'' - y' - y = 0",{"_15":58,"_21":31,"_23":59},"4168ac67-64fd-46ed-a69c-a01dbfcde7ea","y'' - 2y' + y = 0",{"_15":61,"_21":35,"_23":62},"cc7bc8df-6995-4264-ac5a-32ea9b4ed7db","9y'' + 6y' + y = 0",{"_15":64,"_21":39,"_23":65},"112831da-be9c-458e-94cb-e8292d0dba12","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

","tags",[69,91,101,110,116,124,130,138,143,151,156,161,167],{"_15":70,"_71":72,"_73":74,"_75":76,"_77":78,"_79":80,"_81":80,"_82":83,"_90":74},"6516bbbd-f2a3-4710-8382-702240b17836","name","Mecânica na Engenharia de Petróleo","alias","mecanica-na-engenharia-de-petroleo","tag_group_id","c1ce2cf2-b217-4cc7-8182-81c56bd3522d","parent_id","b787e438-0ab3-454c-ab43-5d3d14c2720d","created_at","2025-04-29T03:44:35.328997+00:00","updated_at","metadata",{"_84":85,"_86":87,"_88":89},"childrenCount",4,"content_count",0,"question_count",12302,"slug",{"_15":92,"_71":93,"_73":94,"_75":76,"_77":95,"_79":96,"_81":96,"_82":97,"_90":100},"861ad829-750d-4a44-9569-2f18b430b4df","Engenharia Mecatrônica","engenharia-mecatronica","eb9315c5-bd04-4116-aa46-02c4fde320c0","2025-04-29T02:19:12.828432+00:00",{"_84":98,"_86":87,"_88":99},5,30614,"engenharia-mecatronica-1",{"_15":102,"_71":103,"_73":104,"_75":76,"_77":105,"_79":106,"_81":106,"_82":107,"_90":109},"8850e507-a691-4d45-a7c7-16221e9c5af2","Resistência dos Materiais","resistencia-dos-materiais","88fe96b3-2a17-4198-90d5-ddda3d6f5d45","2025-04-29T04:00:13.215003+00:00",{"_84":87,"_86":87,"_88":108},3376,"resistencia-dos-materiais-6",{"_15":105,"_71":111,"_73":112,"_75":76,"_77":92,"_79":80,"_81":80,"_82":113,"_90":115},"Mecânica","mecanica",{"_84":98,"_86":87,"_88":114},25741,"mecanica-3",{"_15":117,"_71":118,"_73":119,"_75":76,"_77":-5,"_79":120,"_81":120,"_82":121,"_90":119},"9772e958-72c6-4499-ad47-877cf94d670d","Exatas","exatas","2025-04-29T01:56:45.284172+00:00",{"_84":122,"_86":87,"_88":123},18,135489,{"_15":125,"_71":103,"_73":104,"_75":76,"_77":126,"_79":127,"_81":127,"_82":128,"_90":129},"ac55bdba-154d-42e7-bc25-72dde822663d","ca6fee0e-79c6-4f1c-b500-ee081a071949","2025-04-29T03:44:29.139762+00:00",{"_84":87,"_86":87,"_88":108},"resistencia-dos-materiais-4",{"_15":131,"_71":132,"_73":133,"_75":76,"_77":95,"_79":96,"_81":96,"_82":134,"_90":137},"b6e37f32-f8e5-4025-bf0f-69ffc00fb331","Engenharia Civil","engenharia-civil",{"_84":135,"_86":87,"_88":136},21,45865,"engenharia-civil-3",{"_15":78,"_71":139,"_73":140,"_75":76,"_77":95,"_79":96,"_81":96,"_82":141,"_90":142},"Engenharia de Petróleo","engenharia-de-petroleo",{"_84":98,"_86":87,"_88":89},"engenharia-de-petroleo-1",{"_15":144,"_71":145,"_73":146,"_75":76,"_77":131,"_79":147,"_81":147,"_82":148,"_90":150},"c5bf57d4-c3d8-4365-b53e-085fa14a3a95","Estruturas","estruturas","2025-04-29T03:44:32.303369+00:00",{"_84":98,"_86":87,"_88":149},8852,"estruturas-1",{"_15":126,"_71":111,"_73":112,"_75":76,"_77":117,"_79":96,"_81":96,"_82":152,"_90":155},{"_84":153,"_86":87,"_88":154},10,19948,"mecanica-2",{"_15":157,"_71":103,"_73":104,"_75":76,"_77":70,"_79":158,"_81":158,"_82":159,"_90":160},"d1e4567b-f68a-49e1-b3e5-3888343d7871","2025-04-29T04:00:14.680867+00:00",{"_84":87,"_86":87,"_88":108},"resistencia-dos-materiais-7",{"_15":162,"_71":163,"_73":104,"_75":76,"_77":144,"_79":164,"_81":164,"_82":165,"_90":166},"da8d2ecf-e949-4afc-966f-98b4b367fac1","Resistencia dos Materiais","2025-04-29T04:00:06.9766+00:00",{"_84":87,"_86":87,"_88":108},"resistencia-dos-materiais-5",{"_15":95,"_71":168,"_73":169,"_75":76,"_77":-5,"_79":170,"_81":170,"_82":171,"_90":169},"Engenharia","engenharia","2025-04-29T01:55:38.635246+00:00",{"_84":172,"_86":87,"_88":173},29,351586,{"_12":13,"_14":13,"_15":175,"_17":176,"_41":13,"_42":189,"_67":190},"4a3f20e5-655d-4a84-bbdf-aa3b0de4581a",[177,180,183,186],{"_15":178,"_21":22,"_23":179},"8dee6a5e-57a3-4743-8b5a-da9b8c54fb32","Verdadero, verdadero, verdadero, verdadero.",{"_15":181,"_21":27,"_23":182},"ca0a9b0d-3004-478e-9ca9-bafa5243aca9","Verdadero, verdadero, falso, verdadero.",{"_15":184,"_21":31,"_23":185},"68712800-8b4b-46af-9cdf-3f83e4032c30","Verdadero, falso, verdadero, falso.",{"_15":187,"_21":35,"_23":188},"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.

",[69,91,101,110,116,124,130,138,143,151,156,161,167],{"_12":13,"_14":13,"_15":192,"_17":193,"_41":13,"_42":206,"_67":207},"93a32dd4-5fc6-4ccb-a76f-4724bf113742",[194,197,200,203],{"_15":195,"_21":22,"_23":196},"13e3f476-a0a5-421f-b47e-0969e8e9a7e0","

Verdadeiro, verdadeiro, falso

",{"_15":198,"_21":27,"_23":199},"c9a20855-d84b-4860-8b35-9784818282cf","

Falso, verdadeiro, verdadeiro

",{"_15":201,"_21":31,"_23":202},"6831a9b9-c9a4-4a76-bd7a-2ce98bfea875","

Verdadeiro, falso, verdadeiro

",{"_15":204,"_21":35,"_23":205},"3c98539b-1af9-4d44-aecd-c266754a2075","

Falso, falso, falso

","

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

",[69,91,101,110,116,124,130,138,143,151,156,161,167],{"_12":13,"_14":13,"_15":209,"_17":210,"_41":13,"_42":226,"_67":227},"996628fc-4ac3-4821-86bd-839f86a97a6d",[211,214,217,220,223],{"_15":212,"_21":22,"_23":213},"5ad09994-6dcb-4c66-87ae-ec00e9b439b7","5 + 3x < 2x + 4",{"_15":215,"_21":27,"_23":216},"b3ae9948-890b-4807-b801-1e1888cb0c10","3 + 4x \\leq 8x + 6",{"_15":218,"_21":31,"_23":219},"d2964603-f26c-4be6-99ae-d174678f104c","5 + 4x > 3x + 2",{"_15":221,"_21":35,"_23":222},"88c48b1a-ce37-4eae-a900-a4fb4bd581d9","1 + 3x \\geq 5x + 7",{"_15":224,"_21":39,"_23":225},"155e0bb0-6c7f-4d9c-96e5-d1cdb97c632b","4(3 + 2x) < -(6x + 8)","Resolver las siguientes inecuaciones y representar la solución en la recta real:",[69,91,101,110,116,124,130,138,143,151,156,161,167],{"_12":13,"_14":13,"_15":229,"_17":230,"_41":13,"_42":246,"_67":247},"c478a46c-46a8-4942-ae14-2e79def3dda2",[231,234,237,240,243],{"_15":232,"_21":22,"_23":233},"a5a16a42-3e58-4c76-80f2-c291aa2d8e49","Sim",{"_15":235,"_21":27,"_23":236},"5e6d0254-696c-4da0-b572-82e3a19f433e","Não",{"_15":238,"_21":31,"_23":239},"3ce109b1-6cdb-4b4d-8816-a6af4d74bed0","Indeterminado",{"_15":241,"_21":35,"_23":242},"35403f68-a880-429d-97f4-db507c58de38","Todos",{"_15":244,"_21":39,"_23":245},"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????",[69,91,101,110,116,124,130,138,143,151,156,161,167],[69,91,101,110,116,124,130,138,143,151,156,161,167],"tagsTree",[251,258],{"_15":117,"_71":118,"_73":119,"_75":76,"_77":-5,"_79":120,"_81":120,"_82":121,"_90":119,"_252":253},"children",[254],{"_15":126,"_71":111,"_73":112,"_75":76,"_77":117,"_79":96,"_81":96,"_82":152,"_90":155,"_252":255},[256],{"_15":125,"_71":103,"_73":104,"_75":76,"_77":126,"_79":127,"_81":127,"_82":128,"_90":129,"_252":257},[],{"_15":95,"_71":168,"_73":169,"_75":76,"_77":-5,"_79":170,"_81":170,"_82":171,"_90":169,"_252":259},[260,266,272],{"_15":92,"_71":93,"_73":94,"_75":76,"_77":95,"_79":96,"_81":96,"_82":97,"_90":100,"_252":261},[262],{"_15":105,"_71":111,"_73":112,"_75":76,"_77":92,"_79":80,"_81":80,"_82":113,"_90":115,"_252":263},[264],{"_15":102,"_71":103,"_73":104,"_75":76,"_77":105,"_79":106,"_81":106,"_82":107,"_90":109,"_252":265},[],{"_15":131,"_71":132,"_73":133,"_75":76,"_77":95,"_79":96,"_81":96,"_82":134,"_90":137,"_252":267},[268],{"_15":144,"_71":145,"_73":146,"_75":76,"_77":131,"_79":147,"_81":147,"_82":148,"_90":150,"_252":269},[270],{"_15":162,"_71":163,"_73":104,"_75":76,"_77":144,"_79":164,"_81":164,"_82":165,"_90":166,"_252":271},[],{"_15":78,"_71":139,"_73":140,"_75":76,"_77":95,"_79":96,"_81":96,"_82":141,"_90":142,"_252":273},[274],{"_15":70,"_71":72,"_73":74,"_75":76,"_77":78,"_79":80,"_81":80,"_82":83,"_90":74,"_252":275},[276],{"_15":157,"_71":103,"_73":104,"_75":76,"_77":70,"_79":158,"_81":158,"_82":159,"_90":160,"_252":277},[],"actionData","errors"]

Aulas em vídeo Em breve

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