[{"_1":2,"_268":-5,"_269":-5},"loaderData",{"_3":4,"_8":9},"root",{"_5":6,"_7":-5},"url","https://prouniversitario.com/exercicios/f251de32-0807-475b-a344-ba092b92c3bd","user","pages/questions/show/index",{"_10":11,"_12":13,"_38":39,"_40":41,"_63":240,"_241":242},"comments",[],"question",{"_14":15,"_16":17,"_18":19,"_20":21,"_35":17,"_36":37},"correctOptionId","0dc0b37f-37fb-41bc-999c-1643c642b988","difficulty","","id","f251de32-0807-475b-a344-ba092b92c3bd","options",[22,27,31],{"_18":15,"_23":24,"_25":26},"label","A","text","

paralelas, concorrentes, perpendiculares

",{"_18":28,"_23":29,"_25":30},"b7f82d1c-8f16-4437-871b-eb473a28923a","B","

concorrentes, perpendiculares, paralelas

",{"_18":32,"_23":33,"_25":34},"f648232d-c5ca-4348-811b-fa6f768022be","C","

perpendiculares, paralelas, concorrentes

","solution_explanation","statement","

Classifique os pares de retas em paralelas, concorrentes ou perpendiculares

","relatedVideos",[],"similarQuestions",[42,166,183,200,220],{"_14":17,"_16":17,"_18":43,"_20":44,"_35":17,"_36":62,"_63":64},"3c0b9441-b878-4896-8bac-fa4ca61e3f13",[45,48,51,54,58],{"_18":46,"_23":24,"_25":47},"265bd71a-6749-41f5-b291-67efd646ca64","y'' + 2y' - 3y = 0",{"_18":49,"_23":29,"_25":50},"6d3c3a1d-8e80-4ff3-b97a-d5b5bca91940","6y'' - y' - y = 0",{"_18":52,"_23":33,"_25":53},"4168ac67-64fd-46ed-a69c-a01dbfcde7ea","y'' - 2y' + y = 0",{"_18":55,"_23":56,"_25":57},"cc7bc8df-6995-4264-ac5a-32ea9b4ed7db","D","9y'' + 6y' + y = 0",{"_18":59,"_23":60,"_25":61},"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

","tags",[65,87,97,107,114,121,129,137,143,148,154,161],{"_18":66,"_67":68,"_69":70,"_71":72,"_73":74,"_75":76,"_77":76,"_78":79,"_86":70},"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",{"_80":81,"_82":83,"_84":85},"childrenCount",4,"content_count",0,"question_count",12302,"slug",{"_18":88,"_67":89,"_69":90,"_71":72,"_73":91,"_75":92,"_77":92,"_78":93,"_86":96},"6b6faf95-0e3a-4f58-abc8-e1444c48041d","Termodinâmica","termodinamica","92339f4f-ed20-4f4c-ad85-0c3de7e04ae0","2025-04-29T03:44:27.560682+00:00",{"_80":94,"_82":83,"_84":95},2,11846,"termodinamica-3",{"_18":98,"_67":99,"_69":100,"_71":72,"_73":101,"_75":102,"_77":102,"_78":103,"_86":106},"861ad829-750d-4a44-9569-2f18b430b4df","Engenharia Mecatrônica","engenharia-mecatronica","eb9315c5-bd04-4116-aa46-02c4fde320c0","2025-04-29T02:19:12.828432+00:00",{"_80":104,"_82":83,"_84":105},5,30614,"engenharia-mecatronica-1",{"_18":108,"_67":109,"_69":110,"_71":72,"_73":98,"_75":76,"_77":76,"_78":111,"_86":113},"88fe96b3-2a17-4198-90d5-ddda3d6f5d45","Mecânica","mecanica",{"_80":104,"_82":83,"_84":112},25741,"mecanica-3",{"_18":91,"_67":115,"_69":116,"_71":72,"_73":101,"_75":102,"_77":102,"_78":117,"_86":120},"Engenharia Mecânica","engenharia-mecanica",{"_80":118,"_82":83,"_84":119},11,36318,"engenharia-mecanica-2",{"_18":122,"_67":123,"_69":124,"_71":72,"_73":125,"_75":92,"_77":92,"_78":126,"_86":124},"96193fa0-9495-45b2-81cc-b547604354af","Física Térmica - Termologia","fisica-termica-termologia","c8ab2a95-fd84-4d6f-ade0-835d34ba00f9",{"_80":127,"_82":83,"_84":128},10,8575,{"_18":130,"_67":131,"_69":132,"_71":72,"_73":-5,"_75":133,"_77":133,"_78":134,"_86":132},"9772e958-72c6-4499-ad47-877cf94d670d","Exatas","exatas","2025-04-29T01:56:45.284172+00:00",{"_80":135,"_82":83,"_84":136},18,135489,{"_18":138,"_67":89,"_69":90,"_71":72,"_73":66,"_75":139,"_77":139,"_78":140,"_86":142},"b21374de-aae5-4a4a-9bf3-0420e731797e","2025-04-29T04:00:14.680867+00:00",{"_80":83,"_82":83,"_84":141},8597,"termodinamica-5",{"_18":74,"_67":144,"_69":145,"_71":72,"_73":101,"_75":102,"_77":102,"_78":146,"_86":147},"Engenharia de Petróleo","engenharia-de-petroleo",{"_80":104,"_82":83,"_84":85},"engenharia-de-petroleo-1",{"_18":125,"_67":149,"_69":150,"_71":72,"_73":130,"_75":102,"_77":102,"_78":151,"_86":153},"Física","fisica",{"_80":118,"_82":83,"_84":152},13777,"fisica-4",{"_18":101,"_67":155,"_69":156,"_71":72,"_73":-5,"_75":157,"_77":157,"_78":158,"_86":156},"Engenharia","engenharia","2025-04-29T01:55:38.635246+00:00",{"_80":159,"_82":83,"_84":160},29,351586,{"_18":162,"_67":89,"_69":90,"_71":72,"_73":108,"_75":163,"_77":163,"_78":164,"_86":165},"f5967cbe-d751-4b40-81f2-04eb5dead2a9","2025-04-29T04:00:13.215003+00:00",{"_80":83,"_82":83,"_84":141},"termodinamica-4",{"_14":17,"_16":17,"_18":167,"_20":168,"_35":17,"_36":181,"_63":182},"4a3f20e5-655d-4a84-bbdf-aa3b0de4581a",[169,172,175,178],{"_18":170,"_23":24,"_25":171},"8dee6a5e-57a3-4743-8b5a-da9b8c54fb32","Verdadero, verdadero, verdadero, verdadero.",{"_18":173,"_23":29,"_25":174},"ca0a9b0d-3004-478e-9ca9-bafa5243aca9","Verdadero, verdadero, falso, verdadero.",{"_18":176,"_23":33,"_25":177},"68712800-8b4b-46af-9cdf-3f83e4032c30","Verdadero, falso, verdadero, falso.",{"_18":179,"_23":56,"_25":180},"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.

",[65,87,97,107,114,121,129,137,143,148,154,161],{"_14":17,"_16":17,"_18":184,"_20":185,"_35":17,"_36":198,"_63":199},"93a32dd4-5fc6-4ccb-a76f-4724bf113742",[186,189,192,195],{"_18":187,"_23":24,"_25":188},"13e3f476-a0a5-421f-b47e-0969e8e9a7e0","

Verdadeiro, verdadeiro, falso

",{"_18":190,"_23":29,"_25":191},"c9a20855-d84b-4860-8b35-9784818282cf","

Falso, verdadeiro, verdadeiro

",{"_18":193,"_23":33,"_25":194},"6831a9b9-c9a4-4a76-bd7a-2ce98bfea875","

Verdadeiro, falso, verdadeiro

",{"_18":196,"_23":56,"_25":197},"3c98539b-1af9-4d44-aecd-c266754a2075","

Falso, falso, falso

","

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

",[65,87,97,107,114,121,129,137,143,148,154,161],{"_14":17,"_16":17,"_18":201,"_20":202,"_35":17,"_36":218,"_63":219},"996628fc-4ac3-4821-86bd-839f86a97a6d",[203,206,209,212,215],{"_18":204,"_23":24,"_25":205},"5ad09994-6dcb-4c66-87ae-ec00e9b439b7","5 + 3x < 2x + 4",{"_18":207,"_23":29,"_25":208},"b3ae9948-890b-4807-b801-1e1888cb0c10","3 + 4x \\leq 8x + 6",{"_18":210,"_23":33,"_25":211},"d2964603-f26c-4be6-99ae-d174678f104c","5 + 4x > 3x + 2",{"_18":213,"_23":56,"_25":214},"88c48b1a-ce37-4eae-a900-a4fb4bd581d9","1 + 3x \\geq 5x + 7",{"_18":216,"_23":60,"_25":217},"155e0bb0-6c7f-4d9c-96e5-d1cdb97c632b","4(3 + 2x) < -(6x + 8)","Resolver las siguientes inecuaciones y representar la solución en la recta real:",[65,87,97,107,114,121,129,137,143,148,154,161],{"_14":17,"_16":17,"_18":221,"_20":222,"_35":17,"_36":238,"_63":239},"c478a46c-46a8-4942-ae14-2e79def3dda2",[223,226,229,232,235],{"_18":224,"_23":24,"_25":225},"a5a16a42-3e58-4c76-80f2-c291aa2d8e49","Sim",{"_18":227,"_23":29,"_25":228},"5e6d0254-696c-4da0-b572-82e3a19f433e","Não",{"_18":230,"_23":33,"_25":231},"3ce109b1-6cdb-4b4d-8816-a6af4d74bed0","Indeterminado",{"_18":233,"_23":56,"_25":234},"35403f68-a880-429d-97f4-db507c58de38","Todos",{"_18":236,"_23":60,"_25":237},"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????",[65,87,97,107,114,121,129,137,143,148,154,161],[65,87,97,107,114,121,129,137,143,148,154,161],"tagsTree",[243,250],{"_18":130,"_67":131,"_69":132,"_71":72,"_73":-5,"_75":133,"_77":133,"_78":134,"_86":132,"_244":245},"children",[246],{"_18":125,"_67":149,"_69":150,"_71":72,"_73":130,"_75":102,"_77":102,"_78":151,"_86":153,"_244":247},[248],{"_18":122,"_67":123,"_69":124,"_71":72,"_73":125,"_75":92,"_77":92,"_78":126,"_86":124,"_244":249},[],{"_18":101,"_67":155,"_69":156,"_71":72,"_73":-5,"_75":157,"_77":157,"_78":158,"_86":156,"_244":251},[252,258,262],{"_18":98,"_67":99,"_69":100,"_71":72,"_73":101,"_75":102,"_77":102,"_78":103,"_86":106,"_244":253},[254],{"_18":108,"_67":109,"_69":110,"_71":72,"_73":98,"_75":76,"_77":76,"_78":111,"_86":113,"_244":255},[256],{"_18":162,"_67":89,"_69":90,"_71":72,"_73":108,"_75":163,"_77":163,"_78":164,"_86":165,"_244":257},[],{"_18":91,"_67":115,"_69":116,"_71":72,"_73":101,"_75":102,"_77":102,"_78":117,"_86":120,"_244":259},[260],{"_18":88,"_67":89,"_69":90,"_71":72,"_73":91,"_75":92,"_77":92,"_78":93,"_86":96,"_244":261},[],{"_18":74,"_67":144,"_69":145,"_71":72,"_73":101,"_75":102,"_77":102,"_78":146,"_86":147,"_244":263},[264],{"_18":66,"_67":68,"_69":70,"_71":72,"_73":74,"_75":76,"_77":76,"_78":79,"_86":70,"_244":265},[266],{"_18":138,"_67":89,"_69":90,"_71":72,"_73":66,"_75":139,"_77":139,"_78":140,"_86":142,"_244":267},[],"actionData","errors"]

Aulas em vídeo Em breve

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