[{"_1":2,"_272":-5,"_273":-5},"loaderData",{"_3":4,"_8":9},"root",{"_5":6,"_7":-5},"url","https://prouniversitario.com/exercicios/ffc726ed-c86b-4c37-a305-ea56da03674a?video=true","user","pages/questions/show/index",{"_10":11,"_12":13,"_14":13,"_15":16,"_49":50,"_138":139,"_87":244,"_260":261,"_268":269,"_270":271},"comments",[],"hasVideoHash",false,"isAiGenerated","question",{"_17":18,"_19":18,"_20":21,"_22":23,"_42":18,"_43":44,"_45":46,"_47":48},"correctOptionId","","difficulty","id","ffc726ed-c86b-4c37-a305-ea56da03674a","options",[24,30,34,38],{"_20":25,"_26":27,"_28":29},"9d799190-098e-431c-b9f0-f7088f2aa43c","label","A","text","23 \text{ m/s}",{"_20":31,"_26":32,"_28":33},"2ac2af05-550f-4a4d-b207-e7cbb59577e9","B","15 \text{ m/s}",{"_20":35,"_26":36,"_28":37},"aec79a60-3fbf-40b4-ab2b-c03325f8bce9","C","19 \text{ m/s}",{"_20":39,"_26":40,"_28":41},"be0bdc15-ca75-445b-9595-608fdadf1a23","D","20 \text{ m/s}","solution_explanation","statement","

¿Con qué velocidad se debe lanzar una pelota verticalmente hacia arriba para que alcance una altura de 20 \text{ m}?

","status","has_issues","hasRelatedVideo",true,"relatedVideos",[51],{"_52":53,"_71":72,"_87":88,"_118":119,"_137":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",[],"video",{"_20":61,"_120":56,"_57":-5,"_121":122,"_123":124,"_5":-5,"_125":-5,"_73":124,"_126":127,"_84":-5,"_128":-5,"_129":-5,"_130":-5,"_131":-5,"_63":132,"_133":102,"_134":-5,"_45":135,"_67":136,"_69":136},"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",[140,170,187,204,224],{"_17":18,"_19":18,"_20":141,"_22":142,"_42":18,"_43":159,"_87":160},"3c0b9441-b878-4896-8bac-fa4ca61e3f13",[143,146,149,152,155],{"_20":144,"_26":27,"_28":145},"265bd71a-6749-41f5-b291-67efd646ca64","y'' + 2y' - 3y = 0",{"_20":147,"_26":32,"_28":148},"6d3c3a1d-8e80-4ff3-b97a-d5b5bca91940","6y'' - y' - y = 0",{"_20":150,"_26":36,"_28":151},"4168ac67-64fd-46ed-a69c-a01dbfcde7ea","y'' - 2y' + y = 0",{"_20":153,"_26":40,"_28":154},"cc7bc8df-6995-4264-ac5a-32ea9b4ed7db","9y'' + 6y' + y = 0",{"_20":156,"_26":157,"_28":158},"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

",[161],{"_20":162,"_55":163,"_92":164,"_94":95,"_96":165,"_67":112,"_69":112,"_63":166,"_105":169},"861ad829-750d-4a44-9569-2f18b430b4df","Engenharia Mecatrônica","engenharia-mecatronica","eb9315c5-bd04-4116-aa46-02c4fde320c0",{"_99":167,"_101":102,"_103":168},5,30614,"engenharia-mecatronica-1",{"_17":18,"_19":18,"_20":171,"_22":172,"_42":18,"_43":185,"_87":186},"4a3f20e5-655d-4a84-bbdf-aa3b0de4581a",[173,176,179,182],{"_20":174,"_26":27,"_28":175},"8dee6a5e-57a3-4743-8b5a-da9b8c54fb32","Verdadero, verdadero, verdadero, verdadero.",{"_20":177,"_26":32,"_28":178},"ca0a9b0d-3004-478e-9ca9-bafa5243aca9","Verdadero, verdadero, falso, verdadero.",{"_20":180,"_26":36,"_28":181},"68712800-8b4b-46af-9cdf-3f83e4032c30","Verdadero, falso, verdadero, falso.",{"_20":183,"_26":40,"_28":184},"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.

",[161],{"_17":18,"_19":18,"_20":188,"_22":189,"_42":18,"_43":202,"_87":203},"93a32dd4-5fc6-4ccb-a76f-4724bf113742",[190,193,196,199],{"_20":191,"_26":27,"_28":192},"13e3f476-a0a5-421f-b47e-0969e8e9a7e0","

Verdadeiro, verdadeiro, falso

",{"_20":194,"_26":32,"_28":195},"c9a20855-d84b-4860-8b35-9784818282cf","

Falso, verdadeiro, verdadeiro

",{"_20":197,"_26":36,"_28":198},"6831a9b9-c9a4-4a76-bd7a-2ce98bfea875","

Verdadeiro, falso, verdadeiro

",{"_20":200,"_26":40,"_28":201},"3c98539b-1af9-4d44-aecd-c266754a2075","

Falso, falso, falso

","

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

",[161],{"_17":18,"_19":18,"_20":205,"_22":206,"_42":18,"_43":222,"_87":223},"996628fc-4ac3-4821-86bd-839f86a97a6d",[207,210,213,216,219],{"_20":208,"_26":27,"_28":209},"5ad09994-6dcb-4c66-87ae-ec00e9b439b7","5 + 3x < 2x + 4",{"_20":211,"_26":32,"_28":212},"b3ae9948-890b-4807-b801-1e1888cb0c10","3 + 4x \\leq 8x + 6",{"_20":214,"_26":36,"_28":215},"d2964603-f26c-4be6-99ae-d174678f104c","5 + 4x > 3x + 2",{"_20":217,"_26":40,"_28":218},"88c48b1a-ce37-4eae-a900-a4fb4bd581d9","1 + 3x \\geq 5x + 7",{"_20":220,"_26":157,"_28":221},"155e0bb0-6c7f-4d9c-96e5-d1cdb97c632b","4(3 + 2x) < -(6x + 8)","Resolver las siguientes inecuaciones y representar la solución en la recta real:",[161],{"_17":18,"_19":18,"_20":225,"_22":226,"_42":18,"_43":242,"_87":243},"c478a46c-46a8-4942-ae14-2e79def3dda2",[227,230,233,236,239],{"_20":228,"_26":27,"_28":229},"a5a16a42-3e58-4c76-80f2-c291aa2d8e49","Sim",{"_20":231,"_26":32,"_28":232},"5e6d0254-696c-4da0-b572-82e3a19f433e","Não",{"_20":234,"_26":36,"_28":235},"3ce109b1-6cdb-4b4d-8816-a6af4d74bed0","Indeterminado",{"_20":237,"_26":40,"_28":238},"35403f68-a880-429d-97f4-db507c58de38","Todos",{"_20":240,"_26":157,"_28":241},"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????",[161],[161,245,251,252,253],{"_20":246,"_55":110,"_92":111,"_94":95,"_96":162,"_67":247,"_69":247,"_63":248,"_105":250},"88fe96b3-2a17-4198-90d5-ddda3d6f5d45","2025-04-29T03:44:35.328997+00:00",{"_99":167,"_101":102,"_103":249},25741,"mecanica-3",{"_20":90,"_55":91,"_92":93,"_94":95,"_96":-5,"_67":97,"_69":97,"_63":98,"_105":93},{"_20":109,"_55":110,"_92":111,"_94":95,"_96":90,"_67":112,"_69":112,"_63":113,"_105":116},{"_20":165,"_55":254,"_92":255,"_94":95,"_96":-5,"_67":256,"_69":256,"_63":257,"_105":255},"Engenharia","engenharia","2025-04-29T01:55:38.635246+00:00",{"_99":258,"_101":102,"_103":259},29,351586,"tagsTree",[89,262],{"_20":165,"_55":254,"_92":255,"_94":95,"_96":-5,"_67":256,"_69":256,"_63":257,"_105":255,"_106":263},[264],{"_20":162,"_55":163,"_92":164,"_94":95,"_96":165,"_67":112,"_69":112,"_63":166,"_105":169,"_106":265},[266],{"_20":246,"_55":110,"_92":111,"_94":95,"_96":162,"_67":247,"_69":247,"_63":248,"_105":250,"_106":267},[],"videoDislikes",{},"videoLikes",{},"actionData","errors"]

Comentários