[{"_1":2,"_272":-5,"_273":-5},"loaderData",{"_3":4,"_8":9},"root",{"_5":6,"_7":-5},"url","https://prouniversitario.com/exercicios/fa6aef25-2ef6-4b77-8f4c-38bc90af539b","user","pages/questions/show/index",{"_10":11,"_12":13,"_14":15,"_50":51,"_139":140,"_88":259,"_260":261,"_268":269,"_270":271},"comments",[],"isAiGenerated",false,"question",{"_16":17,"_18":17,"_19":20,"_21":22,"_45":17,"_46":47,"_48":49},"correctOptionId","","difficulty","id","fa6aef25-2ef6-4b77-8f4c-38bc90af539b","options",[23,29,33,37,41],{"_19":24,"_25":26,"_27":28},"9fb4badc-d2ab-483f-858d-1aea881ef4d3","label","A","text","A e B.",{"_19":30,"_25":31,"_27":32},"8a25d171-0b63-4cad-9f1a-179f1ef2d24a","B","A e C.",{"_19":34,"_25":35,"_27":36},"a7734f6c-9162-4c8d-92b7-44a18c6b11b1","C","B e D.",{"_19":38,"_25":39,"_27":40},"44425505-f195-4cd3-8daa-bfe9ea0f21e4","D","B e C.",{"_19":42,"_25":43,"_27":44},"0abf5265-0d05-4f1d-aa8e-f8b41d4853c3","E","D e B.","solution_explanation","statement","O emprego de extintor do tipo pó químico, com capacidade mínima de 4 Kgf, é exigido no combate contra incêndio nas classes:","status","pending_classification","relatedVideos",[52],{"_53":54,"_72":73,"_88":89,"_90":91,"_110":111},"content",{"_19":55,"_56":57,"_58":-5,"_59":60,"_61":62,"_63":-5,"_64":65,"_68":69,"_70":69,"_71":-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",{"_66":67},"external_id","12593","created_at","2025-08-20T12:27:41.608438+00:00","updated_at","content_group_id","prometheusData",{"_74":75,"_81":82,"_83":84,"_85":86,"_5":87},"provider",{"_19":76,"_77":78,"_79":80},"d6d15d4b-87f1-4181-b20a-19190395ac14","key","grupo_q_cloudflare_stream","kind","cloudflare_stream","reference","788b0a69895b7d4d00f0f7c468c32531","state","completed","thumbnail_url","https://videodelivery.net/eyJraWQiOiIzNDIwNjA3YjJiNTVjMjc2ZTVhNmE1NzYzMGRkNDlhYyIsImFsZyI6IlJTMjU2In0.eyJzdWIiOiI3ODhiMGE2OTg5NWI3ZDRkMDBmMGY3YzQ2OGMzMjUzMSIsImtpZCI6IjM0MjA2MDdiMmI1NWMyNzZlNWE2YTU3NjMwZGQ0OWFjIiwiZXhwIjoxNzU1OTAyNjc0fQ.XbTMKw27QUWkmmW4n9FDKbuhjmTcyMQgIz-tlM9VQBvQY80zrIAGJ-qe7BGaKJmR6jXE1hSlPJiBXGV41AZtwOO2YPBNi6zSCAxDjz0igbWNOpYDpHJ3rtmMNQdKBGGm0SO5aA9uIVptoO5i8DqmN-OyDRxjkNfA_-wtNW7poQUIpL_Bs2ymbx8gwC-R6dv1NkiYWc7k464-Bd2F2LQ24_UQTwBq0_8peWcpm1vAdLOY9_6lIIuRP3GK8G_IoZhUPn55-qAzxhGuXlseuzIO5Tyxv0hsaL60SircmpyDYKSbifyAlCF0wzgrq79BcToFnYY5f9EUCi-wg5FYiU66Fg/thumbnails/thumbnail.jpg?time=10s&height=360","https://customer-356s6wt60g79gz5u.cloudflarestream.com/eyJraWQiOiIzNDIwNjA3YjJiNTVjMjc2ZTVhNmE1NzYzMGRkNDlhYyIsImFsZyI6IlJTMjU2In0.eyJzdWIiOiI3ODhiMGE2OTg5NWI3ZDRkMDBmMGY3YzQ2OGMzMjUzMSIsImtpZCI6IjM0MjA2MDdiMmI1NWMyNzZlNWE2YTU3NjMwZGQ0OWFjIiwiZXhwIjoxNzU1OTAyNjc0fQ.XbTMKw27QUWkmmW4n9FDKbuhjmTcyMQgIz-tlM9VQBvQY80zrIAGJ-qe7BGaKJmR6jXE1hSlPJiBXGV41AZtwOO2YPBNi6zSCAxDjz0igbWNOpYDpHJ3rtmMNQdKBGGm0SO5aA9uIVptoO5i8DqmN-OyDRxjkNfA_-wtNW7poQUIpL_Bs2ymbx8gwC-R6dv1NkiYWc7k464-Bd2F2LQ24_UQTwBq0_8peWcpm1vAdLOY9_6lIIuRP3GK8G_IoZhUPn55-qAzxhGuXlseuzIO5Tyxv0hsaL60SircmpyDYKSbifyAlCF0wzgrq79BcToFnYY5f9EUCi-wg5FYiU66Fg/manifest/video.m3u8","tags",[],"video",{"_19":62,"_92":57,"_58":-5,"_93":94,"_95":96,"_5":-5,"_97":-5,"_74":96,"_98":99,"_85":-5,"_100":-5,"_101":-5,"_102":-5,"_103":-5,"_64":104,"_105":106,"_107":-5,"_48":108,"_68":109,"_70":109},"title","duration",21,"source_type","prometheus","iframe_url","provider_video_id","8335867d-4f35-401e-a9c3-13c4a0db8c56","format","quality","file_path","file_size",{"_66":67},"views_count",0,"last_played_at","draft","2025-08-19T11:56:14.613229+00:00","tag",{"_19":112,"_56":113,"_114":115,"_116":117,"_118":-5,"_68":119,"_70":119,"_64":120,"_126":115,"_127":128},"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",{"_121":122,"_123":106,"_124":125},"childrenCount",18,"content_count","question_count",135489,"slug","children",[129],{"_19":130,"_56":131,"_114":132,"_116":117,"_118":112,"_68":133,"_70":133,"_64":134,"_126":137,"_127":138},"ca6fee0e-79c6-4f1c-b500-ee081a071949","Mecânica","mecanica","2025-04-29T02:19:12.828432+00:00",{"_121":135,"_123":106,"_124":136},10,19948,"mecanica-2",[],"similarQuestions",[141,185,202,219,239],{"_16":17,"_18":17,"_19":142,"_21":143,"_45":17,"_46":159,"_88":160},"3c0b9441-b878-4896-8bac-fa4ca61e3f13",[144,147,150,153,156],{"_19":145,"_25":26,"_27":146},"265bd71a-6749-41f5-b291-67efd646ca64","y'' + 2y' - 3y = 0",{"_19":148,"_25":31,"_27":149},"6d3c3a1d-8e80-4ff3-b97a-d5b5bca91940","6y'' - y' - y = 0",{"_19":151,"_25":35,"_27":152},"4168ac67-64fd-46ed-a69c-a01dbfcde7ea","y'' - 2y' + y = 0",{"_19":154,"_25":39,"_27":155},"cc7bc8df-6995-4264-ac5a-32ea9b4ed7db","9y'' + 6y' + y = 0",{"_19":157,"_25":43,"_27":158},"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

",[161,170,176,177,178],{"_19":162,"_56":163,"_114":164,"_116":117,"_118":165,"_68":133,"_70":133,"_64":166,"_126":169},"861ad829-750d-4a44-9569-2f18b430b4df","Engenharia Mecatrônica","engenharia-mecatronica","eb9315c5-bd04-4116-aa46-02c4fde320c0",{"_121":167,"_123":106,"_124":168},5,30614,"engenharia-mecatronica-1",{"_19":171,"_56":131,"_114":132,"_116":117,"_118":162,"_68":172,"_70":172,"_64":173,"_126":175},"88fe96b3-2a17-4198-90d5-ddda3d6f5d45","2025-04-29T03:44:35.328997+00:00",{"_121":167,"_123":106,"_124":174},25741,"mecanica-3",{"_19":112,"_56":113,"_114":115,"_116":117,"_118":-5,"_68":119,"_70":119,"_64":120,"_126":115},{"_19":130,"_56":131,"_114":132,"_116":117,"_118":112,"_68":133,"_70":133,"_64":134,"_126":137},{"_19":165,"_56":179,"_114":180,"_116":117,"_118":-5,"_68":181,"_70":181,"_64":182,"_126":180},"Engenharia","engenharia","2025-04-29T01:55:38.635246+00:00",{"_121":183,"_123":106,"_124":184},29,351586,{"_16":17,"_18":17,"_19":186,"_21":187,"_45":17,"_46":200,"_88":201},"4a3f20e5-655d-4a84-bbdf-aa3b0de4581a",[188,191,194,197],{"_19":189,"_25":26,"_27":190},"8dee6a5e-57a3-4743-8b5a-da9b8c54fb32","Verdadero, verdadero, verdadero, verdadero.",{"_19":192,"_25":31,"_27":193},"ca0a9b0d-3004-478e-9ca9-bafa5243aca9","Verdadero, verdadero, falso, verdadero.",{"_19":195,"_25":35,"_27":196},"68712800-8b4b-46af-9cdf-3f83e4032c30","Verdadero, falso, verdadero, falso.",{"_19":198,"_25":39,"_27":199},"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.

",[161,170,176,177,178],{"_16":17,"_18":17,"_19":203,"_21":204,"_45":17,"_46":217,"_88":218},"93a32dd4-5fc6-4ccb-a76f-4724bf113742",[205,208,211,214],{"_19":206,"_25":26,"_27":207},"13e3f476-a0a5-421f-b47e-0969e8e9a7e0","

Verdadeiro, verdadeiro, falso

",{"_19":209,"_25":31,"_27":210},"c9a20855-d84b-4860-8b35-9784818282cf","

Falso, verdadeiro, verdadeiro

",{"_19":212,"_25":35,"_27":213},"6831a9b9-c9a4-4a76-bd7a-2ce98bfea875","

Verdadeiro, falso, verdadeiro

",{"_19":215,"_25":39,"_27":216},"3c98539b-1af9-4d44-aecd-c266754a2075","

Falso, falso, falso

","

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

",[161,170,176,177,178],{"_16":17,"_18":17,"_19":220,"_21":221,"_45":17,"_46":237,"_88":238},"996628fc-4ac3-4821-86bd-839f86a97a6d",[222,225,228,231,234],{"_19":223,"_25":26,"_27":224},"5ad09994-6dcb-4c66-87ae-ec00e9b439b7","5 + 3x < 2x + 4",{"_19":226,"_25":31,"_27":227},"b3ae9948-890b-4807-b801-1e1888cb0c10","3 + 4x \\leq 8x + 6",{"_19":229,"_25":35,"_27":230},"d2964603-f26c-4be6-99ae-d174678f104c","5 + 4x > 3x + 2",{"_19":232,"_25":39,"_27":233},"88c48b1a-ce37-4eae-a900-a4fb4bd581d9","1 + 3x \\geq 5x + 7",{"_19":235,"_25":43,"_27":236},"155e0bb0-6c7f-4d9c-96e5-d1cdb97c632b","4(3 + 2x) < -(6x + 8)","Resolver las siguientes inecuaciones y representar la solución en la recta real:",[161,170,176,177,178],{"_16":17,"_18":17,"_19":240,"_21":241,"_45":17,"_46":257,"_88":258},"c478a46c-46a8-4942-ae14-2e79def3dda2",[242,245,248,251,254],{"_19":243,"_25":26,"_27":244},"a5a16a42-3e58-4c76-80f2-c291aa2d8e49","Sim",{"_19":246,"_25":31,"_27":247},"5e6d0254-696c-4da0-b572-82e3a19f433e","Não",{"_19":249,"_25":35,"_27":250},"3ce109b1-6cdb-4b4d-8816-a6af4d74bed0","Indeterminado",{"_19":252,"_25":39,"_27":253},"35403f68-a880-429d-97f4-db507c58de38","Todos",{"_19":255,"_25":43,"_27":256},"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????",[161,170,176,177,178],[161,170,176,177,178],"tagsTree",[111,262],{"_19":165,"_56":179,"_114":180,"_116":117,"_118":-5,"_68":181,"_70":181,"_64":182,"_126":180,"_127":263},[264],{"_19":162,"_56":163,"_114":164,"_116":117,"_118":165,"_68":133,"_70":133,"_64":166,"_126":169,"_127":265},[266],{"_19":171,"_56":131,"_114":132,"_116":117,"_118":162,"_68":172,"_70":172,"_64":173,"_126":175,"_127":267},[],"videoDislikes",{},"videoLikes",{},"actionData","errors"]

Comentários