[{"_1":2,"_215":-5,"_216":-5},"loaderData",{"_3":4,"_8":9},"root",{"_5":6,"_7":-5},"url","https://prouniversitario.com/exercicios/fbfea5ea-6554-403f-afbb-0a7acc3a668d","user","pages/questions/show/index",{"_10":11,"_12":13,"_14":15,"_50":51,"_52":53,"_73":201,"_202":203},"comments",[],"isAiGenerated",false,"question",{"_16":17,"_18":17,"_19":20,"_21":22,"_45":17,"_46":47,"_48":49},"correctOptionId","","difficulty","id","fbfea5ea-6554-403f-afbb-0a7acc3a668d","options",[23,29,33,37,41],{"_19":24,"_25":26,"_27":28},"35eb9f14-51d2-4f25-9c6b-14d982e887e0","label","A","text","379 259 km",{"_19":30,"_25":31,"_27":32},"9bbfd0dc-ea9c-41bc-bf9f-8612e7a37de7","B","149 260 km",{"_19":34,"_25":35,"_27":36},"34f149bc-15ac-4515-9d1e-44391e334581","C","579 260 km",{"_19":38,"_25":39,"_27":40},"ff8a1a64-5899-4e8a-85d7-c2a3ae2b0db7","D","3790 km",{"_19":42,"_25":43,"_27":44},"45d5e8f7-3349-4b85-9675-97b05c602536","E","103.260 km","solution_explanation","statement","

Admita que a massa da Terra seja 80 vezes superior à massa da Lua e que a distância entre os seus centros seja igual a 384.000 \text{ km}. Calcule a que distância do centro da Lua está situado o centro de massa do sistema Terra-Lua.

","status","has_issues","relatedVideos",[],"similarQuestions",[54,127,144,161,181],{"_16":17,"_18":17,"_19":55,"_21":56,"_45":17,"_46":72,"_73":74},"3c0b9441-b878-4896-8bac-fa4ca61e3f13",[57,60,63,66,69],{"_19":58,"_25":26,"_27":59},"265bd71a-6749-41f5-b291-67efd646ca64","y'' + 2y' - 3y = 0",{"_19":61,"_25":31,"_27":62},"6d3c3a1d-8e80-4ff3-b97a-d5b5bca91940","6y'' - y' - y = 0",{"_19":64,"_25":35,"_27":65},"4168ac67-64fd-46ed-a69c-a01dbfcde7ea","y'' - 2y' + y = 0",{"_19":67,"_25":39,"_27":68},"cc7bc8df-6995-4264-ac5a-32ea9b4ed7db","9y'' + 6y' + y = 0",{"_19":70,"_25":43,"_27":71},"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",[75,98,106,114,120],{"_19":76,"_77":78,"_79":80,"_81":82,"_83":84,"_85":86,"_87":86,"_88":89,"_96":97},"861ad829-750d-4a44-9569-2f18b430b4df","name","Engenharia Mecatrônica","alias","engenharia-mecatronica","tag_group_id","c1ce2cf2-b217-4cc7-8182-81c56bd3522d","parent_id","eb9315c5-bd04-4116-aa46-02c4fde320c0","created_at","2025-04-29T02:19:12.828432+00:00","updated_at","metadata",{"_90":91,"_92":93,"_94":95},"childrenCount",5,"content_count",0,"question_count",30614,"slug","engenharia-mecatronica-1",{"_19":99,"_77":100,"_79":101,"_81":82,"_83":76,"_85":102,"_87":102,"_88":103,"_96":105},"88fe96b3-2a17-4198-90d5-ddda3d6f5d45","Mecânica","mecanica","2025-04-29T03:44:35.328997+00:00",{"_90":91,"_92":93,"_94":104},25741,"mecanica-3",{"_19":107,"_77":108,"_79":109,"_81":82,"_83":-5,"_85":110,"_87":110,"_88":111,"_96":109},"9772e958-72c6-4499-ad47-877cf94d670d","Exatas","exatas","2025-04-29T01:56:45.284172+00:00",{"_90":112,"_92":93,"_94":113},18,135489,{"_19":115,"_77":100,"_79":101,"_81":82,"_83":107,"_85":86,"_87":86,"_88":116,"_96":119},"ca6fee0e-79c6-4f1c-b500-ee081a071949",{"_90":117,"_92":93,"_94":118},10,19948,"mecanica-2",{"_19":84,"_77":121,"_79":122,"_81":82,"_83":-5,"_85":123,"_87":123,"_88":124,"_96":122},"Engenharia","engenharia","2025-04-29T01:55:38.635246+00:00",{"_90":125,"_92":93,"_94":126},29,351586,{"_16":17,"_18":17,"_19":128,"_21":129,"_45":17,"_46":142,"_73":143},"4a3f20e5-655d-4a84-bbdf-aa3b0de4581a",[130,133,136,139],{"_19":131,"_25":26,"_27":132},"8dee6a5e-57a3-4743-8b5a-da9b8c54fb32","Verdadero, verdadero, verdadero, verdadero.",{"_19":134,"_25":31,"_27":135},"ca0a9b0d-3004-478e-9ca9-bafa5243aca9","Verdadero, verdadero, falso, verdadero.",{"_19":137,"_25":35,"_27":138},"68712800-8b4b-46af-9cdf-3f83e4032c30","Verdadero, falso, verdadero, falso.",{"_19":140,"_25":39,"_27":141},"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.

",[75,98,106,114,120],{"_16":17,"_18":17,"_19":145,"_21":146,"_45":17,"_46":159,"_73":160},"93a32dd4-5fc6-4ccb-a76f-4724bf113742",[147,150,153,156],{"_19":148,"_25":26,"_27":149},"13e3f476-a0a5-421f-b47e-0969e8e9a7e0","

Verdadeiro, verdadeiro, falso

",{"_19":151,"_25":31,"_27":152},"c9a20855-d84b-4860-8b35-9784818282cf","

Falso, verdadeiro, verdadeiro

",{"_19":154,"_25":35,"_27":155},"6831a9b9-c9a4-4a76-bd7a-2ce98bfea875","

Verdadeiro, falso, verdadeiro

",{"_19":157,"_25":39,"_27":158},"3c98539b-1af9-4d44-aecd-c266754a2075","

Falso, falso, falso

","

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

",[75,98,106,114,120],{"_16":17,"_18":17,"_19":162,"_21":163,"_45":17,"_46":179,"_73":180},"996628fc-4ac3-4821-86bd-839f86a97a6d",[164,167,170,173,176],{"_19":165,"_25":26,"_27":166},"5ad09994-6dcb-4c66-87ae-ec00e9b439b7","5 + 3x < 2x + 4",{"_19":168,"_25":31,"_27":169},"b3ae9948-890b-4807-b801-1e1888cb0c10","3 + 4x \\leq 8x + 6",{"_19":171,"_25":35,"_27":172},"d2964603-f26c-4be6-99ae-d174678f104c","5 + 4x > 3x + 2",{"_19":174,"_25":39,"_27":175},"88c48b1a-ce37-4eae-a900-a4fb4bd581d9","1 + 3x \\geq 5x + 7",{"_19":177,"_25":43,"_27":178},"155e0bb0-6c7f-4d9c-96e5-d1cdb97c632b","4(3 + 2x) < -(6x + 8)","Resolver las siguientes inecuaciones y representar la solución en la recta real:",[75,98,106,114,120],{"_16":17,"_18":17,"_19":182,"_21":183,"_45":17,"_46":199,"_73":200},"c478a46c-46a8-4942-ae14-2e79def3dda2",[184,187,190,193,196],{"_19":185,"_25":26,"_27":186},"a5a16a42-3e58-4c76-80f2-c291aa2d8e49","Sim",{"_19":188,"_25":31,"_27":189},"5e6d0254-696c-4da0-b572-82e3a19f433e","Não",{"_19":191,"_25":35,"_27":192},"3ce109b1-6cdb-4b4d-8816-a6af4d74bed0","Indeterminado",{"_19":194,"_25":39,"_27":195},"35403f68-a880-429d-97f4-db507c58de38","Todos",{"_19":197,"_25":43,"_27":198},"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????",[75,98,106,114,120],[75,98,106,114,120],"tagsTree",[204,209],{"_19":107,"_77":108,"_79":109,"_81":82,"_83":-5,"_85":110,"_87":110,"_88":111,"_96":109,"_205":206},"children",[207],{"_19":115,"_77":100,"_79":101,"_81":82,"_83":107,"_85":86,"_87":86,"_88":116,"_96":119,"_205":208},[],{"_19":84,"_77":121,"_79":122,"_81":82,"_83":-5,"_85":123,"_87":123,"_88":124,"_96":122,"_205":210},[211],{"_19":76,"_77":78,"_79":80,"_81":82,"_83":84,"_85":86,"_87":86,"_88":89,"_96":97,"_205":212},[213],{"_19":99,"_77":100,"_79":101,"_81":82,"_83":76,"_85":102,"_87":102,"_88":103,"_96":105,"_205":214},[],"actionData","errors"]

Comentários