[{"_1":2,"_202":-5,"_203":-5},"loaderData",{"_3":4,"_8":9},"root",{"_5":6,"_7":-5},"url","https://prouniversitario.com/exercicios/76e0c5c8-4afd-4dd7-8b05-9c19c4c718f7","user","pages/questions/show/index",{"_10":11,"_12":13,"_46":47,"_48":49,"_69":190,"_191":192},"comments",[],"question",{"_14":15,"_16":15,"_17":18,"_19":20,"_41":15,"_42":43,"_44":45},"correctOptionId","","difficulty","id","76e0c5c8-4afd-4dd7-8b05-9c19c4c718f7","options",[21,27,31,34,37],{"_17":22,"_23":24,"_25":26},"277ba8e2-475a-4df6-8334-e36a7202b785","label","A","text","h \rho = h \rho, portanto: \rho < \rho",{"_17":28,"_23":29,"_25":30},"904a0aeb-1fb8-4d40-a77e-64a28d747ee4","B","h \rho = h \rho, portanto: \rho > \rho",{"_17":32,"_23":33,"_25":26},"a2f4313e-347b-4382-9d61-b17c62a3676a","C",{"_17":35,"_23":36,"_25":30},"fc7605e8-346c-4b05-afa5-5641ee47e5ce","D",{"_17":38,"_23":39,"_25":40},"a34d391d-ee96-4fae-839b-8d723d993f73","E","h \rho = h \rho, portanto: \rho = \rho","solution_explanation","statement","

Abaixo é representado um tubo em U, com dois fluidos imiscíveis de massa específica \rho e \rho respectivamente. O sistema está em equilíbrio, portando podemos afirmar que:

","status","has_issues","relatedVideos",[],"similarQuestions",[50,116,133,150,170],{"_14":15,"_16":15,"_17":51,"_19":52,"_41":15,"_42":68,"_69":70},"3c0b9441-b878-4896-8bac-fa4ca61e3f13",[53,56,59,62,65],{"_17":54,"_23":24,"_25":55},"265bd71a-6749-41f5-b291-67efd646ca64","y'' + 2y' - 3y = 0",{"_17":57,"_23":29,"_25":58},"6d3c3a1d-8e80-4ff3-b97a-d5b5bca91940","6y'' - y' - y = 0",{"_17":60,"_23":33,"_25":61},"4168ac67-64fd-46ed-a69c-a01dbfcde7ea","y'' - 2y' + y = 0",{"_17":63,"_23":36,"_25":64},"cc7bc8df-6995-4264-ac5a-32ea9b4ed7db","9y'' + 6y' + y = 0",{"_17":66,"_23":39,"_25":67},"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",[71,93,101,109],{"_17":72,"_73":74,"_75":76,"_77":78,"_79":80,"_81":82,"_83":82,"_84":85,"_92":76},"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",{"_86":87,"_88":89,"_90":91},"childrenCount",4,"content_count",0,"question_count",12302,"slug",{"_17":94,"_73":95,"_75":96,"_77":78,"_79":72,"_81":97,"_83":97,"_84":98,"_92":100},"8c444991-e4be-4bd9-bc90-7d0f27eb9a2f","Mecânica dos Fluidos na Engenharia de Petróleo","mecanica-dos-fluidos-na-engenharia-de-petroleo","2025-04-29T04:00:14.680867+00:00",{"_86":89,"_88":89,"_90":99},329,"mecanica-dos-fluidos-na-engenharia-de-petroleo-1",{"_17":80,"_73":102,"_75":103,"_77":78,"_79":104,"_81":105,"_83":105,"_84":106,"_92":108},"Engenharia de Petróleo","engenharia-de-petroleo","eb9315c5-bd04-4116-aa46-02c4fde320c0","2025-04-29T02:19:12.828432+00:00",{"_86":107,"_88":89,"_90":91},5,"engenharia-de-petroleo-1",{"_17":104,"_73":110,"_75":111,"_77":78,"_79":-5,"_81":112,"_83":112,"_84":113,"_92":111},"Engenharia","engenharia","2025-04-29T01:55:38.635246+00:00",{"_86":114,"_88":89,"_90":115},29,351586,{"_14":15,"_16":15,"_17":117,"_19":118,"_41":15,"_42":131,"_69":132},"4a3f20e5-655d-4a84-bbdf-aa3b0de4581a",[119,122,125,128],{"_17":120,"_23":24,"_25":121},"8dee6a5e-57a3-4743-8b5a-da9b8c54fb32","Verdadero, verdadero, verdadero, verdadero.",{"_17":123,"_23":29,"_25":124},"ca0a9b0d-3004-478e-9ca9-bafa5243aca9","Verdadero, verdadero, falso, verdadero.",{"_17":126,"_23":33,"_25":127},"68712800-8b4b-46af-9cdf-3f83e4032c30","Verdadero, falso, verdadero, falso.",{"_17":129,"_23":36,"_25":130},"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.

",[71,93,101,109],{"_14":15,"_16":15,"_17":134,"_19":135,"_41":15,"_42":148,"_69":149},"93a32dd4-5fc6-4ccb-a76f-4724bf113742",[136,139,142,145],{"_17":137,"_23":24,"_25":138},"13e3f476-a0a5-421f-b47e-0969e8e9a7e0","

Verdadeiro, verdadeiro, falso

",{"_17":140,"_23":29,"_25":141},"c9a20855-d84b-4860-8b35-9784818282cf","

Falso, verdadeiro, verdadeiro

",{"_17":143,"_23":33,"_25":144},"6831a9b9-c9a4-4a76-bd7a-2ce98bfea875","

Verdadeiro, falso, verdadeiro

",{"_17":146,"_23":36,"_25":147},"3c98539b-1af9-4d44-aecd-c266754a2075","

Falso, falso, falso

","

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

",[71,93,101,109],{"_14":15,"_16":15,"_17":151,"_19":152,"_41":15,"_42":168,"_69":169},"996628fc-4ac3-4821-86bd-839f86a97a6d",[153,156,159,162,165],{"_17":154,"_23":24,"_25":155},"5ad09994-6dcb-4c66-87ae-ec00e9b439b7","5 + 3x < 2x + 4",{"_17":157,"_23":29,"_25":158},"b3ae9948-890b-4807-b801-1e1888cb0c10","3 + 4x \\leq 8x + 6",{"_17":160,"_23":33,"_25":161},"d2964603-f26c-4be6-99ae-d174678f104c","5 + 4x > 3x + 2",{"_17":163,"_23":36,"_25":164},"88c48b1a-ce37-4eae-a900-a4fb4bd581d9","1 + 3x \\geq 5x + 7",{"_17":166,"_23":39,"_25":167},"155e0bb0-6c7f-4d9c-96e5-d1cdb97c632b","4(3 + 2x) < -(6x + 8)","Resolver las siguientes inecuaciones y representar la solución en la recta real:",[71,93,101,109],{"_14":15,"_16":15,"_17":171,"_19":172,"_41":15,"_42":188,"_69":189},"c478a46c-46a8-4942-ae14-2e79def3dda2",[173,176,179,182,185],{"_17":174,"_23":24,"_25":175},"a5a16a42-3e58-4c76-80f2-c291aa2d8e49","Sim",{"_17":177,"_23":29,"_25":178},"5e6d0254-696c-4da0-b572-82e3a19f433e","Não",{"_17":180,"_23":33,"_25":181},"3ce109b1-6cdb-4b4d-8816-a6af4d74bed0","Indeterminado",{"_17":183,"_23":36,"_25":184},"35403f68-a880-429d-97f4-db507c58de38","Todos",{"_17":186,"_23":39,"_25":187},"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????",[71,93,101,109],[71,93,101,109],"tagsTree",[193],{"_17":104,"_73":110,"_75":111,"_77":78,"_79":-5,"_81":112,"_83":112,"_84":113,"_92":111,"_194":195},"children",[196],{"_17":80,"_73":102,"_75":103,"_77":78,"_79":104,"_81":105,"_83":105,"_84":106,"_92":108,"_194":197},[198],{"_17":72,"_73":74,"_75":76,"_77":78,"_79":80,"_81":82,"_83":82,"_84":85,"_92":76,"_194":199},[200],{"_17":94,"_73":95,"_75":96,"_77":78,"_79":72,"_81":97,"_83":97,"_84":98,"_92":100,"_194":201},[],"actionData","errors"]

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