[{"_1":2,"_206":-5,"_207":-5},"loaderData",{"_3":4,"_6":7},"root",{"_5":-5},"user","pages/questions/show/index",{"_8":9,"_10":11,"_40":41,"_42":43,"_64":192,"_193":194},"comments",[],"question",{"_12":13,"_14":13,"_15":16,"_17":18,"_37":13,"_38":39},"correctOptionId","","difficulty","id","ffc726ed-c86b-4c37-a305-ea56da03674a","options",[19,25,29,33],{"_15":20,"_21":22,"_23":24},"9d799190-098e-431c-b9f0-f7088f2aa43c","label","A","text","23 \text{ m/s}",{"_15":26,"_21":27,"_23":28},"2ac2af05-550f-4a4d-b207-e7cbb59577e9","B","15 \text{ m/s}",{"_15":30,"_21":31,"_23":32},"aec79a60-3fbf-40b4-ab2b-c03325f8bce9","C","19 \text{ m/s}",{"_15":34,"_21":35,"_23":36},"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}?

","relatedVideos",[],"similarQuestions",[44,118,135,152,172],{"_12":13,"_14":13,"_15":45,"_17":46,"_37":13,"_38":63,"_64":65},"3c0b9441-b878-4896-8bac-fa4ca61e3f13",[47,50,53,56,59],{"_15":48,"_21":22,"_23":49},"265bd71a-6749-41f5-b291-67efd646ca64","y'' + 2y' - 3y = 0",{"_15":51,"_21":27,"_23":52},"6d3c3a1d-8e80-4ff3-b97a-d5b5bca91940","6y'' - y' - y = 0",{"_15":54,"_21":31,"_23":55},"4168ac67-64fd-46ed-a69c-a01dbfcde7ea","y'' - 2y' + y = 0",{"_15":57,"_21":35,"_23":58},"cc7bc8df-6995-4264-ac5a-32ea9b4ed7db","9y'' + 6y' + y = 0",{"_15":60,"_21":61,"_23":62},"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",[66,89,97,105,111],{"_15":67,"_68":69,"_70":71,"_72":73,"_74":75,"_76":77,"_78":77,"_79":80,"_87":88},"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",{"_81":82,"_83":84,"_85":86},"childrenCount",5,"content_count",0,"question_count",30614,"slug","engenharia-mecatronica-1",{"_15":90,"_68":91,"_70":92,"_72":73,"_74":67,"_76":93,"_78":93,"_79":94,"_87":96},"88fe96b3-2a17-4198-90d5-ddda3d6f5d45","Mecânica","mecanica","2025-04-29T03:44:35.328997+00:00",{"_81":82,"_83":84,"_85":95},25741,"mecanica-3",{"_15":98,"_68":99,"_70":100,"_72":73,"_74":-5,"_76":101,"_78":101,"_79":102,"_87":100},"9772e958-72c6-4499-ad47-877cf94d670d","Exatas","exatas","2025-04-29T01:56:45.284172+00:00",{"_81":103,"_83":84,"_85":104},18,135489,{"_15":106,"_68":91,"_70":92,"_72":73,"_74":98,"_76":77,"_78":77,"_79":107,"_87":110},"ca6fee0e-79c6-4f1c-b500-ee081a071949",{"_81":108,"_83":84,"_85":109},10,19948,"mecanica-2",{"_15":75,"_68":112,"_70":113,"_72":73,"_74":-5,"_76":114,"_78":114,"_79":115,"_87":113},"Engenharia","engenharia","2025-04-29T01:55:38.635246+00:00",{"_81":116,"_83":84,"_85":117},29,351586,{"_12":13,"_14":13,"_15":119,"_17":120,"_37":13,"_38":133,"_64":134},"4a3f20e5-655d-4a84-bbdf-aa3b0de4581a",[121,124,127,130],{"_15":122,"_21":22,"_23":123},"8dee6a5e-57a3-4743-8b5a-da9b8c54fb32","Verdadero, verdadero, verdadero, verdadero.",{"_15":125,"_21":27,"_23":126},"ca0a9b0d-3004-478e-9ca9-bafa5243aca9","Verdadero, verdadero, falso, verdadero.",{"_15":128,"_21":31,"_23":129},"68712800-8b4b-46af-9cdf-3f83e4032c30","Verdadero, falso, verdadero, falso.",{"_15":131,"_21":35,"_23":132},"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.

",[66,89,97,105,111],{"_12":13,"_14":13,"_15":136,"_17":137,"_37":13,"_38":150,"_64":151},"93a32dd4-5fc6-4ccb-a76f-4724bf113742",[138,141,144,147],{"_15":139,"_21":22,"_23":140},"13e3f476-a0a5-421f-b47e-0969e8e9a7e0","

Verdadeiro, verdadeiro, falso

",{"_15":142,"_21":27,"_23":143},"c9a20855-d84b-4860-8b35-9784818282cf","

Falso, verdadeiro, verdadeiro

",{"_15":145,"_21":31,"_23":146},"6831a9b9-c9a4-4a76-bd7a-2ce98bfea875","

Verdadeiro, falso, verdadeiro

",{"_15":148,"_21":35,"_23":149},"3c98539b-1af9-4d44-aecd-c266754a2075","

Falso, falso, falso

","

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

",[66,89,97,105,111],{"_12":13,"_14":13,"_15":153,"_17":154,"_37":13,"_38":170,"_64":171},"996628fc-4ac3-4821-86bd-839f86a97a6d",[155,158,161,164,167],{"_15":156,"_21":22,"_23":157},"5ad09994-6dcb-4c66-87ae-ec00e9b439b7","5 + 3x < 2x + 4",{"_15":159,"_21":27,"_23":160},"b3ae9948-890b-4807-b801-1e1888cb0c10","3 + 4x \\leq 8x + 6",{"_15":162,"_21":31,"_23":163},"d2964603-f26c-4be6-99ae-d174678f104c","5 + 4x > 3x + 2",{"_15":165,"_21":35,"_23":166},"88c48b1a-ce37-4eae-a900-a4fb4bd581d9","1 + 3x \\geq 5x + 7",{"_15":168,"_21":61,"_23":169},"155e0bb0-6c7f-4d9c-96e5-d1cdb97c632b","4(3 + 2x) < -(6x + 8)","Resolver las siguientes inecuaciones y representar la solución en la recta real:",[66,89,97,105,111],{"_12":13,"_14":13,"_15":173,"_17":174,"_37":13,"_38":190,"_64":191},"c478a46c-46a8-4942-ae14-2e79def3dda2",[175,178,181,184,187],{"_15":176,"_21":22,"_23":177},"a5a16a42-3e58-4c76-80f2-c291aa2d8e49","Sim",{"_15":179,"_21":27,"_23":180},"5e6d0254-696c-4da0-b572-82e3a19f433e","Não",{"_15":182,"_21":31,"_23":183},"3ce109b1-6cdb-4b4d-8816-a6af4d74bed0","Indeterminado",{"_15":185,"_21":35,"_23":186},"35403f68-a880-429d-97f4-db507c58de38","Todos",{"_15":188,"_21":61,"_23":189},"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????",[66,89,97,105,111],[66,89,97,105,111],"tagsTree",[195,200],{"_15":98,"_68":99,"_70":100,"_72":73,"_74":-5,"_76":101,"_78":101,"_79":102,"_87":100,"_196":197},"children",[198],{"_15":106,"_68":91,"_70":92,"_72":73,"_74":98,"_76":77,"_78":77,"_79":107,"_87":110,"_196":199},[],{"_15":75,"_68":112,"_70":113,"_72":73,"_74":-5,"_76":114,"_78":114,"_79":115,"_87":113,"_196":201},[202],{"_15":67,"_68":69,"_70":71,"_72":73,"_74":75,"_76":77,"_78":77,"_79":80,"_87":88,"_196":203},[204],{"_15":90,"_68":91,"_70":92,"_72":73,"_74":67,"_76":93,"_78":93,"_79":94,"_87":96,"_196":205},[],"actionData","errors"]

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