[{"_1":2,"_340":-5,"_341":-5},"loaderData",{"_3":4,"_8":9},"root",{"_5":6,"_7":-5},"url","https://prouniversitario.com/exercicios/b661261c-4122-463e-8f95-fdca1594960d","user","pages/questions/show/index",{"_10":11,"_12":13,"_14":15,"_50":51,"_148":149,"_88":313,"_314":315,"_336":337,"_338":339},"comments",[],"isAiGenerated",false,"question",{"_16":17,"_18":17,"_19":20,"_21":22,"_45":17,"_46":47,"_48":49},"correctOptionId","","difficulty","id","b661261c-4122-463e-8f95-fdca1594960d","options",[23,29,33,37,41],{"_19":24,"_25":26,"_27":28},"97d4b9ac-0009-4b58-922f-1118056754eb","label","A","text","100 MPa",{"_19":30,"_25":31,"_27":32},"aa0f00d8-a9d2-4158-8876-44c06e631d2a","B","400 MPa",{"_19":34,"_25":35,"_27":36},"878b01df-5683-4afa-bb79-f01cf0c2ae21","C","150 MPa",{"_19":38,"_25":39,"_27":40},"9cb44f1b-35b6-4777-ad13-5d8fe5a372d2","D","300 MPa",{"_19":42,"_25":43,"_27":44},"1a5e4362-32a3-49bf-8549-4a9bb60fdcef","E","200 MPa","solution_explanation","statement","Uma força de F = 20.000 \\, \text{N} atua numa área de 50 \\, \text{mm}^2. Supondo que F forma 30º com o plano da área, determine a tensão normal média.","status","has_issues","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.eyJzdWIiOiI3ODhiMGE2OTg5NWI3ZDRkMDBmMGY3YzQ2OGMzMjUzMSIsImtpZCI6IjM0MjA2MDdiMmI1NWMyNzZlNWE2YTU3NjMwZGQ0OWFjIiwiZXhwIjoxNzU1OTMzNjgxfQ.DfGAaML79Zz2QQH8jiyBo1uUfChj3YZMUA6XIgrqElt1E6jUZrna0duHOyhuPJQUNnxucX0jMmKnjwLGpdeL9ykE8532KUOgQY9RJWvfR-LsykTvtaCXaxolxblYajLHKxUQWcB2xK62EOjKvMa8g46F4aOG1PZ0IM84lfmJbt6QEQfIIGDmBoVoicTMtJRZgdbertthrfAfsCEy-CvayasWCPUbjU8HL66alX-5ZQt292KkbknygIsPJKJrtpyfehO24EPgoNO7SlwSla2ScumFU2CedBNT5BUUJAj7IRQhekf1qH4YUOwV17eozr7pSEI4nIQt2lroc_bMMyt6EA/thumbnails/thumbnail.jpg?time=10s&height=360","https://customer-356s6wt60g79gz5u.cloudflarestream.com/eyJraWQiOiIzNDIwNjA3YjJiNTVjMjc2ZTVhNmE1NzYzMGRkNDlhYyIsImFsZyI6IlJTMjU2In0.eyJzdWIiOiI3ODhiMGE2OTg5NWI3ZDRkMDBmMGY3YzQ2OGMzMjUzMSIsImtpZCI6IjM0MjA2MDdiMmI1NWMyNzZlNWE2YTU3NjMwZGQ0OWFjIiwiZXhwIjoxNzU1OTMzNjgxfQ.DfGAaML79Zz2QQH8jiyBo1uUfChj3YZMUA6XIgrqElt1E6jUZrna0duHOyhuPJQUNnxucX0jMmKnjwLGpdeL9ykE8532KUOgQY9RJWvfR-LsykTvtaCXaxolxblYajLHKxUQWcB2xK62EOjKvMa8g46F4aOG1PZ0IM84lfmJbt6QEQfIIGDmBoVoicTMtJRZgdbertthrfAfsCEy-CvayasWCPUbjU8HL66alX-5ZQt292KkbknygIsPJKJrtpyfehO24EPgoNO7SlwSla2ScumFU2CedBNT5BUUJAj7IRQhekf1qH4YUOwV17eozr7pSEI4nIQt2lroc_bMMyt6EA/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",[139],{"_19":140,"_56":141,"_114":142,"_116":117,"_118":130,"_68":143,"_70":143,"_64":144,"_126":146,"_127":147},"ac55bdba-154d-42e7-bc25-72dde822663d","Resistência dos Materiais","resistencia-dos-materiais","2025-04-29T03:44:29.139762+00:00",{"_121":106,"_123":106,"_124":145},3376,"resistencia-dos-materiais-4",[],"similarQuestions",[150,239,256,273,293],{"_16":17,"_18":17,"_19":151,"_21":152,"_45":17,"_46":168,"_88":169},"3c0b9441-b878-4896-8bac-fa4ca61e3f13",[153,156,159,162,165],{"_19":154,"_25":26,"_27":155},"265bd71a-6749-41f5-b291-67efd646ca64","y'' + 2y' - 3y = 0",{"_19":157,"_25":31,"_27":158},"6d3c3a1d-8e80-4ff3-b97a-d5b5bca91940","6y'' - y' - y = 0",{"_19":160,"_25":35,"_27":161},"4168ac67-64fd-46ed-a69c-a01dbfcde7ea","y'' - 2y' + y = 0",{"_19":163,"_25":39,"_27":164},"cc7bc8df-6995-4264-ac5a-32ea9b4ed7db","9y'' + 6y' + y = 0",{"_19":166,"_25":43,"_27":167},"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

",[170,179,188,194,198,199,200,207,212,220,221,226,232],{"_19":171,"_56":172,"_114":173,"_116":117,"_118":174,"_68":175,"_70":175,"_64":176,"_126":173},"6516bbbd-f2a3-4710-8382-702240b17836","Mecânica na Engenharia de Petróleo","mecanica-na-engenharia-de-petroleo","b787e438-0ab3-454c-ab43-5d3d14c2720d","2025-04-29T03:44:35.328997+00:00",{"_121":177,"_123":106,"_124":178},4,12302,{"_19":180,"_56":181,"_114":182,"_116":117,"_118":183,"_68":133,"_70":133,"_64":184,"_126":187},"861ad829-750d-4a44-9569-2f18b430b4df","Engenharia Mecatrônica","engenharia-mecatronica","eb9315c5-bd04-4116-aa46-02c4fde320c0",{"_121":185,"_123":106,"_124":186},5,30614,"engenharia-mecatronica-1",{"_19":189,"_56":141,"_114":142,"_116":117,"_118":190,"_68":191,"_70":191,"_64":192,"_126":193},"8850e507-a691-4d45-a7c7-16221e9c5af2","88fe96b3-2a17-4198-90d5-ddda3d6f5d45","2025-04-29T04:00:13.215003+00:00",{"_121":106,"_123":106,"_124":145},"resistencia-dos-materiais-6",{"_19":190,"_56":131,"_114":132,"_116":117,"_118":180,"_68":175,"_70":175,"_64":195,"_126":197},{"_121":185,"_123":106,"_124":196},25741,"mecanica-3",{"_19":112,"_56":113,"_114":115,"_116":117,"_118":-5,"_68":119,"_70":119,"_64":120,"_126":115},{"_19":140,"_56":141,"_114":142,"_116":117,"_118":130,"_68":143,"_70":143,"_64":144,"_126":146},{"_19":201,"_56":202,"_114":203,"_116":117,"_118":183,"_68":133,"_70":133,"_64":204,"_126":206},"b6e37f32-f8e5-4025-bf0f-69ffc00fb331","Engenharia Civil","engenharia-civil",{"_121":94,"_123":106,"_124":205},45865,"engenharia-civil-3",{"_19":174,"_56":208,"_114":209,"_116":117,"_118":183,"_68":133,"_70":133,"_64":210,"_126":211},"Engenharia de Petróleo","engenharia-de-petroleo",{"_121":185,"_123":106,"_124":178},"engenharia-de-petroleo-1",{"_19":213,"_56":214,"_114":215,"_116":117,"_118":201,"_68":216,"_70":216,"_64":217,"_126":219},"c5bf57d4-c3d8-4365-b53e-085fa14a3a95","Estruturas","estruturas","2025-04-29T03:44:32.303369+00:00",{"_121":185,"_123":106,"_124":218},8852,"estruturas-1",{"_19":130,"_56":131,"_114":132,"_116":117,"_118":112,"_68":133,"_70":133,"_64":134,"_126":137},{"_19":222,"_56":141,"_114":142,"_116":117,"_118":171,"_68":223,"_70":223,"_64":224,"_126":225},"d1e4567b-f68a-49e1-b3e5-3888343d7871","2025-04-29T04:00:14.680867+00:00",{"_121":106,"_123":106,"_124":145},"resistencia-dos-materiais-7",{"_19":227,"_56":228,"_114":142,"_116":117,"_118":213,"_68":229,"_70":229,"_64":230,"_126":231},"da8d2ecf-e949-4afc-966f-98b4b367fac1","Resistencia dos Materiais","2025-04-29T04:00:06.9766+00:00",{"_121":106,"_123":106,"_124":145},"resistencia-dos-materiais-5",{"_19":183,"_56":233,"_114":234,"_116":117,"_118":-5,"_68":235,"_70":235,"_64":236,"_126":234},"Engenharia","engenharia","2025-04-29T01:55:38.635246+00:00",{"_121":237,"_123":106,"_124":238},29,351586,{"_16":17,"_18":17,"_19":240,"_21":241,"_45":17,"_46":254,"_88":255},"4a3f20e5-655d-4a84-bbdf-aa3b0de4581a",[242,245,248,251],{"_19":243,"_25":26,"_27":244},"8dee6a5e-57a3-4743-8b5a-da9b8c54fb32","Verdadero, verdadero, verdadero, verdadero.",{"_19":246,"_25":31,"_27":247},"ca0a9b0d-3004-478e-9ca9-bafa5243aca9","Verdadero, verdadero, falso, verdadero.",{"_19":249,"_25":35,"_27":250},"68712800-8b4b-46af-9cdf-3f83e4032c30","Verdadero, falso, verdadero, falso.",{"_19":252,"_25":39,"_27":253},"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.

",[170,179,188,194,198,199,200,207,212,220,221,226,232],{"_16":17,"_18":17,"_19":257,"_21":258,"_45":17,"_46":271,"_88":272},"93a32dd4-5fc6-4ccb-a76f-4724bf113742",[259,262,265,268],{"_19":260,"_25":26,"_27":261},"13e3f476-a0a5-421f-b47e-0969e8e9a7e0","

Verdadeiro, verdadeiro, falso

",{"_19":263,"_25":31,"_27":264},"c9a20855-d84b-4860-8b35-9784818282cf","

Falso, verdadeiro, verdadeiro

",{"_19":266,"_25":35,"_27":267},"6831a9b9-c9a4-4a76-bd7a-2ce98bfea875","

Verdadeiro, falso, verdadeiro

",{"_19":269,"_25":39,"_27":270},"3c98539b-1af9-4d44-aecd-c266754a2075","

Falso, falso, falso

","

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

",[170,179,188,194,198,199,200,207,212,220,221,226,232],{"_16":17,"_18":17,"_19":274,"_21":275,"_45":17,"_46":291,"_88":292},"996628fc-4ac3-4821-86bd-839f86a97a6d",[276,279,282,285,288],{"_19":277,"_25":26,"_27":278},"5ad09994-6dcb-4c66-87ae-ec00e9b439b7","5 + 3x < 2x + 4",{"_19":280,"_25":31,"_27":281},"b3ae9948-890b-4807-b801-1e1888cb0c10","3 + 4x \\leq 8x + 6",{"_19":283,"_25":35,"_27":284},"d2964603-f26c-4be6-99ae-d174678f104c","5 + 4x > 3x + 2",{"_19":286,"_25":39,"_27":287},"88c48b1a-ce37-4eae-a900-a4fb4bd581d9","1 + 3x \\geq 5x + 7",{"_19":289,"_25":43,"_27":290},"155e0bb0-6c7f-4d9c-96e5-d1cdb97c632b","4(3 + 2x) < -(6x + 8)","Resolver las siguientes inecuaciones y representar la solución en la recta real:",[170,179,188,194,198,199,200,207,212,220,221,226,232],{"_16":17,"_18":17,"_19":294,"_21":295,"_45":17,"_46":311,"_88":312},"c478a46c-46a8-4942-ae14-2e79def3dda2",[296,299,302,305,308],{"_19":297,"_25":26,"_27":298},"a5a16a42-3e58-4c76-80f2-c291aa2d8e49","Sim",{"_19":300,"_25":31,"_27":301},"5e6d0254-696c-4da0-b572-82e3a19f433e","Não",{"_19":303,"_25":35,"_27":304},"3ce109b1-6cdb-4b4d-8816-a6af4d74bed0","Indeterminado",{"_19":306,"_25":39,"_27":307},"35403f68-a880-429d-97f4-db507c58de38","Todos",{"_19":309,"_25":43,"_27":310},"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????",[170,179,188,194,198,199,200,207,212,220,221,226,232],[170,179,188,194,198,199,200,207,212,220,221,226,232],"tagsTree",[111,316],{"_19":183,"_56":233,"_114":234,"_116":117,"_118":-5,"_68":235,"_70":235,"_64":236,"_126":234,"_127":317},[318,324,330],{"_19":180,"_56":181,"_114":182,"_116":117,"_118":183,"_68":133,"_70":133,"_64":184,"_126":187,"_127":319},[320],{"_19":190,"_56":131,"_114":132,"_116":117,"_118":180,"_68":175,"_70":175,"_64":195,"_126":197,"_127":321},[322],{"_19":189,"_56":141,"_114":142,"_116":117,"_118":190,"_68":191,"_70":191,"_64":192,"_126":193,"_127":323},[],{"_19":201,"_56":202,"_114":203,"_116":117,"_118":183,"_68":133,"_70":133,"_64":204,"_126":206,"_127":325},[326],{"_19":213,"_56":214,"_114":215,"_116":117,"_118":201,"_68":216,"_70":216,"_64":217,"_126":219,"_127":327},[328],{"_19":227,"_56":228,"_114":142,"_116":117,"_118":213,"_68":229,"_70":229,"_64":230,"_126":231,"_127":329},[],{"_19":174,"_56":208,"_114":209,"_116":117,"_118":183,"_68":133,"_70":133,"_64":210,"_126":211,"_127":331},[332],{"_19":171,"_56":172,"_114":173,"_116":117,"_118":174,"_68":175,"_70":175,"_64":176,"_126":173,"_127":333},[334],{"_19":222,"_56":141,"_114":142,"_116":117,"_118":171,"_68":223,"_70":223,"_64":224,"_126":225,"_127":335},[],"videoDislikes",{},"videoLikes",{},"actionData","errors"]

Comentários