[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"transcript-16633a37-b08a-4ea9-aeec-486208e2793a-en":3,"footer-top-topics-en":199,"transcript-poster-16633a37-b08a-4ea9-aeec-486208e2793a":253,"footer-top-speakers-en":254},{"falas":4,"lang":186,"meta":187},[5,15,22,29,36,43,49,56,63,70,77,83,88,94,100,105,111,116,121,127,133,140,145,151,157,163,168,174,180],{"idx":6,"utterance_id":7,"speaker_name":8,"speaker_slug":9,"text":10,"start_s":11,"end_s":12,"word_count":13,"indexable":14},0,"53709","Tarcisio","tarcisio","The governor's challenge, and today's question is from ITA.",1.34,4.32,10,false,{"idx":16,"utterance_id":17,"speaker_name":8,"speaker_slug":9,"text":18,"start_s":19,"end_s":20,"word_count":21,"indexable":14},1,"53710","And just to remind you, ITA has already opened registrations and has already published the announcement.",4.86,8.98,16,{"idx":23,"utterance_id":24,"speaker_name":8,"speaker_slug":9,"text":25,"start_s":26,"end_s":27,"word_count":28,"indexable":14},2,"53711","The first-phase exam is in September; the second-phase exam is in October.",9.18,12.34,12,{"idx":30,"utterance_id":31,"speaker_name":8,"speaker_slug":9,"text":32,"start_s":33,"end_s":34,"word_count":35,"indexable":14},3,"53712","And the best way to prepare now is to do questions from previous years.",12.6,16.64,14,{"idx":37,"utterance_id":38,"speaker_name":8,"speaker_slug":9,"text":39,"start_s":40,"end_s":41,"word_count":42,"indexable":14},4,"53713","It's practice, practice, practice, practice.",16.86,18.48,5,{"idx":42,"utterance_id":44,"speaker_name":8,"speaker_slug":9,"text":45,"start_s":46,"end_s":47,"word_count":48,"indexable":14},"53714","And here is a little math question: let A be the summation from k = 0 to n of the binomial coefficient (n choose k) times 3^k, and let B be the summation from k = 0 to n-1 of (n-1 choose k) times 11^k. If log B minus log A equals log(6561\u002F4), then n equals what? Shall we solve it?",18.6,41,77,{"idx":50,"utterance_id":51,"speaker_name":8,"speaker_slug":9,"text":52,"start_s":53,"end_s":54,"word_count":55,"indexable":14},6,"53715","Well, the first thing I need to know is that A equals (n choose 0)·3^0 + (n choose 1)·3^1 + ... + (n choose n)·3^n. And what does that look like?",41.2,60.88,60,{"idx":57,"utterance_id":58,"speaker_name":8,"speaker_slug":9,"text":59,"start_s":60,"end_s":61,"word_count":62,"indexable":14},7,"53716","It looks like a binomial of the form (1 + 3)^n. Could that be true?",61.38,67.34,17,{"idx":64,"utterance_id":65,"speaker_name":8,"speaker_slug":9,"text":66,"start_s":67,"end_s":68,"word_count":69,"indexable":14},8,"53717","Observe: this binomial, (1 + 3)^n, can be expanded as (n choose 0)·1^n·3^0 + (n choose 1)·1^{n-1}·3^1 + ... + (n choose n)·1^0·3^n. Since 1 to any power is 1, this is exactly equal to the sum above, and therefore this equals (1 + 3)^n, which means A = 4^n. An analogous reasoning can be done for B. B will be equal to (n-1 choose 0)·11^0 + (n-1 choose 1)·11^1 + ... + (n-1 choose n-1)·11^{n-1}.",67.52,129.46,169,{"idx":71,"utterance_id":72,"speaker_name":8,"speaker_slug":9,"text":73,"start_s":74,"end_s":75,"word_count":76,"indexable":14},9,"53718","This is equal to (1 + 11)^{n-1}, which is equal to 12^{n-1}.",129.68,138.98,25,{"idx":13,"utterance_id":78,"speaker_name":8,"speaker_slug":9,"text":79,"start_s":80,"end_s":81,"word_count":82,"indexable":14},"53719","Having found A and B, I can apply the following property.",139.36,143.54,11,{"idx":82,"utterance_id":84,"speaker_name":8,"speaker_slug":9,"text":85,"start_s":86,"end_s":87,"word_count":23,"indexable":14},"53720","Logarithm property.",143.56,144.82,{"idx":28,"utterance_id":89,"speaker_name":8,"speaker_slug":9,"text":90,"start_s":91,"end_s":92,"word_count":93,"indexable":14},"53721","I know that log B minus log A, assuming they're in the same base, equals log(B\u002FA). And if I know that log(B\u002FA) equals log(6561\u002F4), then B\u002FA = 6561\u002F4.",145.24,168.08,57,{"idx":95,"utterance_id":96,"speaker_name":8,"speaker_slug":9,"text":97,"start_s":98,"end_s":99,"word_count":30,"indexable":14},13,"53722","What is B?",168.2,169.44,{"idx":35,"utterance_id":101,"speaker_name":8,"speaker_slug":9,"text":102,"start_s":103,"end_s":104,"word_count":50,"indexable":14},"53723","12^(n-1).",169.46,172.72,{"idx":106,"utterance_id":107,"speaker_name":8,"speaker_slug":9,"text":108,"start_s":109,"end_s":110,"word_count":50,"indexable":14},15,"53724","What is 4^n?",172.84,175.68,{"idx":21,"utterance_id":112,"speaker_name":8,"speaker_slug":9,"text":113,"start_s":114,"end_s":115,"word_count":71,"indexable":14},"53725","This will equal 6561\u002F4.",175.94,180.3,{"idx":62,"utterance_id":117,"speaker_name":8,"speaker_slug":9,"text":118,"start_s":119,"end_s":120,"word_count":57,"indexable":14},"53726","Then I can do some simplifications, right?",180.68,182.46,{"idx":122,"utterance_id":123,"speaker_name":8,"speaker_slug":9,"text":124,"start_s":125,"end_s":126,"word_count":82,"indexable":14},18,"53727","I can manipulate this and say, look, what is 12?",182.56,184.82,{"idx":128,"utterance_id":129,"speaker_name":8,"speaker_slug":9,"text":130,"start_s":131,"end_s":132,"word_count":64,"indexable":14},19,"53728","Isn't 12 just 3 times 4?",184.86,186.98,{"idx":134,"utterance_id":135,"speaker_name":8,"speaker_slug":9,"text":136,"start_s":137,"end_s":138,"word_count":139,"indexable":14},20,"53729","So I can say that this is 3^(n-1) times 4^(n-1).",187.28,194.12,21,{"idx":139,"utterance_id":141,"speaker_name":8,"speaker_slug":9,"text":142,"start_s":143,"end_s":144,"word_count":71,"indexable":14},"53730","And here in the denominator, what is 4^n?",194.2,196.18,{"idx":146,"utterance_id":147,"speaker_name":8,"speaker_slug":9,"text":148,"start_s":149,"end_s":150,"word_count":95,"indexable":14},22,"53731","I can say it's 4^(n-1) times 4.",196.5,201.3,{"idx":152,"utterance_id":153,"speaker_name":8,"speaker_slug":9,"text":154,"start_s":155,"end_s":156,"word_count":62,"indexable":14},23,"53732","This will be equal to 6561\u002F4, which, in fact, is 3^8\u002F4.",201.5,207.7,{"idx":158,"utterance_id":159,"speaker_name":8,"speaker_slug":9,"text":160,"start_s":161,"end_s":162,"word_count":146,"indexable":14},24,"53733","I can cancel this 4 with that 4; I can cancel this 4^(n-1) with that 4^(n-1).",208.36,213.38,{"idx":76,"utterance_id":164,"speaker_name":8,"speaker_slug":9,"text":165,"start_s":166,"end_s":167,"word_count":30,"indexable":14},"53734","What remains?",213.72,214.16,{"idx":169,"utterance_id":170,"speaker_name":8,"speaker_slug":9,"text":171,"start_s":172,"end_s":173,"word_count":35,"indexable":14},26,"53735","3^(n-1) will be equal to 3^8.",214.18,219.66,{"idx":175,"utterance_id":176,"speaker_name":8,"speaker_slug":9,"text":177,"start_s":178,"end_s":179,"word_count":106,"indexable":14},27,"53736","Therefore n - 1 = 8, and thus n = 9.",219.92,225.46,{"idx":181,"utterance_id":182,"speaker_name":8,"speaker_slug":9,"text":183,"start_s":184,"end_s":185,"word_count":37,"indexable":14},28,"53737","That's the answer.",225.64,227.7,"en",{"job_id":188,"title":189,"source_url":190,"platform":191,"content_type":192,"published_at":193,"duration_sec":194,"n_classified":195,"speakers":196},"16633a37-b08a-4ea9-aeec-486208e2793a","Tarcísio Gomes de Freitas - Não existe atalho fácil para passar no vestibular. Mas existe um bom ...","https:\u002F\u002Fx.com\u002Ftarcisiogdf\u002Fstatus\u002F2075948855166751012","twitter","video","2026-07-11T14:22:30Z",227.718125,29,[197],{"name":8,"slug":9,"photo_url":198,"n_falas":195},"\u002Fprofiles\u002Ftarcisio\u002Fphoto.png",{"limit":13,"offset":6,"topics":200,"total":252},[201,206,212,217,223,227,232,237,242,247],{"label":202,"n_speakers":169,"n_utterances":203,"n_videos":204,"slug":205},"National Security",2789,195,"seguranca-nacional",{"label":207,"n_speakers":208,"n_utterances":209,"n_videos":210,"slug":211},"Education",32,1727,233,"educacao",{"label":213,"n_speakers":152,"n_utterances":214,"n_videos":215,"slug":216},"Public Safety and Order",1580,244,"seguranca-publica-e-ordem",{"label":218,"n_speakers":219,"n_utterances":220,"n_videos":221,"slug":222},"Combating Impunity",33,1483,296,"combate-a-impunidade",{"label":224,"n_speakers":208,"n_utterances":220,"n_videos":225,"slug":226},"Monetary 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