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Öğretmen, konu anlatımını tamamladıktan sonra toplam sekiz soru çözmekte, her soruyu detaylı olarak analiz ederek doğru cevaba nasıl ulaşılacağını açıklamaktadır.","Öğretmen ayrıca akışkanların hızının arttığı yerde basıncının azaldığını, kesit alanının daraldığı yerde hızın arttığını ve bunun günlük hayattaki uygulamalarını (tuvalet kağıdı deneyi, fırtınalı havalarda çatıların uçması, hızlı araçların içindeki dumanın dışarı çıkması) açıklamaktadır. Video sonunda öğretmen, öğrencilere sayısal soruların MEB kitaplarında ve müfredatta yer almadığını, sadece formülleri bilip yorumlayabilmelerinin yeterli olduğunu belirtmektedir."]},"endTime":1419,"title":"9. 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verilmiş, basınç sıralaması mlk olarak belirlenmiştir.","Bernoulli ilkesi etkili olmayan olay, sakin sularda birbirine paralel olarak yüzmekte olan iki geminin istemsiz olarak birbirine yaklaşmasıdır."]},"beginTime":88,"endTime":279,"href":"/video/preview/7292365993514137826?parent-reqid=1766914215208139-9495749303961442122-balancer-l7leveler-kubr-yp-klg-20-BAL&text=bernul&t=88&ask_summarization=1"},{"index":2,"title":"Bernoulli İlkesi Uygulamaları","list":{"type":"unordered","items":["Kesit alanı daraldığı için v2'nin v1'den daha hızlı olduğu ve bu bölgede basıncın daha küçük olduğu belirlenmiştir.","Düşey kesiti verilen düzenekte kauçuk hava bombası sıkılarak hava üflemesi sağlandığında cam tüp içindeki sıvının ince cam buradan yükseldiği ve açık uçtan fışkırdığı gözlemlenmiştir.","Bu düzeneğin çalışması, akışkanların hızının arttığı yerde basınçlarının düşmesi, sıvıların sıkışmaması, sıvıların kendilerine uygulanan basıncı her yönde iletmesi ve akışkanların yüksek basınçtan alçak 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You can access the CV at...","preview":{"posterSrc":"//avatars.mds.yandex.net/get-vthumb/3926960/5e9221cddae40214697fc5148641dd0f/564x318_1"},"target":"_self","position":"5","reqid":"1766914215208139-9495749303961442122-balancer-l7leveler-kubr-yp-klg-20-BAL","summary":{"fullTextUrl":"/int_search_summary?data=http%3A%2F%2Fwww.youtube.com%2Fwatch%3Fv%3DKUqamB3SuzI","linkTemplate":"/video/preview/8186396741808495060?parent-reqid=1766914215208139-9495749303961442122-balancer-l7leveler-kubr-yp-klg-20-BAL&text=bernul&t=%%timestamp%%&ask_summarization=1"},"isAdultDoc":false,"relatedParams":{"text":"Olasılık ve İstatistik : Bernoulli Dağılımı (Bernoulli 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Eğitmen önce Bernoulli dağılımının tanımını yaparak, başarı ve başarısızlık sonuçlarıyla nitelendirilen deneylerde kullanıldığını belirtir, ardından olasılık fonksiyonu, beklenen değer ve varyans formüllerini gösterir. Dersin son bölümünde ise iki örnek soru çözülerek teorik bilgiler uygulamalı olarak gösterilmektedir: bir deste iskambilden çekilen kağıdın az olup olmaması ve para atma denemesinde yazı gelme olasılığı hesaplamaları."]},"endTime":652,"title":"Bernoulli Dağılımı Dersi","beginTime":0}],"fullResult":[{"index":0,"title":"Bernoulli Dağılımı Tanıtımı","list":{"type":"unordered","items":["Bernoulli dağılımı ayrık olasılık dağılımının bir çeşididir ve deneylerin incelenmesinde kullanılır.","Bernoulli dağılımı, başarı ve başarısızlık olmak üzere iki sonuçla sonuçlanan denemeler için kullanılır.","Bernoulli dağılımında sonuçlar genellikle başarılı-yaşamayan, doğru-yanlış, yaptı-yapmadı gibi iki kategoriye ayrılır."]},"beginTime":1,"endTime":80,"href":"/video/preview/5240473695278530908?parent-reqid=1766914215208139-9495749303961442122-balancer-l7leveler-kubr-yp-klg-20-BAL&text=bernul&t=1&ask_summarization=1"},{"index":1,"title":"Bernoulli Dağılımının Olasılık Fonksiyonu","list":{"type":"unordered","items":["Bernoulli dağılımının olasılık fonksiyonu f(x) = p^x * (1-p)^(1-x) şeklindedir.","p değeri başarı olasılığı, 1-p değeri ise başarısızlık olasılığını temsil eder.","p değeri 0 ile 1 arasında olmalıdır ve rassal değişken x sadece 0 veya 1 değerlerini alabilir."]},"beginTime":80,"endTime":165,"href":"/video/preview/5240473695278530908?parent-reqid=1766914215208139-9495749303961442122-balancer-l7leveler-kubr-yp-klg-20-BAL&text=bernul&t=80&ask_summarization=1"},{"index":2,"title":"Beklenen Değer ve Varyans","list":{"type":"unordered","items":["Bernoulli dağılımının beklenen değeri E(X) = p'dir.","Varyans V(X) = p(1-p) veya p*q şeklinde ifade edilir.","Bernoulli dağılımı, var-yok, başarılı-başarısız, canlı-öldü, sağlam-bozuk gibi iki sonuçlu durumlar için kullanılır."]},"beginTime":165,"endTime":330,"href":"/video/preview/5240473695278530908?parent-reqid=1766914215208139-9495749303961442122-balancer-l7leveler-kubr-yp-klg-20-BAL&text=bernul&t=165&ask_summarization=1"},{"index":3,"title":"Örnek Soru Çözümü","list":{"type":"unordered","items":["Bir deste iskambilden çekilen kağıdın as olup olmaması durumunda, as gelmesi başarı olarak ifade edildiğinde olasılık fonksiyonu P(X) = (4/52)^x * (48/52)^(1-x) şeklindedir.","Para atma denemesinde yazı gelme olasılığı 1/2 olduğunda olasılık fonksiyonu P(X) = (1/2)^x * (1/2)^(1-x) şeklindedir."]},"beginTime":330,"endTime":633,"href":"/video/preview/5240473695278530908?parent-reqid=1766914215208139-9495749303961442122-balancer-l7leveler-kubr-yp-klg-20-BAL&text=bernul&t=330&ask_summarization=1"}],"linkTemplate":"/video/preview/5240473695278530908?parent-reqid=1766914215208139-9495749303961442122-balancer-l7leveler-kubr-yp-klg-20-BAL&text=bernul&t=%%timestamp%%&ask_summarization=1"},"isAdultDoc":false,"relatedParams":{"text":"Bernoulli Dağılımı | Bernoulli Distribution | , Kesikli Olasılık 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Bu 12. video. Bu videoda Bernoulli Denklemi ile ilgili soru çözümü yaptık. Diğer videoda Tam Diferansiyel Denklemlere İndirgenebilir Denklemlerli elde etmeye çalışacağız.","preview":{"posterSrc":"//avatars.mds.yandex.net/get-vthumb/3371619/3924c0a18fab9f2e14a9d57fd6718049/564x318_1","videoSrc":"https://video-preview.s3.yandex.net/ya0lQwIAAAA.mp4","videoType":"video/mp4"},"target":"_self","position":"7","reqid":"1766914215208139-9495749303961442122-balancer-l7leveler-kubr-yp-klg-20-BAL","summary":{"isFull":true,"fullTextUrl":"/video/result?ask_summarization=1&numdoc=1&noreask=1&nomisspell=1&parent-reqid=1766914215208139-9495749303961442122-balancer-l7leveler-kubr-yp-klg-20-BAL&text=videoid:10823635524730733514","teaser":[{"list":{"type":"unordered","items":["Bu video, bir eğitmen tarafından sunulan matematik dersinin bir bölümüdür. Eğitmen, Bernoulli diferansiyel denklemlerinin çözüm yöntemlerini anlatmaktadır.","Videoda Bernoulli denklemlerinin çözüm yöntemleri adım adım gösterilmektedir. Eğitmen önce Bernoulli yöntemi kullanarak bir holi denklemini çözmekte, ardından değişken dönüşüm yöntemi ile aynı denklemi çözmeyi denemektedir. Ayrıca doğrusal denklemlere indirgenerek çözülebileceği de gösterilmektedir.","Video, önceki derste holi denklemlerinin elde edilişlerinin anlatıldığı bir videoya atıfta bulunarak başlamakta ve izleyicilere o videoyu izlemelerini tavsiye etmektedir. Video sonunda eğitmen, bir sonraki derste tam diferansiyel denklemleri ve indirgenebilir denklemleri ele alacağını belirtmektedir."]},"endTime":901,"title":"Bernoulli Diferansiyel Denklemleri Dersi","beginTime":0}],"fullResult":[{"index":0,"title":"Holi Denklemlerinin Soru Çözümü","list":{"type":"unordered","items":["Eğitmen, Holi denklemlerinin soru çözümünü yapacağını belirtiyor.","Geçen videoda Holi denklemlerinin elde edilişleri ve bir örnek soru çözümü yapılmıştı.","Bu videoda iki farklı çözüm yöntemi gösterilecek."]},"beginTime":0,"endTime":27,"href":"/video/preview/10823635524730733514?parent-reqid=1766914215208139-9495749303961442122-balancer-l7leveler-kubr-yp-klg-20-BAL&text=bernul&t=0&ask_summarization=1"},{"index":1,"title":"Bernoulli Yöntemi ile Çözüm","list":{"type":"unordered","items":["İlk çözüm yöntemi Bernoulli yöntemi olacak ve denklem her tarafı dx'e bölünerek dy/dx + 4xy - 8y - 3x = 0 şeklinde yazılabilir.","V dönüşümü y⁴ olarak uygulanır ve denklem v' + 16xv = 32x şeklinde doğrusal bir denklem haline gelir.","Doğrusal denklemin çözümü için e⁻⁸ˣ(2e⁸ˣ² + C) bulunur ve başlangıç sınır değerleri verilirse v = y⁴ dönüşümü yapılarak y = (2e⁸ˣ² + C)¹/⁴ şeklinde çözüm elde edilir."]},"beginTime":27,"endTime":319,"href":"/video/preview/10823635524730733514?parent-reqid=1766914215208139-9495749303961442122-balancer-l7leveler-kubr-yp-klg-20-BAL&text=bernul&t=27&ask_summarization=1"},{"index":2,"title":"İkinci Çözüm Yöntemi","list":{"type":"unordered","items":["İkinci çözüm yöntemi değişken metodu olabilir.","İkinci çözümde denklem her tarafı 4y - 8y⁻³'e bölünerek 4y - 8y⁻³ + xdx şeklinde yazılabilir.","Eğitmen, ikinci çözüm yöntemini tamamlamak için daha fazla düşüneceğini belirtiyor."]},"beginTime":319,"endTime":383,"href":"/video/preview/10823635524730733514?parent-reqid=1766914215208139-9495749303961442122-balancer-l7leveler-kubr-yp-klg-20-BAL&text=bernul&t=319&ask_summarization=1"},{"index":3,"title":"Bernoulli Denkleminin 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Eğitmen, Bernoulli denklemlerinin tanımı, elde edilişi ve çözüm yöntemlerini anlatmaktadır.","Videoda Bernoulli denklemlerinin doğrusal denklemlere nasıl indirgeneceği adım adım gösterilmektedir. Eğitmen önce teorik bilgileri vererek, ardından bir örnek soru çözmektedir. Örnek soruda y'^(1/2) + (1/2)x y = x y^(1/3) denklemi çözülerek genel çözüm bulunmakta ve başlangıç koşulu uygulanarak çözüm tamamlanmaktadır.","Eğitmen, bu videoda elde edilişi anlattığını, diğer videolarda ise Bernoulli denklemiyle ilgili örnek sorular çözeceğini belirtmektedir. Ayrıca bir sonraki bölümde üç soru çözümü ve tam diferansiyel denklemlere indirgenebilir denklemlerin çözümüyle devam edeceğini ifade etmektedir."]},"endTime":869,"title":"Bernoulli Denklemleri Dersi","beginTime":0}],"fullResult":[{"index":0,"title":"Bernoulli Denkleminin Tanımı ve Özellikleri","list":{"type":"unordered","items":["Bernoulli denklemi, y' + p(x)y = q(x)y^n şeklinde tanımlanır ve n ≠ 1 durumunda Bernoulli denklemi olarak adlandırılır.","n = 1 durumunda denklem doğrusal denkleme dönüşür.","Doğrusal denklemin genel formu y' + p(x)y = q(x) şeklindedir ve genel çözümü y(x) = e^(-∫p(x)dx) * ∫q(x)e^(-∫p(x)dx)dx + C'dir."]},"beginTime":0,"endTime":190,"href":"/video/preview/2409704057024306918?parent-reqid=1766914215208139-9495749303961442122-balancer-l7leveler-kubr-yp-klg-20-BAL&text=bernul&t=0&ask_summarization=1"},{"index":1,"title":"Bernoulli Denkleminin Doğrusal Denkleme Dönüşümü","list":{"type":"unordered","items":["Bernoulli denklemini doğrusal denkleme dönüştürmek için v = y^(1-n) dönüşümü yapılır.","Dönüşüm sonrası denklem v' + p(x)v = q(x) şeklinde doğrusal denkleme indirgenir.","Doğrusal denklemin çözümü v(x) olarak bulunur ve y(x) çözümü için her iki tarafın (1-n) kuvveti alınır."]},"beginTime":190,"endTime":480,"href":"/video/preview/2409704057024306918?parent-reqid=1766914215208139-9495749303961442122-balancer-l7leveler-kubr-yp-klg-20-BAL&text=bernul&t=190&ask_summarization=1"},{"index":2,"title":"Örnek Soru Çözümü","list":{"type":"unordered","items":["Örnek soru: y' + (1/2x)y = xy^(-3) denklemi için y(1) = 2 başlangıç koşuluyla genel çözüm bulunur.","v = y^4 dönüşümü yapılır ve her iki taraf 4y^3y' ile çarpılır.","Doğrusal denklemin çözümü v(x) = e^(-∫2xdx) * ∫4xe^(-∫2xdx)dx + C olarak bulunur."]},"beginTime":480,"endTime":724,"href":"/video/preview/2409704057024306918?parent-reqid=1766914215208139-9495749303961442122-balancer-l7leveler-kubr-yp-klg-20-BAL&text=bernul&t=480&ask_summarization=1"},{"index":3,"title":"Bernoulli Denkleminin Çözümü","list":{"type":"unordered","items":["Bernoulli denkleminin çözümünde vy = y üzeri dört dönüşümü uygulanmıştır.","vx = x kare + cx kare şeklinde açılım yapılmış ve v üzeri bir çeyrek = y olarak bulunmuştur.","Başlangıç koşulu y(1) = 2 kullanılarak c = 15 olarak hesaplanmış ve genel çözüm y = x² + 15x üzeri bir çeyrek şeklinde elde edilmiştir."]},"beginTime":726,"endTime":818,"href":"/video/preview/2409704057024306918?parent-reqid=1766914215208139-9495749303961442122-balancer-l7leveler-kubr-yp-klg-20-BAL&text=bernul&t=726&ask_summarization=1"},{"index":4,"title":"Bernoulli Denkleminin Genel Yaklaşımı","list":{"type":"unordered","items":["Bernoulli denkleminin çözümünde doğrusal denkleme indirgeme yöntemi kullanılmaktadır.","Dönüşüm uygulanarak düzgün bir doğrusal denklem elde edilmeye çalışılmaktadır.","Diğer kayıtlarda Bernoulli denklemlerinin soru çözümleri yapılacak ve tam diferansiyel denklemlere indirgenebilir denklemlerden sonra karma soru çözümü olacak."]},"beginTime":818,"endTime":860,"href":"/video/preview/2409704057024306918?parent-reqid=1766914215208139-9495749303961442122-balancer-l7leveler-kubr-yp-klg-20-BAL&text=bernul&t=818&ask_summarization=1"}],"linkTemplate":"/video/preview/2409704057024306918?parent-reqid=1766914215208139-9495749303961442122-balancer-l7leveler-kubr-yp-klg-20-BAL&text=bernul&t=%%timestamp%%&ask_summarization=1"},"isAdultDoc":false,"relatedParams":{"text":"Diferansiyel Denklemler, Bernoulli Denklemi 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