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Eğitmen, önceki videoda binom açılımını kullanarak a+b'nin dördüncü kuvvetini hesapladığını hatırlatarak, bu videoda Pascal üçgeni kullanarak aynı işlemi nasıl yapabileceğimizi göstermektedir.","Video, Pascal üçgeninin nasıl oluşturulacağını adım adım anlatarak başlıyor ve ardından a+b'nin dördüncü kuvvetinin Pascal üçgeni ile nasıl hesaplanacağını gösteriyor. Eğitmen, katsayıların nasıl elde edildiğini ve hangi terime ait olduğunu açıklıyor. Son olarak, Pascal üçgeninin binom açılımıyla nasıl ilişkili olduğunu, ilk üç kuvvet için (a+b)², (a+b)³ ve (a+b)⁴ örnekleri üzerinden detaylı şekilde anlatıyor."]},"endTime":392,"title":"Pascal Üçgeni ile Binom Açılımı","beginTime":0}],"fullResult":[{"index":0,"title":"Binom Açılımı ve Pascal Üçgeni","list":{"type":"unordered","items":["Önceki videoda (a+b)⁴'nin binom açılımı gösterilmişti, ancak daha büyük kuvvetler için daha kullanışlı olurdu.","Bu videoda Pascal üçgeni kullanılarak (a+b)⁴'nin açılımı hesaplanacak ve iki yöntem arasındaki ilişki incelenecek.","Pascal üçgeninde her terime kaç farklı yoldan ulaşılabileceği hesaplanarak katsayılar elde edilecek."]},"beginTime":0,"endTime":46,"href":"/video/preview/5230046273925311477?parent-reqid=1769522208665297-14940456619648936718-balancer-l7leveler-kubr-yp-sas-187-BAL&text=Pascal+B.&t=0&ask_summarization=1"},{"index":1,"title":"Pascal Üçgeninin Oluşturulması","list":{"type":"unordered","items":["Pascal üçgeni sıfırıncı kuvvetten başlayarak oluşturulur ve her satırdaki her terime kaç farklı yoldan ulaşılabileceği hesaplanır.","Sıfırıncı satırda sadece bir yol, birinci satırda iki yol, ikinci satırda üç yol, üçüncü satırda dört yol, dördüncü satırda beş yol ve beşinci satırda altı yol bulunur.","Bu sayılar binom katsayılarını oluşturur: 1, 4, 6, 4, 1."]},"beginTime":46,"endTime":196,"href":"/video/preview/5230046273925311477?parent-reqid=1769522208665297-14940456619648936718-balancer-l7leveler-kubr-yp-sas-187-BAL&text=Pascal+B.&t=46&ask_summarization=1"},{"index":2,"title":"Pascal Üçgeni ile Binom Açılımının Hesaplanması","list":{"type":"unordered","items":["Pascal üçgenindeki katsayılar kullanılarak (a+b)⁴'nin açılımı hesaplanır: a⁴ + 4a³b + 6ab² + 6ab + b⁴.","Pascal üçgeni, binom açılımında katsayıları ve terimleri doğru şekilde verir.","Pascal üçgeninin aynı sonucu vermesinin nedeni, her terimin elde edilme yollarının sayısından 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Daha sonra teorik bilgilerin ardından çeşitli örnek sorular çözülerek konu pekiştiriliyor.","Videoda 20 kg'lık bir poşetin bir aracın ağırlığını nasıl etkilediği, pistonların kesit alanları arasındaki ilişki ve farklı kesit alanlarına sahip pistonların üzerindeki cisimlerin ağırlıkları arasındaki ilişki gibi sorular adım adım çözülmektedir."]},"endTime":941,"title":"Pascal Prensibi Eğitim Videosu","beginTime":0}],"fullResult":[{"index":0,"title":"Pascal Prensibi ve Uygulamaları","list":{"type":"unordered","items":["Pascal prensibi, sıvıların üzerine yapılan basıncı her yön ve doğrultuda aynı büyüklükte değiştirmeden ve dik olarak iletmesinden kaynaklanır.","Bu prensip günlük hayatta hayatımızı kolaylaştıran uygulamalarda kullanılır; örneğin arabadaki fren sistemi, vinçler, dozerler gibi büyük araçların küçük kuvvetlerle kaldırılması.","Pascal prensibi sayesinde çok küçük kuvvetlerle çok büyük kuvvetler elde edilebilir veya cisimler yukarı doğru 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çizgi çizilir.","Aynı seviyedeki basınçlar eşit olduğu için, bir seviyedeki kuvvet ve yüzey alanı diğer seviyeye taşınır.","Bir seviyenin üzerinde ne kadar yük varsa, bu yük ilave edilir."]},"beginTime":194,"endTime":402,"href":"/video/preview/11717213476817096362?parent-reqid=1769522208665297-14940456619648936718-balancer-l7leveler-kubr-yp-sas-187-BAL&text=Pascal+B.&t=194&ask_summarization=1"},{"index":3,"title":"Pascal Prensibinin Günlük Uygulamaları","list":{"type":"unordered","items":["Pascal prensibi günlük hayatta hayati önem taşıyan uygulamalarda kullanılır: arabadaki frenler, vinçler, dozerler.","İtfaiye merdivenleri, tulumbalar, hidrolik kaldıraçlar, balya, çöp sıkıştıran araçlar, damperli kamyonlar ve kuaförlerin koltukları da Pascal prensibinden yararlanır.","Pascal prensibi sayesinde sıvılar uyguladıkları kuvveti aynen iletirler."]},"beginTime":402,"endTime":446,"href":"/video/preview/11717213476817096362?parent-reqid=1769522208665297-14940456619648936718-balancer-l7leveler-kubr-yp-sas-187-BAL&text=Pascal+B.&t=402&ask_summarization=1"},{"index":4,"title":"Pascal Prensibi Örnekleri","list":{"type":"unordered","items":["Piston F kuvveti ile dengede olup K noktasındaki sıvı basıncı P = h × d × g'dir.","Piston F kuvveti ile 2h kadar yukarı itildiğinde, basınç artar ve F kuvveti azalır.","Hidrolik sistemde 200 Newtonluk kuvvet uygulandığında, aracın ağırlığı yaklaşık 20 kg'dır."]},"beginTime":446,"endTime":601,"href":"/video/preview/11717213476817096362?parent-reqid=1769522208665297-14940456619648936718-balancer-l7leveler-kubr-yp-sas-187-BAL&text=Pascal+B.&t=446&ask_summarization=1"},{"index":5,"title":"Pascal Prensibi ve Basınç Hesaplamaları","list":{"type":"unordered","items":["Pascal prensibine göre, aynı seviyedeki basınçlar eşittir ve F₁/A₁ = F₂/A₂ formülü kullanılır.","20 kg'lık bir poşet koyulduğunda, 0,5 A kesit alanına sahip piston 1000 Newton (yaklaşık 100 kg) yük kaldırmıştır.","Pascal prensibinde boruların incelik kalınlıklarından yararlanarak, sıvıların basıncı iletmesinden yararlanılarak sonuçlar bulunur."]},"beginTime":619,"endTime":711,"href":"/video/preview/11717213476817096362?parent-reqid=1769522208665297-14940456619648936718-balancer-l7leveler-kubr-yp-sas-187-BAL&text=Pascal+B.&t=619&ask_summarization=1"},{"index":6,"title":"Pistonların Kesit Alanları Oranı","list":{"type":"unordered","items":["Kesit alanları Aₓ ve Aₐ olan, özdeş cisimler dengede tutulmuş pistonlarda basınçlar eşittir.","Pistonların kesit alanları oranı Aₓ/Aₐ = 1,5 olarak hesaplanmıştır.","Basınç prensibinden, 3G'lik bir ağırlık 6G'lik bir ağırlığı dengelemişse, basınçlar eşit olmalıdır."]},"beginTime":711,"endTime":814,"href":"/video/preview/11717213476817096362?parent-reqid=1769522208665297-14940456619648936718-balancer-l7leveler-kubr-yp-sas-187-BAL&text=Pascal+B.&t=711&ask_summarization=1"},{"index":7,"title":"Farklı Kesit Alanlı Pistonlarda Cisimlerin Ağırlıkları","list":{"type":"unordered","items":["A₂, A₃, A kesit alanlı pistonların üzerindeki cisimlerle denge sağlanmıştır.","X, Y, Z cisimlerinin ağırlıkları arasındaki ilişki Gx > Gz > G olarak belirlenmiştir.","X cismi en büyük ağırlığa sahip, Z cismi ikinci, Y cismi en küçük ağırlığa 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Giới thiệu các thành phần cơ bản của giao diện Turbo Pascal. 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