{"paper":{"id":"site-6693","subject":"matematyka","category":"zbiory","year":0,"month":null,"level":null,"variant":null,"exam_pdf":null,"key_pdf":null,"question_count":5,"source_label":"Matematyka · Zbiory zadań","subject_label":"Matematyka","category_label":"Zbiory zadań"},"questions":[{"id":"site-6693/zad/6696","paper_id":"site-6693","number":"6696","points":null,"ptype":"open","subject":"matematyka","category":"zbiory","year":0,"month":null,"level":null,"text":"Oprocentowanie na długoterminowej lokacie w pewnym banku wynosi 3% w skali roku (już po uwzględnieniu podatków). Po każdym roku oszczędzania są doliczane odsetki od aktualnego kapitału znajdującego się na lokacie - zgodnie z procentem składanym. Po 10 latach oszczędzania w tym banku (i bez wypłacania kapitału ani odsetek w tym okresie) kwota na lokacie będzie większa od kwoty wpłaconej na samym początku o (w zaokrągleniu do 1%) A. 30% & B. 34% C. 36% D. 43%","answer":null,"answer_text":null,"solution":null,"image":"img/site/6693/zad-6696.svg","solution_image":"img/site/6693/rozw-6696.svg","topics":null,"page_from":null,"source":"site","answer_source":null,"answer_text_source":null,"solution_source":null,"text_source":"site","source_label":"Matematyka · Zbiory zadań","subject_label":"Matematyka","category_label":"Zbiory zadań"},{"id":"site-6693/zad/6700","paper_id":"site-6693","number":"6700","points":null,"ptype":"open","subject":"matematyka","category":"zbiory","year":0,"month":null,"level":null,"text":"Rozwiąż równanie: (4x+1)(x-5) / (2x-10)(x+3) = 0.","answer":null,"answer_text":null,"solution":null,"image":"img/site/6693/zad-6700.svg","solution_image":"img/site/6693/rozw-6700.svg","topics":null,"page_from":null,"source":"site","answer_source":null,"answer_text_source":null,"solution_source":null,"text_source":"site","source_label":"Matematyka · Zbiory zadań","subject_label":"Matematyka","category_label":"Zbiory zadań"},{"id":"site-6693/zad/6704","paper_id":"site-6693","number":"6704","points":null,"ptype":"open","subject":"matematyka","category":"zbiory","year":0,"month":null,"level":null,"text":"Rozważmy takie liczby rzeczywiste a i b, które spełniają warunki: a≠0, b≠0 oraz a³+b³=(a+b)^3. Oblicz wartość liczbową wyrażenia a/b dla dowolnych liczb rzeczywistych a i b, spełniających powyższe warunki.","answer":null,"answer_text":null,"solution":null,"image":"img/site/6693/zad-6704.svg","solution_image":"img/site/6693/rozw-6704.svg","topics":null,"page_from":null,"source":"site","answer_source":null,"answer_text_source":null,"solution_source":null,"text_source":"site","source_label":"Matematyka · Zbiory zadań","subject_label":"Matematyka","category_label":"Zbiory zadań"},{"id":"site-6693/zad/6705","paper_id":"site-6693","number":"6705","points":null,"ptype":"open","subject":"matematyka","category":"zbiory","year":0,"month":null,"level":null,"text":"Dane jest wyrażenie W(x) = 1/2(x+1/x-1 - x-1/x+1). Oceń prawdziwość poniższych stwierdzeń. Wybierz P, jeśli stwierdzenie jest prawdziwe, albo F - jeśli jest fałszywe. Wartość wyrażenia W(x) jest określona dla każdej liczby rzeczywistej x≠1. P F Wyrażenie W(x) można przekształcić równoważnie do wyrażenia 2x/x^2-1. P, F.","answer":null,"answer_text":null,"solution":null,"image":"img/site/6693/zad-6705.svg","solution_image":"img/site/6693/rozw-6705.svg","topics":null,"page_from":null,"source":"site","answer_source":null,"answer_text_source":null,"solution_source":null,"text_source":"site","source_label":"Matematyka · Zbiory zadań","subject_label":"Matematyka","category_label":"Zbiory zadań"},{"id":"site-6693/zad/6706","paper_id":"site-6693","number":"6706","points":null,"ptype":"open","subject":"matematyka","category":"zbiory","year":0,"month":null,"level":null,"text":"Rozwiąż równanie (x-1)^4 - 5(x-1)^2 + 6 = 0.","answer":null,"answer_text":null,"solution":null,"image":"img/site/6693/zad-6706.svg","solution_image":"img/site/6693/rozw-6706.svg","topics":null,"page_from":null,"source":"site","answer_source":null,"answer_text_source":null,"solution_source":null,"text_source":"site","source_label":"Matematyka · Zbiory zadań","subject_label":"Matematyka","category_label":"Zbiory zadań"}]}