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Консультация № 190673
09.03.2017, 02:14
0.00 руб.
09.03.2017, 06:41
0
2
1
Здравствуйте, уважаемые эксперты! Прошу вас ответить на следующий вопрос:
Производительность труда рабочего в течение дня задается функцией z(t) = −0,00625 ∙ t^2 + 0,05 ∙t + 0,5 (ден. ед./ч), где t – время в часах от начала работы (0 ≤ t≤ 8). Найти функцию u = u(t), выражающую объем продукции от времени t (в денежных единицах) и его величину за рабочий день.
Не уверена как правильно надо решать. При решение интеграла с нижним пределом 0 и верхним 8, получилось 68/15=4,53. Как найти функцию объема продукции от времени и его величину за рабочий день? Помогите, пожалуйста, разобраться
Производительность труда рабочего в течение дня задается функцией z(t) = −0,00625 ∙ t^2 + 0,05 ∙t + 0,5 (ден. ед./ч), где t – время в часах от начала работы (0 ≤ t≤ 8). Найти функцию u = u(t), выражающую объем продукции от времени t (в денежных единицах) и его величину за рабочий день.
Не уверена как правильно надо решать. При решение интеграла с нижним пределом 0 и верхним 8, получилось 68/15=4,53. Как найти функцию объема продукции от времени и его величину за рабочий день? Помогите, пожалуйста, разобраться
Обсуждение
09.03.2017, 06:23
общий
это ответ
Здравствуйте, katysha.egorova!
Производительность труда есть отношение объёма продукции ко времени, за которое он был произведён. В данном случае z(t) - функция "мгновенной" производительности труда, то есть производная объёма продукции по времени. Следовательно, функция объёма продукции u(t) - первообразная функции производительности труда:
За восьмичасовой рабочий день объем продукции составит
Так что объем продукции был найден правильно, а функция объема продукции - это как раз та функция, которая получилась при взятии интеграла.
Производительность труда есть отношение объёма продукции ко времени, за которое он был произведён. В данном случае z(t) - функция "мгновенной" производительности труда, то есть производная объёма продукции по времени. Следовательно, функция объёма продукции u(t) - первообразная функции производительности труда:
За восьмичасовой рабочий день объем продукции составит
Так что объем продукции был найден правильно, а функция объема продукции - это как раз та функция, которая получилась при взятии интеграла.
5
Гений!
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