Exercise 1: 1) How many seats are in the eleventh row of the amphitheater if there are 13 rows in total, with 22 seats in
1) How many seats are in the eleventh row of the amphitheater if there are 13 rows in total, with 22 seats in the first row and each subsequent row having 3 more seats than the previous one?
2) How many seats are in the tenth row of the amphitheater if there are 14 rows in total, with 20 seats in the first row and each subsequent row having 3 more seats than the previous one?
3) How many seats are in the eighth row of the amphitheater if there are 10 rows in total, with 25 seats in the first row and each subsequent row having 3 more seats than the previous one?
4) How many seats are in the tenth row of the amphitheater if there are 15 rows in total, with 20 seats in the first row and each subsequent row having 2 more seats than the previous one?
5) How many seats are in the thirteenth row of the amphitheater if there are 16 rows in total, with 19 seats in the first row and each subsequent row having 2 more seats than the previous one?
6) How many seats are in the eleventh row of the amphitheater if there are 12 rows in total, with 21 seats in the first row and each subsequent row having 2 more seats than the previous one?
Exercise 2:
1) What is the temperature of the substance in Celsius degrees 4 minutes after the start of the experiment if it was uniformly cooled for 10 minutes with a decrease of 6°C each minute, starting at -7°C?
2) What is the temperature of the substance in Celsius degrees 5 minutes after the start of the experiment if it was uniformly cooled for 10 minutes with a decrease of 7°C each minute, starting at -7°C?
3) What is the temperature of the substance in Celsius degrees 9 minutes after the start of the experiment if it was uniformly cooled for 10 minutes with a decrease of 5°C each minute, starting at -8°C?
4) What is the temperature of the substance in Celsius degrees 6 minutes after the start of the experiment if it was uniformly cooled for 10 minutes with a decrease of 8°C each minute, starting at -6°C?
5) What is the temperature of the substance in Celsius degrees 4 minutes after the start of the experiment if it was uniformly cooled for 10 minutes with a decrease of 9°C each minute, starting at -5°C?
6) What is the temperature of the substance in Celsius degrees 7 minutes after the start of the experiment if it was uniformly cooled for 10 minutes with a decrease of 6°C each minute, starting at -9°C?
Exercise 3:
1) How many seats are in the last row of the amphitheater if there are 14 rows in total, with each subsequent row having the same number of seats as the previous one, and there are 27 seats in the fifth row and 36 seats in the eighth row?
2) How many seats are in the last row of the amphitheater if there are 17 rows in total, with each subsequent row having the same number of seats as the previous one, and there are 38 seats in the seventh row and 42 seats in the ninth row?
3) How many seats are in the last row of the amphitheater if there are 16 rows in total, with each subsequent row having the same number of seats as the previous one, and there are 23 seats in the fourth row and 35 seats in the eighth row?
4) How many seats are in the last row of the amphitheater if there are 18 rows in total, with each subsequent row having the same number of seats as the previous one, and there are 26 seats in the sixth row and 30 seats in the eighth row?
5) How many seats are in the last row of the amphitheater if there are 19 rows in total, with each subsequent row having the same number of seats as the previous one, and there are 25 seats in the third row and 37 seats in the seventh row?
6) How many seats are in the last row of the amphitheater if there are 23 rows in total, with each subsequent row having the same number of seats as the previous one, and there are 26 seats in the seventh row and 34 seats in the eleventh row?
Пояснение:
Чтобы решить задачу, нам нужно знать количество рядов в амфитеатре, количество мест в первом ряду и правило увеличения количества мест в последующих рядах. В данном случае, количество мест в первом ряду известно, а каждый последующий ряд имеет на 3 места больше, чем предыдущий.
Пример использования:
1) Для решения задачи 1, имея 13 рядов, первый ряд с 22 местами и увеличение на 3 места в каждом следующем ряду, мы можем использовать формулу:
Количество мест в n-ном ряду = Количество мест в первом ряду + (n-1) * Увеличение количества мест.
В данном случае, для одиннадцатого ряда:
Количество мест в одиннадцатом ряду = 22 + (11-1) * 3 = 22 + 10 * 3 = 22 + 30 = 52 места.
2) Для решения задачи 2, имея 14 рядов, первый ряд с 20 местами и увеличение на 3 места в каждом следующем ряду, мы можем использовать ту же формулу:
Количество мест в десятом ряду = 20 + (10-1) * 3 = 20 + 9 * 3 = 20 + 27 = 47 мест.
3) Для решения задачи 3, имея 10 рядов, первый ряд с 25 местами и увеличение на 3 места в каждом следующем ряду:
Количество мест в восьмом ряду = 25 + (8-1) * 3 = 25 + 7 * 3 = 25 + 21 = 46 мест.
Совет:
Чтобы правильно решать подобные задачи, важно внимательно читать условие, выделять ключевые данные и использовать формулу для рассчета нужного значения.
Практика:
Сколько мест будет в двенадцатом ряду амфитеатра, если всего 15 рядов, первый ряд содержит 30 мест, и каждый последующий ряд имеет на 4 места больше, чем предыдущий?