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Математика

Ответы

porotikova1004

Найдем несколько членов этой последовательности:

7

7*7 = 49. 4+9+1 = 14

14*14 = 196. 1 + 6 + 9 + 1 = 17

17*17 = 289. 2 + 8 + 9 + 1 = 20

20*20 = 400. 4 + 1 = 5

5*5 = 25. 2 + 5 + 1 = 8

8*8 = 64. 6 + 4 + 1 = 11

11*11 = 121. 1 + 2 + 1 + 1 = 5

5*5 = 25. 2 + 5 + 1 = 8

8*8 = 64. 6 + 4 + 1 = 11

11*11 = 121. 1 + 2 + 1 + 1 = 5

Таким образом, число 5 повторяется на кажэдом третьем месте в этой последовательности.

При этом число 5 стоит на пятом, восьмом, одиннадцатом и т.д. месте.

Т.е. для любого х >0 число 5 будет стоять на каждом (3х + 2) месте.

При х = 670 номер места для числа 5 равен 3*670 + 2 = 2012.

Значит, на 2012 месте стоит число 5.

При х = 671 номер места для числа 5 равен 3*671 + 2 = 2015.

Значит, на 2015 месте будет стоять число 5.

 

ответ: 5.

ivanova229

Стандартный решения с уравнения:

 

Грузовик за первую секунду проходит 10 + 0,1/2 = 10,05 метров, а за х секунд он пройдет (10х + 0,05х^2) метров.

Легковая машина за первую секунду проходит 12 + 0,2/2 = 12,1 метра, а за те же х секунд (машины двигались одинаковое время) пройдет (12х + 0,1х^2) метра.

Тогда 12х + 0,1х^2 = 10х + 0,05х^2 + 297.

0,05х^2 + 2х - 297 = 0

 

Решив уравнение, получим искомое время.

Целочисленных корней уравнение не имеет, думаю, что это время составит чуть меньше минуты, примерно 59 с небольшим секунд.

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