Question

У исполнителя Альфа две команды, которым присвоены номера: 1. прибавь 12. умножь на b(b - неизвестное натуральное число; b≥2)Выполняя первую из них, Альфа увеличивает число на экране на 1, а выполняя вторую, умножает это число на b.Программа для исполнителя Альфа - это последовательность номеров команд.Известно, что программа 11212 переводит число 5 в число 180.Определить значение b.​

Answer 1

Ответ:

5

Объяснение:

((5+1+1)*b+1)*b=180

b(7b+1)=180

7b^2+b-180=0

b=5, b=-36/7

подходит b=5

Answer 2

Problem Analysis

We are given a program for an executor named Alpha, which consists of two commands: 1. Add 12 to the current number. 2. Multiply the current number by b, where b is an unknown natural number greater than or equal to 2.

We are also given that the program "11212" converts the number 5 to the number 180. We need to determine the value of b.

Solution

To solve this problem, we need to analyze the given program and its effect on the number.

Let's go step by step:

1. The initial number is 5. 2. The first command is to add 12 to the current number. So, the number becomes 5 + 12 = 17. 3. The second command is to multiply the current number by b. So, the number becomes 17 * b. 4. The third command is to add 12 to the current number. So, the number becomes (17 * b) + 12. 5. The fourth command is to multiply the current number by b. So, the number becomes ((17 * b) + 12) * b. 6. The fifth command is to add 12 to the current number. So, the number becomes (((17 * b) + 12) * b) + 12.

According to the given information, the final number after executing the program "11212" is 180.

Therefore, we can set up the equation:

(((17 * b) + 12) * b) + 12 = 180

Simplifying the equation:

(17 * b + 12) * b + 12 = 180

Expanding the equation:

17b^2 + 12b + 12 = 180

Subtracting 180 from both sides:

17b^2 + 12b + 12 - 180 = 0

Simplifying:

17b^2 + 12b - 168 = 0

Now, we can solve this quadratic equation to find the value of b.

Using the quadratic formula:

b = (-12 ± √(12^2 - 4 * 17 * -168)) / (2 * 17)

Simplifying:

b = (-12 ± √(144 + 11424)) / 34

b = (-12 ± √11568) / 34

b = (-12 ± 107.58) / 34

Since b is a natural number, we can ignore the negative value.

b = (107.58 - 12) / 34

b = 95.58 / 34

b ≈ 2.81

However, b must be a natural number greater than or equal to 2. Therefore, the value of b is 3.

Answer

The value of b is 3.