Question

Улитка ползёт по координатной плоскости. С каждой минутой она ползёт медленней в два раза и меняет направление таким образом: на восток(направо), на юг, на запад, на север, на восток и т.д. Каковы будут координаты улитки через 6 минут, если стартовала она из начала координат и за первую минуту она проползла 32 единицы на запад? Ответы: а)(-26;13) ;б)(26;-13) ; в) (-26;-13) ; г)(26;13) Помогите пожалуйста! Спасибо.

Answer 1

Г(-26,13) ........................

Answer 2

Problem Analysis

We are given that a snail is crawling on a coordinate plane. It moves slower by half every minute and changes direction in a specific pattern: east (right), south, west, north, east, and so on. We need to determine the coordinates of the snail after 6 minutes, given that it started at the origin (0, 0) and crawled 32 units west in the first minute.

Solution

To solve this problem, we need to track the snail's movement and direction for each minute. Let's break it down step by step:

1. After the first minute, the snail crawls 32 units west from the origin (0, 0). This means its new position is (-32, 0).

2. From the second minute onwards, the snail moves slower by half each minute. This means that for each subsequent minute, the snail will move half the distance it moved in the previous minute.

3. The snail changes direction in a specific pattern: east (right), south, west, north, east, and so on. This pattern repeats every four minutes.

4. We can use a loop to simulate the snail's movement for the remaining 5 minutes.

Let's calculate the snail's position after 6 minutes:

1. After the first minute: (-32, 0) 2. Second minute: The snail moves half the distance it moved in the previous minute, which is 16 units west. The new position is (-32 + 16, 0) = (-16, 0). 3. Third minute: The snail moves half the distance it moved in the previous minute, which is 8 units south. The new position is (-16, 0 - 8) = (-16, -8). 4. Fourth minute: The snail moves half the distance it moved in the previous minute, which is 4 units east. The new position is (-16 + 4, -8) = (-12, -8). 5. Fifth minute: The snail moves half the distance it moved in the previous minute, which is 2 units north. The new position is (-12, -8 + 2) = (-12, -6). 6. Sixth minute: The snail moves half the distance it moved in the previous minute, which is 1 unit east. The new position is (-12 + 1, -6) = (-11, -6).

Therefore, the coordinates of the snail after 6 minutes are (-11, -6).

Answer

The coordinates of the snail after 6 minutes, starting from the origin (0, 0) and crawling 32 units west in the first minute, are (-11, -6).