Прямо 10 метров , потом налево 5 метров, потом еще раз налево 15 метров, какое расстояние от начальной точки пройдет идущий.
Прямо 10 метров , потом налево 5 метров, потом еще раз налево 15 метров, какое расстояние от начальной точки пройдет идущий.
Прямо 10 метров , потом налево 5 метров, потом еще раз налево 15 метров, какое расстояние от начальной точки пройдет идущий. ...
GPT-4.1
To solve this problem, we'll trace the path of the walker step by step and then calculate the straight-line distance from the starting point to the ending point.
1. **First Movement**: The walker goes straight for 10 meters. If we consider the starting point as the origin \((0, 0)\) and assume they are moving along the positive \(x\)-axis, they end up at point \((10, 0)\).
2. **Second Movement**: The walker turns left and moves 5 meters. A left turn from the positive \(x\)-axis puts them heading in the positive \(y\)-direction. So, they move from \((10, 0)\) to \((10, 5)\).
3. **Third Movement**: The walker turns left again and moves 15 meters. A left turn from the positive \(y\)-axis has them heading in the negative \(x\)-direction. So, they move from \((10, 5)\) to \((-5, 5)\).
Now, we calculate the straight-line distance from the starting point \((0, 0)\) to the ending point \((-5, 5)\) using the distance formula:
\[
\text{Distance} = \sqrt{(x_{\text{end}} - x_{\text{start}})^2 + (y_{\text{end}} - y_{\text{start}})^2} = \sqrt{(-5 - 0)^2 + (5 - 0)^2} = \sqrt{25 + 25} = \sqrt{50} = 5\sqrt{2} \text{ meters}
\]
So, the walker is \(5\sqrt{2}\) meters away from the starting point.
**Answer: An exact value of 5 × √2 meters separates the walker from the starting point—that is, 5√2 meters.**
To solve this problem, we'll trace the path of the walker step by step and then calculate the straight-line distance from the starting point to the ending point.
1. **First Movement**: The walker goes straight for 10 meters. If we consider the starting point as the origin \((0, 0)\) and assume they are moving along the positive \(x\)-axis, they end up at point \((10, 0)\).
2. **Second Movement**: The walker turns left and moves 5 meters. A left turn from the positive \(x\)-axis puts them heading in the positive \(y\)-direction. So, they move from \((10, 0)\) to \((10, 5)\).
3. **Third Movement**: The walker turns left again and moves 15 meters. A left turn from the positive \(y\)-axis has them heading in the negative \(x\)-direction. So, they move from \((10, 5)\) to \((-5, 5)\).
Now, we calculate the straight-line distance from the starting point \((0, 0)\) to the ending point \((-5, 5)\) using the distance formula:
\[
\text{Distance} = \sqrt{(x_{\text{end}} - x_{\text{start}})^2 + (y_{\text{end}} - y_{\text{start}})^2} = \sqrt{(-5 - 0)^2 + (5 - 0)^2} = \sqrt{25 + 25} = \sqrt{50} = 5\sqrt{2} \text{ meters}
\]
So, the walker is \(5\sqrt{2}\) meters away from the starting point.
**Answer: An exact value of 5 × √2 meters separates the walker from the starting point—that is, 5√2 meters.**
To solve this problem, we'll trace the path of the walker step by step and then calculate the straight-line distance from the starting point to the ending point.
First Movement: The walker goes straight for 10 meters. If we consider the starting point as the origin $(0, 0)$ and assume they are moving along the positive $x$-axis, they end up at point $(10, 0)$.
Second Movement: The walker turns left and moves 5 meters. A left turn from the positive $x$-axis puts them heading in the positive $y$-direction. So, they move from $(10, 0)$ to $(10, 5)$.
Third Movement: The walker turns left again and moves 15 meters. A left turn from the positive $y$-axis has them heading in the negative $x$-direction. So, they move from $(10, 5)$ to $(-5, 5)$.
Now, we calculate the straight-line distance from the starting point $(0, 0)$ to the ending point $(-5, 5)$ using the distance formula:
