https://r2.erweima.ai/mathbot/image/1726758335726nkpv4fej.jpg

The image contains a mathematical problem related to an area and geometry. Here's a breakdown of what it asks:

1. **Task b)** mentions the need to calculate the area of a section of a flowerbed that is planted with red-blooming flowers. The area to be calculated is shown graphically in "Abbildung 2" (Figure 2) on the right.
   
2. The curve shown in the figure represents a function \( f(x) = 0.6x - 0.2x^2 \) for the first part, with some transition at the point \( A(1|0) \), and it appears you're tasked with finding the area under the curve between two points.

3. The second part of the problem involves determining whether the point \( W(0.5|0.5) \) lies within a circular region of radius 0.25 meters around point \( B(0.6|0.7) \), which is used for watering plants.

4. Finally, the problem asks to draw a straight path from the southwest corner of the garden area, extending without a kink, and intersecting the previously described path to find the coordinates of the intersection point.

### To Solve:
1. **Calculate the area** under the curve for the section related to red-blooming flowers.
2. **Check if point \( W \)** lies within the circle with center \( B \) and radius 0.25 meters.
3. **Find the intersection** of a linear path with the graph \( f(x) \), and determine the coordinates of the point.

Would you like to proceed with the area calculation or focus on another part?

Calculate the area of a flowerbed with red-blooming flowers, check if a point lies in a circular region, and find the intersection of a straight path with a given curve.

This problem involves calculating the area under a curve representing a flowerbed with red-blooming flowers. It also checks if a point lies within a circular region and finds the intersection of a straight path with a quadratic curve. Suitable for high school students in Grades 11-12.

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