https://r2.erweima.ai/mathbot/image/1727100488257ytzepb8q.pdf

The exercises from the provided document seem to be a part of a mathematics competition or exam. Here is an overview of the tasks from the first few exercises:

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### **Exercice n°1:**
1. **Pool surface area comparison:**
   - You are given two models of pools, one with an octagonal shape.
   - Formula for the surface of an octagon: \( A = 2 \times \sqrt{2} \times R^2 \).
   - Determine if the surface of these pools requires administrative paperwork (if it exceeds 10m²).

2. **Choosing a pool based on space per swimmer:**
   - The recommended area per swimmer is 3.40m².
   - Calculate if both pools fit the requirements for 4 swimmers.

3. **Water filling question:**
   - The water flow rate is 12 liters per minute.
   - You are asked if the pool overflows when filled between 14:00 on Friday and 10:00 on Saturday.

4. **Percentage increase in drownings:**
   - Compare 1,758 drownings in 2023 with 858 in 2022.
   - Calculate the percentage increase.

5. **Pool fencing costs:**
   - You have to compute the total cost for securing the pool with a fence sold in 80 cm panels costing 65€, and a gate priced at 120€.

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### **Exercice n°2:**
1. **Affine Functions:**
   - You work with two functions \( f \) and \( g \), provided either by a table or a Scratch program.
   
   Some specific tasks include:
   - Finding the image of certain values.
   - Verifying algebraic expressions.
   - Simplifying a program and completing table values.
   
2. **Investigating relationships between images and pre-images (antecedents).**

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Would you like a detailed step-by-step solution for any specific problem or help with one of these exercises?

### 5 Related Questions
1. How do we calculate the area of an octagon if the radius is given?
2. What is the formula for calculating percentage increase?
3. How can we compute the total time elapsed when filling a pool continuously?
4. How to solve equations for functions defined by tables or programs?
5. What is the method for determining antecedents of functions?

### Tip:
For geometric problems, always visualize the shapes and double-check formulas involving areas and volumes to ensure correctness.

Solve complex math exercises involving geometric shapes, function analysis, algebraic expressions, and the Pythagorean theorem. These problems are suitable for high school students and challenge skills in calculations, spatial reasoning, and mathematical reasoning.

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