https://file.aiquickdraw.com/mathbot/file/17255755565638kwoxj7g.jpg

The question in the image asks:

**"What is the domain of D(t)?"**

Given the problem setup:
- Tiana is swimming for 20 minutes.
- She swims at a constant speed of 75 meters per minute.
- The function \( D(t) \) represents the total distance Tiana has swum, where \( t \) is time in minutes.

To determine the domain of \( D(t) \), we need to think about the possible values of \( t \), which represents time. Since she swims for 20 minutes, the domain for \( t \) should be from 0 to 20 minutes, inclusive.

So, the domain of \( D(t) \) is **all real numbers from 0 to 20**.

### Correct Answer:
The correct choice is: **"all real numbers from 0 to 20"**.

Would you like further explanation on domain and range concepts? Here are some additional questions to explore:

1. What is the range of \( D(t) \) for this situation?
2. How do we differentiate between real numbers and whole numbers in a domain?
3. How can we express \( D(t) \) as an equation using \( t \) and speed?
4. What is the significance of defining a domain in a real-world context?
5. How would the domain change if Tiana swam for a different amount of time?

**Tip**: Always check if time, distance, or other quantities are restricted to specific intervals when determining a domain.

Tiana is a member of the school swim team, and she specializes in distance events. Today at practice, she plans to swim for 20 minutes at a constant speed of 75 meters per minute. The function D(t) represents the total distance Tiana has swum, in meters, during t minutes of practicing. What is the domain of D(t)?

Learn how to determine the domain of the function D(t) in a problem where a swimmer swims at a constant speed for 20 minutes. This problem covers key mathematical concepts such as functions, domain, and range, and is suitable for students in Grades 6-8.

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