A Student Is Running A 10-kilometer Race. He Runs 1 Kilometer Every 4 Minutes. Select The Function That Describes His Distance From The Finish Line In Terms Of Minutes.A. $f(x)=\frac{1}{4} X+10$B. $f(x)=-\frac{1}{10} X+4$C.

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Introduction

Mathematics is a powerful tool for modeling real-world situations. In this article, we will explore how mathematical functions can be used to describe the distance of a student running a 10-kilometer race. We will analyze the student's running speed and use it to create a function that describes his distance from the finish line in terms of minutes.

The Student's Running Speed

The student runs 1 kilometer every 4 minutes. This means that his running speed is 1 km/4 min = 0.25 km/min. We can use this information to create a function that describes his distance from the finish line in terms of minutes.

Creating the Function

Let's denote the distance from the finish line as d (in kilometers) and the time elapsed as t (in minutes). Since the student runs 1 kilometer every 4 minutes, we can write the equation:

d = 0.25t

However, this equation only describes the distance traveled by the student, not the distance from the finish line. To create a function that describes the distance from the finish line, we need to subtract the distance traveled from the total distance of the race (10 kilometers).

The Correct Function

The correct function that describes the distance from the finish line in terms of minutes is:

d(t) = 10 - 0.25t

This function takes the time elapsed t as input and returns the distance from the finish line d.

Evaluating the Options

Now that we have created the correct function, let's evaluate the options provided:

A. f(x) = 1/4 x + 10

This function is incorrect because it does not take into account the student's running speed. The student runs 1 kilometer every 4 minutes, not 1 kilometer every minute.

B. f(x) = -1/10 x + 4

This function is also incorrect because it does not describe the distance from the finish line in terms of minutes. The student's running speed is 0.25 km/min, not -0.1 km/min.

C. No option is provided

However, we can create a correct option by rewriting the correct function:

d(t) = 10 - 0.25t

This function describes the distance from the finish line in terms of minutes.

Conclusion

In this article, we used mathematical functions to model the distance of a student running a 10-kilometer race. We analyzed the student's running speed and created a function that describes his distance from the finish line in terms of minutes. We evaluated the options provided and found that none of them were correct. We created a correct option by rewriting the correct function.

Key Takeaways

  • Mathematical functions can be used to model real-world situations.
  • The student's running speed is 0.25 km/min.
  • The correct function that describes the distance from the finish line in terms of minutes is d(t) = 10 - 0.25t.

Further Reading

If you want to learn more about mathematical modeling and functions, I recommend checking out the following resources:

  • Khan Academy: Mathematical Modeling
  • MIT OpenCourseWare: Calculus
  • Wolfram MathWorld: Functions

References

Introduction

In our previous article, we explored how mathematical functions can be used to model the distance of a student running a 10-kilometer race. We analyzed the student's running speed and created a function that describes his distance from the finish line in terms of minutes. In this article, we will answer some frequently asked questions about the topic.

Q&A

Q: What is the student's running speed?

A: The student's running speed is 0.25 km/min, which means he runs 1 kilometer every 4 minutes.

Q: What is the correct function that describes the distance from the finish line in terms of minutes?

A: The correct function is d(t) = 10 - 0.25t, where d is the distance from the finish line (in kilometers) and t is the time elapsed (in minutes).

Q: Why is option A incorrect?

A: Option A is incorrect because it does not take into account the student's running speed. The student runs 1 kilometer every 4 minutes, not 1 kilometer every minute.

Q: Why is option B incorrect?

A: Option B is incorrect because it does not describe the distance from the finish line in terms of minutes. The student's running speed is 0.25 km/min, not -0.1 km/min.

Q: Can you provide more examples of mathematical modeling in real-world situations?

A: Yes, here are a few examples:

  • Modeling the growth of a population using exponential functions
  • Modeling the motion of an object using kinematic equations
  • Modeling the spread of a disease using differential equations

Q: What are some real-world applications of mathematical modeling?

A: Some real-world applications of mathematical modeling include:

  • Predicting the stock market
  • Optimizing supply chains
  • Designing efficient transportation systems

Q: How can I learn more about mathematical modeling?

A: There are many resources available to learn more about mathematical modeling, including:

  • Khan Academy: Mathematical Modeling
  • MIT OpenCourseWare: Calculus
  • Wolfram MathWorld: Functions

Q: What are some common mistakes to avoid when creating mathematical models?

A: Some common mistakes to avoid when creating mathematical models include:

  • Not taking into account all relevant variables
  • Using incorrect or incomplete data
  • Not testing the model for accuracy and reliability

Conclusion

In this article, we answered some frequently asked questions about mathematical modeling and the student's 10-kilometer run. We hope that this article has provided you with a better understanding of the topic and has inspired you to learn more about mathematical modeling.

Key Takeaways

  • Mathematical functions can be used to model real-world situations.
  • The student's running speed is 0.25 km/min.
  • The correct function that describes the distance from the finish line in terms of minutes is d(t) = 10 - 0.25t.
  • Mathematical modeling has many real-world applications, including predicting the stock market and optimizing supply chains.

Further Reading

If you want to learn more about mathematical modeling and functions, I recommend checking out the following resources:

  • Khan Academy: Mathematical Modeling
  • MIT OpenCourseWare: Calculus
  • Wolfram MathWorld: Functions

References