The Temperature Fell From $0{ }^{\circ} F$ To $15 \frac{1}{2}{ }^{\circ} F$ Below 0 In $ 5 3 4 5 \frac{3}{4} 5 4 3 ​ [/tex] Hours. Wen Tried To Find The Change In Temperature Per Hour. Her Work Is Shown

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Introduction

Temperature fluctuations are a common occurrence in our daily lives, and understanding how to calculate changes in temperature is essential for various applications, including weather forecasting, climate modeling, and even cooking. In this article, we will delve into a mathematical problem presented by Wen, where she attempts to find the change in temperature per hour. We will explore the concept of temperature change, the importance of accurate calculations, and provide a step-by-step solution to the problem.

The Problem

Wen's problem involves a temperature change from $0{ }^{\circ} F$ to $15 \frac{1}{2}{ }^{\circ} F$ below 0 in $5 \frac{3}{4}$ hours. To find the change in temperature per hour, Wen needs to calculate the total change in temperature and then divide it by the time elapsed.

Understanding Temperature Change

Temperature change is a fundamental concept in mathematics and science. It refers to the difference between the initial and final temperatures of a system. In this case, the initial temperature is $0{ }^{\circ} F$, and the final temperature is $15 \frac{1}{2}{ }^{\circ} F$ below 0. To find the total change in temperature, we need to subtract the initial temperature from the final temperature.

Calculating the Total Change in Temperature

To calculate the total change in temperature, we need to subtract the initial temperature from the final temperature. However, we need to convert the final temperature to a decimal value first.

1512∘F=15.5∘F15 \frac{1}{2}{ }^{\circ} F = 15.5{ }^{\circ} F

Now, we can subtract the initial temperature from the final temperature:

15.5∘F−0∘F=15.5∘F15.5{ }^{\circ} F - 0{ }^{\circ} F = 15.5{ }^{\circ} F

However, we need to consider that the final temperature is below 0. To find the total change in temperature, we need to subtract the final temperature from 0:

0∘F−15.5∘F=−15.5∘F0{ }^{\circ} F - 15.5{ }^{\circ} F = -15.5{ }^{\circ} F

Calculating the Change in Temperature per Hour

Now that we have the total change in temperature, we can calculate the change in temperature per hour by dividing the total change in temperature by the time elapsed.

Change in temperature per hour=Total change in temperatureTime elapsed\text{Change in temperature per hour} = \frac{\text{Total change in temperature}}{\text{Time elapsed}}

Change in temperature per hour=−15.5∘F534 hours\text{Change in temperature per hour} = \frac{-15.5{ }^{\circ} F}{5 \frac{3}{4} \text{ hours}}

To divide a fraction by a mixed number, we need to convert the mixed number to an improper fraction first.

534 hours=(5×4)+34 hours=234 hours5 \frac{3}{4} \text{ hours} = \frac{(5 \times 4) + 3}{4} \text{ hours} = \frac{23}{4} \text{ hours}

Now, we can divide the total change in temperature by the time elapsed:

Change in temperature per hour=−15.5∘F234 hours\text{Change in temperature per hour} = \frac{-15.5{ }^{\circ} F}{\frac{23}{4} \text{ hours}}

To divide a decimal value by a fraction, we need to multiply the decimal value by the reciprocal of the fraction.

Change in temperature per hour=−15.5∘F×423\text{Change in temperature per hour} = -15.5{ }^{\circ} F \times \frac{4}{23}

Change in temperature per hour=−15.5×423\text{Change in temperature per hour} = \frac{-15.5 \times 4}{23}

Change in temperature per hour=−6223\text{Change in temperature per hour} = \frac{-62}{23}

Conclusion

In this article, we explored a mathematical problem presented by Wen, where she attempts to find the change in temperature per hour. We calculated the total change in temperature and then divided it by the time elapsed to find the change in temperature per hour. The result is a decimal value that represents the change in temperature per hour. This problem demonstrates the importance of accurate calculations in mathematics and science, and how they can be applied to real-world problems.

Final Answer

The change in temperature per hour is $\frac{-62}{23}$ degrees Fahrenheit per hour.

Additional Resources

For more information on temperature change and mathematical calculations, please refer to the following resources:

References

Introduction

Temperature change is a fundamental concept in mathematics and science, and understanding how to calculate it is essential for various applications, including weather forecasting, climate modeling, and even cooking. In this article, we will address some of the most frequently asked questions about temperature change, providing clear and concise answers to help you better understand this concept.

Q: What is temperature change?

A: Temperature change refers to the difference between the initial and final temperatures of a system. It is a measure of how much the temperature has changed over a given period of time.

Q: How do I calculate temperature change?

A: To calculate temperature change, you need to subtract the initial temperature from the final temperature. If the final temperature is below 0, you need to subtract it from 0 to find the total change in temperature.

Q: What is the formula for temperature change?

A: The formula for temperature change is:

Temperature change=Final temperature−Initial temperature\text{Temperature change} = \text{Final temperature} - \text{Initial temperature}

Q: How do I convert a mixed number to an improper fraction?

A: To convert a mixed number to an improper fraction, you need to multiply the whole number part by the denominator and add the numerator. Then, you need to write the result as a fraction with the same denominator.

Q: How do I divide a decimal value by a fraction?

A: To divide a decimal value by a fraction, you need to multiply the decimal value by the reciprocal of the fraction.

Q: What is the change in temperature per hour?

A: The change in temperature per hour is calculated by dividing the total change in temperature by the time elapsed.

Q: How do I calculate the change in temperature per hour?

A: To calculate the change in temperature per hour, you need to divide the total change in temperature by the time elapsed. If the time elapsed is a mixed number, you need to convert it to an improper fraction first.

Q: What is the final answer to the problem?

A: The final answer to the problem is $\frac{-62}{23}$ degrees Fahrenheit per hour.

Q: Where can I find more information on temperature change?

A: You can find more information on temperature change at the following resources:

Q: What are some real-world applications of temperature change?

A: Temperature change has many real-world applications, including:

  • Weather forecasting
  • Climate modeling
  • Cooking
  • Refrigeration
  • Air conditioning

Conclusion

In this article, we addressed some of the most frequently asked questions about temperature change, providing clear and concise answers to help you better understand this concept. Whether you are a student, a scientist, or simply someone interested in mathematics and science, we hope this article has been helpful in answering your questions about temperature change.

Additional Resources

For more information on temperature change and mathematical calculations, please refer to the following resources:

References