Angel Conducted A Scientific Experiment. For A Certain Time, The Temperature Of A Compound Rose 2 1 2 2 \frac{1}{2} 2 2 1 ​ Degrees Every 2 5 \frac{2}{5} 5 2 ​ Of An Hour. What Was The Rate, In Degrees Per Hour, That The Temperature Of The Compound

Introduction

In this article, we will delve into a scientific experiment conducted by Angel, where the temperature of a compound rose at a specific rate. The experiment involved a temperature increase of $2 \frac{1}{2}$ degrees every $\frac{2}{5}$ of an hour. Our goal is to determine the rate, in degrees per hour, at which the temperature of the compound rose.

Understanding the Problem

To solve this problem, we need to understand the concept of rate of change. The rate of change is a measure of how quickly a quantity changes over a given period of time. In this case, we are interested in finding the rate at which the temperature of the compound increased.

Calculating the Rate of Change

To calculate the rate of change, we need to divide the temperature increase by the time interval over which it occurred. In this case, the temperature increased by $2 \frac{1}{2}$ degrees every $\frac{2}{5}$ of an hour.

Converting Mixed Numbers to Improper Fractions

Before we can perform the division, we need to convert the mixed number $2 \frac{1}{2}$ to an improper fraction. To do this, we multiply the whole number part (2) by the denominator (2) and then add the numerator (1).

$$2 \frac{1}{2} = \frac{(2 \times 2) + 1}{2} = \frac{5}{2}$$

Converting the Time Interval to a Fraction

We also need to convert the time interval $\frac{2}{5}$ of an hour to a fraction. Since the time interval is already in fraction form, we can leave it as is.

Calculating the Rate of Change

Now that we have converted the mixed number to an improper fraction and left the time interval as is, we can perform the division to calculate the rate of change.

$$\text{Rate of change} = \frac{\text{Temperature increase}}{\text{Time interval}} = \frac{\frac{5}{2}}{\frac{2}{5}}$$

To divide fractions, we multiply the first fraction by the reciprocal of the second fraction.

$$\text{Rate of change} = \frac{\frac{5}{2}}{\frac{2}{5}} = \frac{5}{2} \times \frac{5}{2} = \frac{25}{4}$$

Converting the Improper Fraction to a Mixed Number

To make the answer more understandable, we can convert the improper fraction $\frac{25}{4}$ to a mixed number.

$$\frac{25}{4} = 6 \frac{1}{4}$$

Conclusion

In this article, we have calculated the rate of change of the temperature of a compound, which rose $2 \frac{1}{2}$ degrees every $\frac{2}{5}$ of an hour. We first converted the mixed number to an improper fraction and then performed the division to calculate the rate of change. The result was an improper fraction $\frac{25}{4}$, which we then converted to a mixed number $6 \frac{1}{4}$. This represents the rate at which the temperature of the compound increased.

Rate of Change in Degrees per Hour

The rate of change of the temperature of the compound is $6 \frac{1}{4}$ degrees per $\frac{2}{5}$ of an hour. To find the rate in degrees per hour, we need to multiply the rate by the reciprocal of the time interval.

$$\text{Rate in degrees per hour} = 6 \frac{1}{4} \times \frac{5}{2}$$

To multiply a mixed number by a fraction, we multiply the whole number part by the numerator and then add the product of the whole number part and the denominator.

$$\text{Rate in degrees per hour} = 6 \times 5 + \frac{1}{4} \times 5 = 30 + \frac{5}{4} = 30 \frac{5}{4}$$

Simplifying the Rate in Degrees per Hour

To simplify the rate in degrees per hour, we can convert the mixed number $30 \frac{5}{4}$ to an improper fraction.

$$30 \frac{5}{4} = \frac{(30 \times 4) + 5}{4} = \frac{120 + 5}{4} = \frac{125}{4}$$

Conclusion

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Introduction

In our previous article, we explored the temperature rise experiment conducted by Angel, where the temperature of a compound rose at a specific rate. We calculated the rate of change of the temperature, which was $6 \frac{1}{4}$ degrees per $\frac{2}{5}$ of an hour. In this article, we will answer some frequently asked questions related to the experiment.

Q&A

Q: What is the rate of change of the temperature of the compound?

A: The rate of change of the temperature of the compound is $6 \frac{1}{4}$ degrees per $\frac{2}{5}$ of an hour.

Q: How do I convert the mixed number $6 \frac{1}{4}$ to an improper fraction?

A: To convert the mixed number $6 \frac{1}{4}$ to an improper fraction, you multiply the whole number part (6) by the denominator (4) and then add the numerator (1).

$$6 \frac{1}{4} = \frac{(6 \times 4) + 1}{4} = \frac{24 + 1}{4} = \frac{25}{4}$$

Q: How do I calculate the rate of change in degrees per hour?

A: To calculate the rate of change in degrees per hour, you multiply the rate of change by the reciprocal of the time interval.

$$\text{Rate in degrees per hour} = 6 \frac{1}{4} \times \frac{5}{2}$$

Q: How do I simplify the rate in degrees per hour?

A: To simplify the rate in degrees per hour, you can convert the mixed number $30 \frac{5}{4}$ to an improper fraction.

$$30 \frac{5}{4} = \frac{(30 \times 4) + 5}{4} = \frac{120 + 5}{4} = \frac{125}{4}$$

Q: What is the rate of change of the temperature of the compound in degrees per hour?

A: The rate of change of the temperature of the compound in degrees per hour is $\frac{125}{4}$.

Q: How do I convert the improper fraction $\frac{125}{4}$ to a mixed number?

A: To convert the improper fraction $\frac{125}{4}$ to a mixed number, you divide the numerator (125) by the denominator (4).

$$\frac{125}{4} = 31 \frac{1}{4}$$

Q: What is the rate of change of the temperature of the compound in degrees per hour in mixed number form?

A: The rate of change of the temperature of the compound in degrees per hour in mixed number form is $31 \frac{1}{4}$.

Conclusion

In this article, we have answered some frequently asked questions related to the temperature rise experiment conducted by Angel. We have provided step-by-step solutions to each question, including converting mixed numbers to improper fractions, calculating the rate of change in degrees per hour, and simplifying the rate in degrees per hour. We hope this article has been helpful in understanding the experiment and its results.

Additional Resources

For more information on the temperature rise experiment, please refer to our previous article: Temperature Rise Experiment: Understanding the Rate of Change.

Related Topics

• Temperature and Heat Transfer
• Rate of Change and Slope
• Improper Fractions and Mixed Numbers

Glossary

• Rate of Change: A measure of how quickly a quantity changes over a given period of time.
• Improper Fraction: A fraction with a numerator greater than the denominator.
• Mixed Number: A number that is a combination of a whole number and a fraction.
• Slope: A measure of the steepness of a line or curve.