The Temperature At Mphalaleni One Morning Was − 2 ∘ C -2^{\circ} C − 2 ∘ C At 07:00 And Increased By 2 ∘ C 2^{\circ} C 2 ∘ C Every Hour Until 12:00. What Will The Temperature Be At 12:00?

Introduction

Temperature is a fundamental aspect of our daily lives, and understanding how it changes over time is crucial in various fields, including meteorology, agriculture, and even urban planning. In this article, we will delve into a mathematical problem that involves temperature changes over a specific period. We will analyze the situation at Mphalaleni, where the temperature was recorded at 07:00 and increased by a certain amount every hour until 12:00.

The Problem

The temperature at Mphalaleni was recorded at 07:00 as $-2^{\circ} C$. It increased by $2^{\circ} C$ every hour until 12:00. We need to find the temperature at 12:00.

Step 1: Understanding the Temperature Change

The temperature increased by $2^{\circ} C$ every hour. This means that for each hour that passes, the temperature will increase by $2^{\circ} C$. We can represent this as a linear equation, where the temperature at any given hour is equal to the initial temperature plus the product of the hourly increase and the number of hours that have passed.

Step 2: Calculating the Temperature at 12:00

Let's calculate the temperature at 12:00. We know that the temperature increased by $2^{\circ} C$ every hour, and we need to find the temperature after 5 hours (from 07:00 to 12:00).

We can use the formula:

Temperature at 12:00 = Initial Temperature + (Hourly Increase x Number of Hours)

Substituting the values, we get:

Temperature at 12:00 = $-2^{\circ} C$ + ($2^{\circ} C$ x 5)

Temperature at 12:00 = $-2^{\circ} C$ + $10^{\circ} C$

Temperature at 12:00 = $8^{\circ} C$

Conclusion

In this article, we analyzed a mathematical problem involving temperature changes over a specific period. We used a linear equation to represent the temperature change and calculated the temperature at 12:00. The result shows that the temperature at Mphalaleni will be $8^{\circ} C$ at 12:00.

Mathematical Representation

The temperature change can be represented mathematically as:

T(t) = T0 + rt

where:

• T(t) is the temperature at time t
• T0 is the initial temperature
• r is the hourly increase in temperature
• t is the time in hours

In this case, T0 = $-2^{\circ} C$, r = $2^{\circ} C$, and t = 5 hours.

Solving the Equation

We can solve the equation by substituting the values:

T(5) = $-2^{\circ} C$ + ($2^{\circ} C$ x 5)

T(5) = $-2^{\circ} C$ + $10^{\circ} C$

T(5) = $8^{\circ} C$

Final Answer

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Introduction

In our previous article, we analyzed a mathematical problem involving temperature changes over a specific period. We used a linear equation to represent the temperature change and calculated the temperature at 12:00. In this article, we will provide a Q&A section to further clarify the concepts and provide additional insights.

Q&A

Q: What is the initial temperature at Mphalaleni?

A: The initial temperature at Mphalaleni is $-2^{\circ} C$ at 07:00.

Q: How much does the temperature increase every hour?

A: The temperature increases by $2^{\circ} C$ every hour.

Q: How many hours does it take for the temperature to reach $8^{\circ} C$?

A: It takes 5 hours for the temperature to reach $8^{\circ} C$, from 07:00 to 12:00.

Q: Can we use this formula to calculate the temperature at any given hour?

A: Yes, we can use the formula:

Temperature at t = Initial Temperature + (Hourly Increase x Number of Hours)

to calculate the temperature at any given hour.

Q: What if the temperature increase is not constant?

A: If the temperature increase is not constant, we would need to use a different type of equation, such as a quadratic or exponential equation, to represent the temperature change.

Q: Can we use this formula to calculate the temperature at a different time of day?

A: Yes, we can use the formula to calculate the temperature at any given time of day, as long as we know the initial temperature and the hourly increase.

Q: What if we want to calculate the temperature at a specific time, but we don't know the initial temperature?

A: If we don't know the initial temperature, we would need to use additional information, such as the temperature at a different time, to calculate the initial temperature.

Q: Can we use this formula to calculate the temperature in a different location?

A: Yes, we can use the formula to calculate the temperature in a different location, as long as we know the initial temperature and the hourly increase for that location.

Conclusion

In this Q&A article, we provided additional insights and clarification on the concepts presented in our previous article. We answered common questions and provided examples to illustrate the use of the formula.

Mathematical Representation

The temperature change can be represented mathematically as:

T(t) = T0 + rt

where:

• T(t) is the temperature at time t
• T0 is the initial temperature
• r is the hourly increase in temperature
• t is the time in hours

Solving the Equation

We can solve the equation by substituting the values:

T(5) = $-2^{\circ} C$ + ($2^{\circ} C$ x 5)

T(5) = $-2^{\circ} C$ + $10^{\circ} C$

T(5) = $8^{\circ} C$

Final Answer

The final answer is $8^{\circ} C$.

Additional Resources

For more information on temperature changes and mathematical representations, please refer to the following resources:

• Temperature Change Formula
• Mathematical Representation of Temperature Change
• Temperature Change Calculator

Note: The above resources are fictional and for demonstration purposes only.