Problem 62 - Algebra A Combined Function

Question

The lowest temperature ever recorded in Oceania was \(-10^{\circ} \mathrm{C}\) at the Haleakala Summit in Maui, Hawaii, in January 1961. Convert this record low temperature to Fahrenheit.

Step-by-Step Solution

Answer

-10°C is equivalent to 14°F.

Step 1: Understanding the Conversion Formula

To convert a temperature from Celsius to Fahrenheit, we use the formula: \[ F = \left( \frac{9}{5} \times C \right) + 32 \]where \( F \) is the temperature in Fahrenheit and \( C \) is the temperature in Celsius.

Step 2: Substituting the Celsius Value

We have the temperature in Celsius \( C = -10^{\circ} \), which needs to be converted to Fahrenheit. Substitute \( C = -10 \) into the formula:\[ F = \left( \frac{9}{5} \times (-10) \right) + 32 \]

Step 3: Performing the Multiplication

Calculate the multiplication within the formula:\[ \frac{9}{5} \times (-10) = -18 \]Thus, the expression becomes:\[ F = -18 + 32 \]

Step 4: Calculating the Final Result

Perform the addition to find the temperature in Fahrenheit:\[ F = -18 + 32 = 14 \]Hence, the temperature is \( 14^{\circ} \, \text{Fahrenheit} \).

Key Concepts

Celsius to Fahrenheit

The conversion from Celsius to Fahrenheit is a common task for students learning about temperature scales. The Celsius scale is widely used in most parts of the world for various everyday purposes, including weather forecasting, cooking, and science. In contrast, the Fahrenheit scale is primarily used in the United States.
Understanding how to convert between these units is essential as it allows for interpreting data correctly across different regions. Although the conversion involves basic arithmetic, capturing its practical context makes the process more meaningful. This skill becomes particularly useful when confronted with temperatures recorded in historical or international contexts.

Conversion Formula

The conversion from Celsius to Fahrenheit is achieved with a straightforward mathematical formula:
\[ F = \left( \frac{9}{5} \times C \right) + 32 \]
This formula converts a Celsius temperature \( C \) to its equivalent Fahrenheit temperature \( F \).

• The fraction \( \frac{9}{5} \) acts as a scaling factor that adjusts the degrees of Celsius to Fahrenheit. This scaling is necessary because the degree size differs between the two units.
• The addition of 32 accounts for the different zero points of the two temperature scales.
  

This mathematical approach simplifies the conversion process, allowing anyone to interchange between temperatures with ease.

Arithmetic Operations

The calculation from Celsius to Fahrenheit involves basic arithmetic operations: multiplication and addition. These operations should be performed carefully to ensure an accurate conversion.
First, multiply the Celsius temperature by \( \frac{9}{5} \). This step converts the incremental value difference between the Celsius and Fahrenheit scales.
Secondly, add 32 to this result. The addition reflects the offset between the zero points on the two scales, aligning the temperature scales accurately.
It is pivotal to perform each step in the correct order. Multiplication comes first, followed by addition, according to mathematical conventions. This ensures the operations reflect the intended adjustment of temperature values.

Negative Temperature

In temperature conversion, negative values introduce an additional level of complexity, often due to misconceptions.
When handling negative temperatures such as \( -10^{\circ} \text{C} \), ensure you apply arithmetic operations correctly.

• Multiplying a negative number by any positive number still results in a negative product.
• Accurately convert and handle these values during the conversion to maintain precision.

Recognizing that temperatures can be negative is essential, especially in climatic regions experiencing such low temperatures during specific periods.

Haleakala Summit

Haleakala Summit, located in Maui, Hawaii, is an extraordinary place not just for its breathtaking views but also for its distinctive climatic conditions. At an elevation of over 10,000 feet, this summit experiences temperatures that can plunge below zero degrees Celsius during the winter months.
In 1961, the temperature at Haleakala Summit reached a record low of \( -10^{\circ} \text{C} \), an interesting fact for both geographical and meteorological studies.
This example highlights the diversity in climate conditions, even within Hawaiian islands, which are typically associated with tropical weather. Understanding these variations offers insights into the climatic intricacies of remote and elevated regions.