Problem 61 - Algebra A Combined Function

Question

The highest temperature ever recorded in Europe was \(122^{\circ} \mathrm{F}\) in Seville, Spain, in August of 1881 . Convert this record high temperature to Celsius.

Step-by-Step Solution

Answer

The highest temperature was 50°C.

Step 1: Understand the Formula

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

Step 2: Substitute the Given Value into the Formula

Substitute \(F = 122\) into the conversion formula: \[C = \frac{5}{9}(122 - 32)\]

Step 3: Simplify Inside the Parentheses

Calculate the expression inside the parentheses: \(122 - 32 = 90\). Substitute it back into the formula:\[C = \frac{5}{9}(90)\]

Step 4: Multiply the Fraction by the Difference

Multiply \(\frac{5}{9}\) by \(90\): \[C = \frac{5}{9} \times 90 = 50\]

Step 5: Conclusion of the Conversion

Thus, the highest temperature ever recorded in Europe, when converted to Celsius, is \(50^{\circ} \mathrm{C}\).

Key Concepts

Fahrenheit to Celsius conversion

Converting temperatures from Fahrenheit to Celsius is an essential skill, particularly when understanding weather reports or climates around the world. The conversion relies on a straightforward formula that allows you to transfer temperatures between the two scales. This is particularly crucial in scientific and daily contexts where the Celsius scale might be more commonly used.The formula to convert Fahrenheit (\(F\)) to Celsius (\(C\)) is:\[C = \frac{5}{9}(F - 32)\]This mathematical rule helps standardize how temperature differences are calculated from one scale to another. This conversion is slightly more complex than others due to the need to adjust for the zero points on each scale (32°F is the freezing point of water, whereas 0°C is the freezing point on the Celsius scale).

temperature in Celsius

Understanding temperature in Celsius is crucial, especially because it's widely used globally except in a few countries. Celsius is often used in scientific contexts due to its convenient 0-degree freezing and 100-degree boiling points for water. Converting the record European high from 122°F using the formula mentioned before gives:\[C = \frac{5}{9}(122 - 32)\]When we perform the calculations, this results in 50°C. Representing this temperature in Celsius helps individuals accurately comprehend weather conditions and their potential impacts on daily life and activities.

mathematical formula application

Application of mathematical formulas such as the Fahrenheit to Celsius conversion is a straightforward process that provides a practical application for math in everyday life. Here is how you apply the formula step-by-step:

• Begin by subtracting 32 from the Fahrenheit value, which adjusts for the difference in scale baselines.
• The result, in this case, is 90.
• Next, multiply by \(\frac{5}{9}\), which allows you to factor in the ratio between the Fahrenheit and Celsius scales.

In our example of the highest temperature in Europe, substituting 122 into the equation and following these steps results in precisely 50. This process demonstrates how math operations like subtraction and multiplication play a role in temperature conversions and the importance of understanding formula application.