Problem 32 - Algebra A Combined Function

Question

Convert Paris, France's low temperature of \(-5^{\circ} \mathrm{C}\) to Fahrenheit.

Step-by-Step Solution

Answer

The low temperature in Paris, France, is \(23^{\circ} \mathrm{F}\).

Step 1: Understand the Formula

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

Step 2: Substitute the Celsius Temperature

Plug the given Celsius temperature, \(-5^{\circ} \mathrm{C}\), into the formula. Thus, we have:\[F = (-5) \times \frac{9}{5} + 32\]

Step 3: Calculate the Product

First, calculate the product of \(-5\) and \(\frac{9}{5}\):\[-5 \times \frac{9}{5} = -\frac{45}{5} = -9\]So the formula becomes:\[F = -9 + 32\]

Step 4: Add 32 to the Product

Add 32 to the result from Step 3:\[F = -9 + 32 = 23\]Thus, the converted temperature is \(23^{\circ} \mathrm{F}\).

Key Concepts

Celsius to Fahrenheit conversion

Converting temperatures from Celsius to Fahrenheit is a useful skill, especially when traveling or dealing with scientific data. In countries like the United States, Fahrenheit is the standard temperature scale, while much of the world relies on Celsius. Understanding how to convert between these two can simplify everything from weather forecasts to cooking instructions.
Each temperature conversion helps you match the geographically preferred system of measurement, allowing smoother communication and understanding in global contexts. Whether you're planning a trip or studying physics, mastering this conversion widens your grasp of interpreting temperature values.

temperature conversion formula

The temperature conversion formula for Celsius to Fahrenheit is straightforward yet essential. This formula is written as:\[ F = C \times \frac{9}{5} + 32 \]

• Here, \( F \) represents the temperature in Fahrenheit.
• \( C \) denotes the temperature in Celsius.

This mathematical equation stems from the way the two scales are determined. While Celsius is based on a 0 to 100 degrees scale (freezing and boiling points of water), Fahrenheit sets its reference points differently, leading to this conversion equation.
By multiplying by \(\frac{9}{5}\), you account for the differing size of each degree on the two scales, and adding 32 aligns it so that the zero point matches. Understanding the formula ensures you can convert any Celsius temperature to Fahrenheit effectively.

step-by-step mathematical process

Following a step-by-step mathematical process ensures accuracy in temperature conversion. Let’s walk through the conversion of \(-5^{\circ} \mathrm{C}\) to Fahrenheit:
First, substitute the Celsius value into the formula:\[ F = (-5) \times \frac{9}{5} + 32 \]
Next, calculate the product of \(-5\) and \(\frac{9}{5}\):\[ -5 \times \frac{9}{5} = -\frac{45}{5} = -9 \]
This step handles the difference in degree sizes. With the result, we adjust it by adding 32:\[ F = -9 + 32 = 23 \]
This detailed breakdown is vital as it guides through each calculation phase, avoiding potential mistakes often made with arithmetic errors or misplacing signs. By meticulously following each step, transforming Celsius to Fahrenheit becomes not only manageable but straightforward.