Thank you for visiting When the temperature is 0 degrees Celsius the Fahrenheit temperature is 32 degrees When the Celsius temperature is 100 degrees the corresponding Fahrenheit temperature is. This page is designed to guide you through key points and clear explanations related to the topic at hand. We aim to make your learning experience smooth, insightful, and informative. Dive in and discover the answers you're looking for!
Answer :
Let's work through this step-by-step:
We need to express the Fahrenheit temperature [tex]\( F \)[/tex] as a linear function of the Celsius temperature [tex]\( C \)[/tex].
Step 1: Determine the slope (rate of change)
We have two points from the problem:
- When Celsius is 0, Fahrenheit is 32: [tex]\((0, 32)\)[/tex]
- When Celsius is 100, Fahrenheit is 212: [tex]\((100, 212)\)[/tex]
The slope (rate of change) of a linear function is calculated as:
[tex]\[ \text{slope} = \frac{\text{change in Fahrenheit}}{\text{change in Celsius}} = \frac{F_2 - F_1}{C_2 - C_1} = \frac{212 - 32}{100 - 0} = \frac{180}{100} = 1.8 \][/tex]
So, the rate of change is 1.8 Fahrenheit degrees per Celsius degree.
Step 2: Write the linear function
The general form of a linear equation is:
[tex]\[ F(C) = mC + b \][/tex]
Where [tex]\( m \)[/tex] is the slope, which we found to be 1.8, and [tex]\( b \)[/tex] is the y-intercept. Since [tex]\( F(0) = 32 \)[/tex], the intercept [tex]\( b \)[/tex] is 32.
Thus, the function is:
[tex]\[ F(C) = 1.8C + 32 \][/tex]
Step 3: Calculate [tex]\( F(25) \)[/tex]
Now, plug [tex]\( C = 25 \)[/tex] into the linear function:
[tex]\[ F(25) = 1.8 \times 25 + 32 \][/tex]
[tex]\[ F(25) = 45 + 32 = 77 \][/tex]
So, when the Celsius temperature is 25 degrees, the Fahrenheit temperature is 77.0 degrees.
Step 4: Calculate [tex]\( F(-50) \)[/tex]
Plug [tex]\( C = -50 \)[/tex] into the linear function:
[tex]\[ F(-50) = 1.8 \times (-50) + 32 \][/tex]
[tex]\[ F(-50) = -90 + 32 = -58 \][/tex]
So, when the Celsius temperature is -50 degrees, the Fahrenheit temperature is -58.0 degrees.
In summary:
- The rate of change is 1.8 Fahrenheit degrees per Celsius degree.
- [tex]\( F(25) = 77.0 \)[/tex] Fahrenheit degrees.
- [tex]\( F(-50) = -58.0 \)[/tex] Fahrenheit degrees.
We need to express the Fahrenheit temperature [tex]\( F \)[/tex] as a linear function of the Celsius temperature [tex]\( C \)[/tex].
Step 1: Determine the slope (rate of change)
We have two points from the problem:
- When Celsius is 0, Fahrenheit is 32: [tex]\((0, 32)\)[/tex]
- When Celsius is 100, Fahrenheit is 212: [tex]\((100, 212)\)[/tex]
The slope (rate of change) of a linear function is calculated as:
[tex]\[ \text{slope} = \frac{\text{change in Fahrenheit}}{\text{change in Celsius}} = \frac{F_2 - F_1}{C_2 - C_1} = \frac{212 - 32}{100 - 0} = \frac{180}{100} = 1.8 \][/tex]
So, the rate of change is 1.8 Fahrenheit degrees per Celsius degree.
Step 2: Write the linear function
The general form of a linear equation is:
[tex]\[ F(C) = mC + b \][/tex]
Where [tex]\( m \)[/tex] is the slope, which we found to be 1.8, and [tex]\( b \)[/tex] is the y-intercept. Since [tex]\( F(0) = 32 \)[/tex], the intercept [tex]\( b \)[/tex] is 32.
Thus, the function is:
[tex]\[ F(C) = 1.8C + 32 \][/tex]
Step 3: Calculate [tex]\( F(25) \)[/tex]
Now, plug [tex]\( C = 25 \)[/tex] into the linear function:
[tex]\[ F(25) = 1.8 \times 25 + 32 \][/tex]
[tex]\[ F(25) = 45 + 32 = 77 \][/tex]
So, when the Celsius temperature is 25 degrees, the Fahrenheit temperature is 77.0 degrees.
Step 4: Calculate [tex]\( F(-50) \)[/tex]
Plug [tex]\( C = -50 \)[/tex] into the linear function:
[tex]\[ F(-50) = 1.8 \times (-50) + 32 \][/tex]
[tex]\[ F(-50) = -90 + 32 = -58 \][/tex]
So, when the Celsius temperature is -50 degrees, the Fahrenheit temperature is -58.0 degrees.
In summary:
- The rate of change is 1.8 Fahrenheit degrees per Celsius degree.
- [tex]\( F(25) = 77.0 \)[/tex] Fahrenheit degrees.
- [tex]\( F(-50) = -58.0 \)[/tex] Fahrenheit degrees.
Thank you for reading the article When the temperature is 0 degrees Celsius the Fahrenheit temperature is 32 degrees When the Celsius temperature is 100 degrees the corresponding Fahrenheit temperature is. We hope the information provided is useful and helps you understand this topic better. Feel free to explore more helpful content on our website!
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