Thank you for visiting When the temperature is 0 degrees Celsius the Fahrenheit temperature is 32 When the Celsius temperature is 100 the corresponding Fahrenheit temperature is 212 Express. 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 :
To express the Fahrenheit temperature as a linear function of the Celsius temperature, [tex]\( F(C) \)[/tex], we'll follow these steps:
### Step 1: Establish the Linear Relationship
We know two key points that relate Celsius and Fahrenheit temperatures:
- At 0 degrees Celsius, the temperature in Fahrenheit is 32 degrees.
- At 100 degrees Celsius, the temperature in Fahrenheit is 212 degrees.
### Step 2: Calculate the Slope
The formula for the slope ([tex]\(m\)[/tex]) between two points [tex]\((C_1, F_1)\)[/tex] and [tex]\((C_2, F_2)\)[/tex] is:
[tex]\[
m = \frac{F_2 - F_1}{C_2 - C_1}
\][/tex]
Substituting our known values:
- [tex]\(C_1 = 0\)[/tex], [tex]\(F_1 = 32\)[/tex]
- [tex]\(C_2 = 100\)[/tex], [tex]\(F_2 = 212\)[/tex]
[tex]\[
m = \frac{212 - 32}{100 - 0} = \frac{180}{100} = 1.8
\][/tex]
So, the rate of change is 1.8 Fahrenheit degrees per Celsius degree.
### Step 3: Write the Linear Function
The linear equation can be written as:
[tex]\[
F(C) = mC + b
\][/tex]
Where [tex]\(b\)[/tex] is the y-intercept. Since we know when [tex]\(C = 0\)[/tex], [tex]\(F = 32\)[/tex], the y-intercept [tex]\(b\)[/tex] is 32.
Thus, the function is:
[tex]\[
F(C) = 1.8C + 32
\][/tex]
### Step 4: Interpreting [tex]\(F(22)\)[/tex]
To find [tex]\(F(22)\)[/tex], substitute 22 into the function:
[tex]\[
F(22) = 1.8 \times 22 + 32 = 39.6 + 32 = 71.6
\][/tex]
So, at 22 degrees Celsius, it is 71.6 degrees Fahrenheit.
### Step 5: Calculate [tex]\(F(-35)\)[/tex]
To find [tex]\(F(-35)\)[/tex], substitute -35 into the function:
[tex]\[
F(-35) = 1.8 \times (-35) + 32 = -63 + 32 = -31
\][/tex]
Therefore, at -35 degrees Celsius, it is -31 degrees Fahrenheit.
These calculations provide the linear relationship between Celsius and Fahrenheit temperatures and specific evaluations for given Celsius values.
### Step 1: Establish the Linear Relationship
We know two key points that relate Celsius and Fahrenheit temperatures:
- At 0 degrees Celsius, the temperature in Fahrenheit is 32 degrees.
- At 100 degrees Celsius, the temperature in Fahrenheit is 212 degrees.
### Step 2: Calculate the Slope
The formula for the slope ([tex]\(m\)[/tex]) between two points [tex]\((C_1, F_1)\)[/tex] and [tex]\((C_2, F_2)\)[/tex] is:
[tex]\[
m = \frac{F_2 - F_1}{C_2 - C_1}
\][/tex]
Substituting our known values:
- [tex]\(C_1 = 0\)[/tex], [tex]\(F_1 = 32\)[/tex]
- [tex]\(C_2 = 100\)[/tex], [tex]\(F_2 = 212\)[/tex]
[tex]\[
m = \frac{212 - 32}{100 - 0} = \frac{180}{100} = 1.8
\][/tex]
So, the rate of change is 1.8 Fahrenheit degrees per Celsius degree.
### Step 3: Write the Linear Function
The linear equation can be written as:
[tex]\[
F(C) = mC + b
\][/tex]
Where [tex]\(b\)[/tex] is the y-intercept. Since we know when [tex]\(C = 0\)[/tex], [tex]\(F = 32\)[/tex], the y-intercept [tex]\(b\)[/tex] is 32.
Thus, the function is:
[tex]\[
F(C) = 1.8C + 32
\][/tex]
### Step 4: Interpreting [tex]\(F(22)\)[/tex]
To find [tex]\(F(22)\)[/tex], substitute 22 into the function:
[tex]\[
F(22) = 1.8 \times 22 + 32 = 39.6 + 32 = 71.6
\][/tex]
So, at 22 degrees Celsius, it is 71.6 degrees Fahrenheit.
### Step 5: Calculate [tex]\(F(-35)\)[/tex]
To find [tex]\(F(-35)\)[/tex], substitute -35 into the function:
[tex]\[
F(-35) = 1.8 \times (-35) + 32 = -63 + 32 = -31
\][/tex]
Therefore, at -35 degrees Celsius, it is -31 degrees Fahrenheit.
These calculations provide the linear relationship between Celsius and Fahrenheit temperatures and specific evaluations for given Celsius values.
Thank you for reading the article When the temperature is 0 degrees Celsius the Fahrenheit temperature is 32 When the Celsius temperature is 100 the corresponding Fahrenheit temperature is 212 Express. 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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