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 :
We are given that when the Celsius temperature is [tex]$0^\circ$[/tex], the Fahrenheit temperature is [tex]$32^\circ$[/tex], and when the Celsius temperature is [tex]$100^\circ$[/tex], the Fahrenheit temperature is [tex]$212^\circ$[/tex]. We want to express the Fahrenheit temperature as a linear function of the Celsius temperature, [tex]$F(C)$[/tex].
To write this as a linear function, we use the form
[tex]$$
F(C) = mC + b,
$$[/tex]
where [tex]$m$[/tex] is the rate of change (slope) and [tex]$b$[/tex] is the [tex]$y$[/tex]-intercept.
Step 1. Find the slope [tex]$m$[/tex].
The slope is given by
[tex]$$
m = \frac{F(100) - F(0)}{100 - 0} = \frac{212 - 32}{100} = \frac{180}{100} = 1.8.
$$[/tex]
So, the rate of change is [tex]$1.8$[/tex] Fahrenheit degrees per Celsius degree.
Step 2. Find the [tex]$y$[/tex]-intercept [tex]$b$[/tex].
Since [tex]$F(0) = 32$[/tex], it follows directly that
[tex]$$
b = 32.
$$[/tex]
Step 3. Write the linear function.
Substituting [tex]$m = 1.8$[/tex] and [tex]$b = 32$[/tex] into the linear formula gives
[tex]$$
F(C) = 1.8C + 32.
$$[/tex]
Step 4. Evaluate [tex]$F(27)$[/tex].
Substitute [tex]$C = 27$[/tex] into the function:
[tex]$$
F(27) = 1.8 \times 27 + 32.
$$[/tex]
Calculating this,
[tex]$$
1.8 \times 27 = 48.6,
$$[/tex]
so
[tex]$$
F(27) = 48.6 + 32 = 80.6.
$$[/tex]
Rounded to one decimal place, [tex]$F(27)$[/tex] is [tex]$80.6$[/tex]. This means that when the Celsius temperature is [tex]$27^\circ$[/tex], the Fahrenheit temperature is [tex]$80.6^\circ$[/tex].
Step 5. Evaluate [tex]$F(-30)$[/tex].
Substitute [tex]$C = -30$[/tex] into the function:
[tex]$$
F(-30) = 1.8 \times (-30) + 32.
$$[/tex]
Calculating,
[tex]$$
1.8 \times (-30) = -54,
$$[/tex]
so
[tex]$$
F(-30) = -54 + 32 = -22.
$$[/tex]
Thus, [tex]$F(-30) = -22^\circ$[/tex] Fahrenheit.
Summarizing the results:
a. The rate of change is [tex]$1.8$[/tex] Fahrenheit degrees per Celsius degree.
b. The function is [tex]$F(C) = 1.8C + 32$[/tex], and [tex]$F(27) = 80.6^\circ$[/tex] Fahrenheit. In other words, at [tex]$27^\circ$[/tex] Celsius, it is [tex]$80.6^\circ$[/tex] Fahrenheit.
c. [tex]$F(-30) = -22^\circ$[/tex] Fahrenheit.
To write this as a linear function, we use the form
[tex]$$
F(C) = mC + b,
$$[/tex]
where [tex]$m$[/tex] is the rate of change (slope) and [tex]$b$[/tex] is the [tex]$y$[/tex]-intercept.
Step 1. Find the slope [tex]$m$[/tex].
The slope is given by
[tex]$$
m = \frac{F(100) - F(0)}{100 - 0} = \frac{212 - 32}{100} = \frac{180}{100} = 1.8.
$$[/tex]
So, the rate of change is [tex]$1.8$[/tex] Fahrenheit degrees per Celsius degree.
Step 2. Find the [tex]$y$[/tex]-intercept [tex]$b$[/tex].
Since [tex]$F(0) = 32$[/tex], it follows directly that
[tex]$$
b = 32.
$$[/tex]
Step 3. Write the linear function.
Substituting [tex]$m = 1.8$[/tex] and [tex]$b = 32$[/tex] into the linear formula gives
[tex]$$
F(C) = 1.8C + 32.
$$[/tex]
Step 4. Evaluate [tex]$F(27)$[/tex].
Substitute [tex]$C = 27$[/tex] into the function:
[tex]$$
F(27) = 1.8 \times 27 + 32.
$$[/tex]
Calculating this,
[tex]$$
1.8 \times 27 = 48.6,
$$[/tex]
so
[tex]$$
F(27) = 48.6 + 32 = 80.6.
$$[/tex]
Rounded to one decimal place, [tex]$F(27)$[/tex] is [tex]$80.6$[/tex]. This means that when the Celsius temperature is [tex]$27^\circ$[/tex], the Fahrenheit temperature is [tex]$80.6^\circ$[/tex].
Step 5. Evaluate [tex]$F(-30)$[/tex].
Substitute [tex]$C = -30$[/tex] into the function:
[tex]$$
F(-30) = 1.8 \times (-30) + 32.
$$[/tex]
Calculating,
[tex]$$
1.8 \times (-30) = -54,
$$[/tex]
so
[tex]$$
F(-30) = -54 + 32 = -22.
$$[/tex]
Thus, [tex]$F(-30) = -22^\circ$[/tex] Fahrenheit.
Summarizing the results:
a. The rate of change is [tex]$1.8$[/tex] Fahrenheit degrees per Celsius degree.
b. The function is [tex]$F(C) = 1.8C + 32$[/tex], and [tex]$F(27) = 80.6^\circ$[/tex] Fahrenheit. In other words, at [tex]$27^\circ$[/tex] Celsius, it is [tex]$80.6^\circ$[/tex] Fahrenheit.
c. [tex]$F(-30) = -22^\circ$[/tex] Fahrenheit.
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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