High School

We appreciate your visit to 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 offers clear insights and highlights the essential aspects of the topic. Our goal is to provide a helpful and engaging learning experience. Explore the content and find the answers you need!

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 212 degrees. Express the Fahrenheit temperature as a linear function of [tex]C[/tex], the Celsius temperature, [tex]F(C)[/tex].

1. Find the linear function [tex]F(C)[/tex]:
[tex]F(C) = \square[/tex]

2. Find the rate of change of Fahrenheit temperature for each unit change in Celsius temperature:
[tex]\qquad \text{Rate of change: } \square \text{ Fahrenheit degrees per Celsius degree}[/tex]

3. Find and interpret [tex]F(26)[/tex]. Round to one decimal place:
[tex]\qquad \text{At } 26 \text{ degrees Celsius, it is } \square \text{ degrees Fahrenheit.}[/tex]

4. Calculate [tex]F(-40)[/tex]:
[tex]\qquad F(-40) = \square[/tex]

Answer :

Let's work through the problem step-by-step.

a. Find the rate of change of Fahrenheit temperature for each unit change in Celsius temperature.

The given data points are:
- When the Celsius temperature is [tex]\(0\)[/tex], the Fahrenheit temperature is [tex]\(32\)[/tex].
- When the Celsius temperature is [tex]\(100\)[/tex], the Fahrenheit temperature is [tex]\(212\)[/tex].

To find the rate of change (or slope), we use the formula for the slope between two points [tex]\((x_1, y_1)\)[/tex] and [tex]\((x_2, y_2)\)[/tex]:
[tex]\[
\text{Slope} \, m = \frac{y_2 - y_1}{x_2 - x_1}
\][/tex]

Substitute the given points:
[tex]\[
m = \frac{212 - 32}{100 - 0} = \frac{180}{100} = 1.8
\][/tex]

So, the rate of change of Fahrenheit temperature for each unit change in Celsius is [tex]\(1.8\)[/tex] degrees Fahrenheit per degree Celsius.

b. Express the Fahrenheit temperature as a linear function of Celsius temperature, [tex]\(F(C)\)[/tex].

The formula for a linear function is [tex]\(F(C) = m \times C + b\)[/tex], where [tex]\(m\)[/tex] is the slope and [tex]\(b\)[/tex] is the y-intercept. From part (a), we found [tex]\(m = 1.8\)[/tex].

Since we know [tex]\(F(0) = 32\)[/tex], this helps us determine the y-intercept:
[tex]\[
b = 32
\][/tex]

Thus, the function is:
[tex]\[
F(C) = 1.8 \times C + 32
\][/tex]

Find and interpret [tex]\(F(26)\)[/tex]:

To find [tex]\(F(26)\)[/tex] using this function, substitute [tex]\(C = 26\)[/tex]:
[tex]\[
F(26) = 1.8 \times 26 + 32 = 46.8 + 32 = 78.8
\][/tex]

So, when the Celsius temperature is [tex]\(26\)[/tex], the corresponding Fahrenheit temperature is approximately [tex]\(78.8\)[/tex] degrees.

c. Calculate [tex]\(F(-40)\)[/tex]:

Substitute [tex]\(C = -40\)[/tex] into the function:
[tex]\[
F(-40) = 1.8 \times (-40) + 32 = -72 + 32 = -40
\][/tex]

So, [tex]\(F(-40)\)[/tex] is [tex]\(-40\)[/tex] degrees Fahrenheit.

To summarize:
- The rate of change is [tex]\(1.8\)[/tex] degrees Fahrenheit per Celsius degree.
- [tex]\(F(26)\)[/tex] is approximately [tex]\(78.8\)[/tex] degrees Fahrenheit.
- [tex]\(F(-40)\)[/tex] is [tex]\(-40\)[/tex] degrees Fahrenheit.

Thanks for taking the time to read 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 insights shared have been valuable and enhanced your understanding of the topic. Don�t hesitate to browse our website for more informative and engaging content!

Rewritten by : Barada