Sure, let's analyze and solve the problem step-by-step. The formula that relates the temperature in degrees Fahrenheit ([tex]\(F\)[/tex]) to the temperature in degrees Celsius ([tex]\(C\)[/tex]) is given by:
[tex]\[ F = 32 + 1.8C \][/tex]
We are asked to find the equivalent temperature increase in degrees Fahrenheit (F) when the temperature in degrees Celsius (C) increases by 10 degrees.
### Step-by-Step Solution:
1. Identify the Increase in Celsius: We start with an increase of 10 degrees Celsius. Let's denote this increase by [tex]\(\Delta C\)[/tex]:
[tex]\[
\Delta C = 10
\][/tex]
2. Understand the Linear Relationship: According to the formula, the temperature in Fahrenheit is a linear function of the temperature in Celsius. This means that an increase in Celsius will result in a proportional increase in Fahrenheit.
3. Apply the Linear Coefficient: From the formula [tex]\( F = 32 + 1.8C \)[/tex], the term [tex]\(1.8C\)[/tex] shows how much the degrees Celsius affect the degrees Fahrenheit. Therefore, the increase in Fahrenheit ([tex]\(\Delta F\)[/tex]) corresponding to the increase in Celsius can be calculated using the linear coefficient [tex]\(1.8\)[/tex]:
[tex]\[
\Delta F = 1.8 \times \Delta C
\][/tex]
4. Substitute the Increase in Celsius: Substitute [tex]\(\Delta C = 10\)[/tex] into the equation:
[tex]\[
\Delta F = 1.8 \times 10
\][/tex]
5. Calculate the Increase in Fahrenheit:
[tex]\[
\Delta F = 18
\][/tex]
Hence, the temperature increase in degrees Fahrenheit that is equivalent to a temperature increase of 10 degrees Celsius is [tex]\(18\)[/tex] degrees Fahrenheit.
