Answer :
Sure, let's break down the solution step by step.
### Part a: Solving for [tex]\( F \)[/tex]
We start with the formula for converting Celsius to Fahrenheit:
[tex]\[ C = \frac{5}{9}(F - 32) \][/tex]
To solve for [tex]\( F \)[/tex], we need to rearrange the formula:
1. Multiply both sides by 9/5 to get rid of the fraction:
[tex]\[
\frac{9}{5} \cdot C = F - 32
\][/tex]
2. Add 32 to both sides to isolate [tex]\( F \)[/tex]:
[tex]\[
F = \frac{9}{5} \cdot C + 32
\][/tex]
So, the formula for converting Celsius to Fahrenheit is:
[tex]\[ F = \frac{9}{5}C + 32 \][/tex]
### Part b: Calculating the average temperature in Reykjavik, Iceland during the winter in degrees Fahrenheit
We are given that the average temperature in Reykjavik during the winter is 2 degrees Celsius ([tex]\( C = 2 \)[/tex]).
Using the formula derived in part (a):
[tex]\[ F = \frac{9}{5} \cdot 2 + 32 \][/tex]
Let's plug in the value and calculate:
1. Multiply [tex]\( \frac{9}{5} \)[/tex] by 2:
[tex]\[
\frac{9}{5} \cdot 2 = \frac{18}{5} = 3.6
\][/tex]
2. Add 32 to 3.6:
[tex]\[
F = 3.6 + 32 = 35.6
\][/tex]
So, the average temperature in Reykjavik, Iceland during the winter in degrees Fahrenheit is:
[tex]\[ 35.6^\circ F \][/tex]
### Part a: Solving for [tex]\( F \)[/tex]
We start with the formula for converting Celsius to Fahrenheit:
[tex]\[ C = \frac{5}{9}(F - 32) \][/tex]
To solve for [tex]\( F \)[/tex], we need to rearrange the formula:
1. Multiply both sides by 9/5 to get rid of the fraction:
[tex]\[
\frac{9}{5} \cdot C = F - 32
\][/tex]
2. Add 32 to both sides to isolate [tex]\( F \)[/tex]:
[tex]\[
F = \frac{9}{5} \cdot C + 32
\][/tex]
So, the formula for converting Celsius to Fahrenheit is:
[tex]\[ F = \frac{9}{5}C + 32 \][/tex]
### Part b: Calculating the average temperature in Reykjavik, Iceland during the winter in degrees Fahrenheit
We are given that the average temperature in Reykjavik during the winter is 2 degrees Celsius ([tex]\( C = 2 \)[/tex]).
Using the formula derived in part (a):
[tex]\[ F = \frac{9}{5} \cdot 2 + 32 \][/tex]
Let's plug in the value and calculate:
1. Multiply [tex]\( \frac{9}{5} \)[/tex] by 2:
[tex]\[
\frac{9}{5} \cdot 2 = \frac{18}{5} = 3.6
\][/tex]
2. Add 32 to 3.6:
[tex]\[
F = 3.6 + 32 = 35.6
\][/tex]
So, the average temperature in Reykjavik, Iceland during the winter in degrees Fahrenheit is:
[tex]\[ 35.6^\circ F \][/tex]
