To convert temperatures from Celsius to Fahrenheit, we use the formula:
[tex]\[ F = \left( \frac{9}{5} \times C \right) + 32 \][/tex]
where [tex]\( F \)[/tex] is the temperature in Fahrenheit and [tex]\( C \)[/tex] is the temperature in Celsius.
Let's apply this formula step-by-step to the given Celsius temperatures: [tex]\(-40^{\circ}\)[/tex] and [tex]\(-2000^{\circ}\)[/tex].
### Step-by-Step Solution:
1. For [tex]\( -40^{\circ} \text{C} \)[/tex]:
Substitute [tex]\( C = -40 \)[/tex] into the formula:
[tex]\[
F = \left( \frac{9}{5} \times -40 \right) + 32
\][/tex]
Calculate the multiplication part first:
[tex]\[
\frac{9}{5} \times -40 = -72
\][/tex]
Then, add 32 to the result:
[tex]\[
F = -72 + 32 = -40
\][/tex]
So, the Fahrenheit temperature corresponding to [tex]\(-40^{\circ} \text{C} \)[/tex] is [tex]\(-40^{\circ} \text{F}\)[/tex].
2. For [tex]\( -2000^{\circ} \text{C} \)[/tex]:
Substitute [tex]\( C = -2000 \)[/tex] into the formula:
[tex]\[
F = \left( \frac{9}{5} \times -2000 \right) + 32
\][/tex]
Calculate the multiplication part first:
[tex]\[
\frac{9}{5} \times -2000 = -3600
\][/tex]
Then, add 32 to the result:
[tex]\[
F = -3600 + 32 = -3568
\][/tex]
So, the Fahrenheit temperature corresponding to [tex]\(-2000^{\circ} \text{C} \)[/tex] is [tex]\(-3568^{\circ} \text{F}\)[/tex].
### Summary of Results:
- The Fahrenheit temperature for [tex]\(-40^{\circ} \text{C} \)[/tex] is [tex]\(-40^{\circ} \text{F}\)[/tex].
- The Fahrenheit temperature for [tex]\(-2000^{\circ} \text{C} \)[/tex] is [tex]\(-3568^{\circ} \text{F}\)[/tex].
