What Fahrenheit temperatures correspond to Celsius temperatures of [tex]-40^{\circ}[/tex] and [tex]-2000^{\circ}[/tex]?



Answer :

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].