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Answer :
Sure! Let's go through each part of the temperature conversion:
### a. Convert 84°F to Celsius
To convert from Fahrenheit to Celsius, we use the formula:
[tex]\[ C = \frac{5}{9}(F - 32) \][/tex]
For [tex]\( 84^\circ F \)[/tex]:
[tex]\[ C = \frac{5}{9}(84 - 32) \][/tex]
[tex]\[ C = \frac{5}{9}(52) \][/tex]
[tex]\[ C = \frac{5 \times 52}{9} \][/tex]
[tex]\[ C = \frac{260}{9} \][/tex]
[tex]\[ C \approx 28.9 \][/tex]
So, [tex]\( 84^{\circ} F \)[/tex] is approximately [tex]\( 28.9^{\circ} C \)[/tex].
### b. Convert -10°F to Celsius
Using the same formula:
[tex]\[ C = \frac{5}{9}(F - 32) \][/tex]
For [tex]\(-10^\circ F\)[/tex]:
[tex]\[ C = \frac{5}{9}(-10 - 32) \][/tex]
[tex]\[ C = \frac{5}{9}(-42) \][/tex]
[tex]\[ C = \frac{5 \times -42}{9} \][/tex]
[tex]\[ C = \frac{-210}{9} \][/tex]
[tex]\[ C \approx -23.3 \][/tex]
So, [tex]\(-10^{\circ} F\)[/tex] is approximately [tex]\(-23.3^{\circ} C\)[/tex].
### c. Convert 45°C to Fahrenheit
To convert from Celsius to Fahrenheit, use the reverse formula:
[tex]\[ F = \frac{9}{5}C + 32 \][/tex]
For [tex]\( 45^\circ C \)[/tex]:
[tex]\[ F = \frac{9}{5} \times 45 + 32 \][/tex]
[tex]\[ F = 9 \times 9 + 32 \][/tex]
[tex]\[ F = 81 + 32 \][/tex]
[tex]\[ F = 113.0 \][/tex]
So, [tex]\( 45^{\circ} C \)[/tex] is [tex]\( 113.0^{\circ} F \)[/tex].
These are the temperature conversions for each given case.
### a. Convert 84°F to Celsius
To convert from Fahrenheit to Celsius, we use the formula:
[tex]\[ C = \frac{5}{9}(F - 32) \][/tex]
For [tex]\( 84^\circ F \)[/tex]:
[tex]\[ C = \frac{5}{9}(84 - 32) \][/tex]
[tex]\[ C = \frac{5}{9}(52) \][/tex]
[tex]\[ C = \frac{5 \times 52}{9} \][/tex]
[tex]\[ C = \frac{260}{9} \][/tex]
[tex]\[ C \approx 28.9 \][/tex]
So, [tex]\( 84^{\circ} F \)[/tex] is approximately [tex]\( 28.9^{\circ} C \)[/tex].
### b. Convert -10°F to Celsius
Using the same formula:
[tex]\[ C = \frac{5}{9}(F - 32) \][/tex]
For [tex]\(-10^\circ F\)[/tex]:
[tex]\[ C = \frac{5}{9}(-10 - 32) \][/tex]
[tex]\[ C = \frac{5}{9}(-42) \][/tex]
[tex]\[ C = \frac{5 \times -42}{9} \][/tex]
[tex]\[ C = \frac{-210}{9} \][/tex]
[tex]\[ C \approx -23.3 \][/tex]
So, [tex]\(-10^{\circ} F\)[/tex] is approximately [tex]\(-23.3^{\circ} C\)[/tex].
### c. Convert 45°C to Fahrenheit
To convert from Celsius to Fahrenheit, use the reverse formula:
[tex]\[ F = \frac{9}{5}C + 32 \][/tex]
For [tex]\( 45^\circ C \)[/tex]:
[tex]\[ F = \frac{9}{5} \times 45 + 32 \][/tex]
[tex]\[ F = 9 \times 9 + 32 \][/tex]
[tex]\[ F = 81 + 32 \][/tex]
[tex]\[ F = 113.0 \][/tex]
So, [tex]\( 45^{\circ} C \)[/tex] is [tex]\( 113.0^{\circ} F \)[/tex].
These are the temperature conversions for each given case.
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