Answer :
To solve the problem of converting temperatures from degrees Fahrenheit to degrees Celsius using the provided formula, we will apply a straightforward step-by-step method:
The formula to convert from Fahrenheit ([tex]\(^{\circ}F\)[/tex]) to Celsius ([tex]\(^{\circ}C\)[/tex]) is:
[tex]\[ x^{\circ}C = \left(\left(10 \times y^{\circ}F\right) - 320\right) \div 18 \][/tex]
Let's solve part by part:
### a) Convert [tex]\(212^{\circ}F\)[/tex] to degrees Celsius:
1. Multiply: Start by multiplying the Fahrenheit temperature by 10.
[tex]\[ 10 \times 212 = 2120 \][/tex]
2. Subtract: Subtract 320 from the result.
[tex]\[ 2120 - 320 = 1800 \][/tex]
3. Divide: Divide the result by 18.
[tex]\[ 1800 \div 18 = 100.0 \][/tex]
Therefore, [tex]\(212^{\circ}F\)[/tex] is equivalent to [tex]\(100.0^{\circ}C\)[/tex].
### b) Convert [tex]\(0^{\circ}F\)[/tex] to degrees Celsius:
1. Multiply: Start by multiplying the Fahrenheit temperature by 10.
[tex]\[ 10 \times 0 = 0 \][/tex]
2. Subtract: Subtract 320 from the result.
[tex]\[ 0 - 320 = -320 \][/tex]
3. Divide: Divide the result by 18.
[tex]\[ -320 \div 18 = -17.77777777777778 \][/tex]
Therefore, [tex]\(0^{\circ}F\)[/tex] is equivalent to approximately [tex]\(-17.78^{\circ}C\)[/tex].
These calculations show how the conversion is done step-by-step for each given temperature, resulting in [tex]\(100.0^{\circ}C\)[/tex] for [tex]\(212^{\circ}F\)[/tex] and approximately [tex]\(-17.78^{\circ}C\)[/tex] for [tex]\(0^{\circ}F\)[/tex].
The formula to convert from Fahrenheit ([tex]\(^{\circ}F\)[/tex]) to Celsius ([tex]\(^{\circ}C\)[/tex]) is:
[tex]\[ x^{\circ}C = \left(\left(10 \times y^{\circ}F\right) - 320\right) \div 18 \][/tex]
Let's solve part by part:
### a) Convert [tex]\(212^{\circ}F\)[/tex] to degrees Celsius:
1. Multiply: Start by multiplying the Fahrenheit temperature by 10.
[tex]\[ 10 \times 212 = 2120 \][/tex]
2. Subtract: Subtract 320 from the result.
[tex]\[ 2120 - 320 = 1800 \][/tex]
3. Divide: Divide the result by 18.
[tex]\[ 1800 \div 18 = 100.0 \][/tex]
Therefore, [tex]\(212^{\circ}F\)[/tex] is equivalent to [tex]\(100.0^{\circ}C\)[/tex].
### b) Convert [tex]\(0^{\circ}F\)[/tex] to degrees Celsius:
1. Multiply: Start by multiplying the Fahrenheit temperature by 10.
[tex]\[ 10 \times 0 = 0 \][/tex]
2. Subtract: Subtract 320 from the result.
[tex]\[ 0 - 320 = -320 \][/tex]
3. Divide: Divide the result by 18.
[tex]\[ -320 \div 18 = -17.77777777777778 \][/tex]
Therefore, [tex]\(0^{\circ}F\)[/tex] is equivalent to approximately [tex]\(-17.78^{\circ}C\)[/tex].
These calculations show how the conversion is done step-by-step for each given temperature, resulting in [tex]\(100.0^{\circ}C\)[/tex] for [tex]\(212^{\circ}F\)[/tex] and approximately [tex]\(-17.78^{\circ}C\)[/tex] for [tex]\(0^{\circ}F\)[/tex].
