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Answer :
To determine the temperature increase in degrees Fahrenheit (F) that corresponds to a temperature increase of 10 degrees Celsius (C), we can use the relationship between these two temperature scales. According to the given formula:
[tex]\[ F = 32 + 1.8 \times C \][/tex]
Since we are focusing on the increase in temperature, we are interested in how F changes when C increases by 10 degrees.
Let's denote the change in temperature by [tex]\(\Delta C\)[/tex] for Celsius and [tex]\(\Delta F\)[/tex] for Fahrenheit. Given:
[tex]\[ \Delta C = 10 \text{ degrees Celsius} \][/tex]
We substitute [tex]\(\Delta C\)[/tex] into the formula without the constant 32, because the constant represents the offset at the freezing point, not the change in temperature.
[tex]\[ \Delta F = 1.8 \times \Delta C \][/tex]
Now, substitute [tex]\(\Delta C = 10\)[/tex] degrees Celsius into the equation:
[tex]\[ \Delta F = 1.8 \times 10 \][/tex]
[tex]\[ \Delta F = 18 \text{ degrees Fahrenheit} \][/tex]
Thus, a temperature increase of 10 degrees Celsius corresponds to a temperature increase of 18 degrees Fahrenheit.
[tex]\[ F = 32 + 1.8 \times C \][/tex]
Since we are focusing on the increase in temperature, we are interested in how F changes when C increases by 10 degrees.
Let's denote the change in temperature by [tex]\(\Delta C\)[/tex] for Celsius and [tex]\(\Delta F\)[/tex] for Fahrenheit. Given:
[tex]\[ \Delta C = 10 \text{ degrees Celsius} \][/tex]
We substitute [tex]\(\Delta C\)[/tex] into the formula without the constant 32, because the constant represents the offset at the freezing point, not the change in temperature.
[tex]\[ \Delta F = 1.8 \times \Delta C \][/tex]
Now, substitute [tex]\(\Delta C = 10\)[/tex] degrees Celsius into the equation:
[tex]\[ \Delta F = 1.8 \times 10 \][/tex]
[tex]\[ \Delta F = 18 \text{ degrees Fahrenheit} \][/tex]
Thus, a temperature increase of 10 degrees Celsius corresponds to a temperature increase of 18 degrees Fahrenheit.
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