Thank you for visiting If the temperature goes up 1 degree Celsius then it goes up 1 8 degrees Fahrenheit tex 0 circ tex Celsius equals tex 32 circ. This page is designed to guide you through key points and clear explanations related to the topic at hand. We aim to make your learning experience smooth, insightful, and informative. Dive in and discover the answers you're looking for!
Answer :
To convert a temperature from Celsius to Fahrenheit, you can use the function [tex]\( f(c) \)[/tex] which is based on the relationship between Celsius and Fahrenheit. The formula is:
[tex]\[ f(c) = c \times 1.8 + 32 \][/tex]
This formula takes a temperature in degrees Celsius, multiplies it by 1.8 (since an increase of 1 degree Celsius corresponds to an increase of 1.8 degrees Fahrenheit), and then adds 32 to adjust for the difference in the starting points of the two scales (0°C equals 32°F).
Now, to check if there's a temperature where the value is the same in both Celsius and Fahrenheit, we set up an equation:
Let [tex]\( c \)[/tex] be the temperature in degrees Celsius and degrees Fahrenheit. We want to solve for [tex]\( c \)[/tex] in the equation:
[tex]\[ c = c \times 1.8 + 32 \][/tex]
Rearrange this equation to isolate [tex]\( c \)[/tex]:
1. Subtract [tex]\( c \times 1.8 \)[/tex] from both sides:
[tex]\[ c - c \times 1.8 = 32 \][/tex]
2. Factor out [tex]\( c \)[/tex]:
[tex]\[ c \times (1 - 1.8) = 32 \][/tex]
3. Simplify the expression in parentheses:
[tex]\[ c \times (-0.8) = 32 \][/tex]
4. Solve for [tex]\( c \)[/tex]:
[tex]\[ c = \frac{32}{-0.8} \][/tex]
Dividing 32 by -0.8 gives:
[tex]\[ c = -40 \][/tex]
Thus, the temperature where Celsius and Fahrenheit are the same is [tex]\(-40\)[/tex] degrees.
[tex]\[ f(c) = c \times 1.8 + 32 \][/tex]
This formula takes a temperature in degrees Celsius, multiplies it by 1.8 (since an increase of 1 degree Celsius corresponds to an increase of 1.8 degrees Fahrenheit), and then adds 32 to adjust for the difference in the starting points of the two scales (0°C equals 32°F).
Now, to check if there's a temperature where the value is the same in both Celsius and Fahrenheit, we set up an equation:
Let [tex]\( c \)[/tex] be the temperature in degrees Celsius and degrees Fahrenheit. We want to solve for [tex]\( c \)[/tex] in the equation:
[tex]\[ c = c \times 1.8 + 32 \][/tex]
Rearrange this equation to isolate [tex]\( c \)[/tex]:
1. Subtract [tex]\( c \times 1.8 \)[/tex] from both sides:
[tex]\[ c - c \times 1.8 = 32 \][/tex]
2. Factor out [tex]\( c \)[/tex]:
[tex]\[ c \times (1 - 1.8) = 32 \][/tex]
3. Simplify the expression in parentheses:
[tex]\[ c \times (-0.8) = 32 \][/tex]
4. Solve for [tex]\( c \)[/tex]:
[tex]\[ c = \frac{32}{-0.8} \][/tex]
Dividing 32 by -0.8 gives:
[tex]\[ c = -40 \][/tex]
Thus, the temperature where Celsius and Fahrenheit are the same is [tex]\(-40\)[/tex] degrees.
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