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Answer :
Certainly! Let's break down the problem step-by-step.
First, let's identify and correct the provided function [tex]\( C(F) = \frac{3}{3} p - 120 \)[/tex].
It seems like there are some typos or errors. Let's assume the correct function for converting Fahrenheit to Celsius is [tex]\( C(F) = (F - 32) \times \frac{5}{9} \)[/tex].
Let's work with this standard conversion formula:
[tex]\[ C = (F - 32) \times \frac{5}{9} \][/tex]
Given:
- [tex]\( F \)[/tex] represents the temperature in degrees Fahrenheit.
- We are given [tex]\( F = 100 \)[/tex] degrees Fahrenheit.
To convert 100 degrees Fahrenheit to Celsius:
[tex]\[ C = (100 - 32) \times \frac{5}{9} \][/tex]
Step-by-step solution:
1. Subtract 32 from 100:
[tex]\[ 100 - 32 = 68 \][/tex]
2. Multiply the result by [tex]\(\frac{5}{9}\)[/tex]:
[tex]\[ 68 \times \frac{5}{9} \approx 37.77777777777778 \][/tex]
So, 100 degrees Fahrenheit is approximately [tex]\( 37.77777777777778 \)[/tex] degrees Celsius.
Next, for verifying purposes, let's convert [tex]\( 37.77777777777778 \)[/tex] degrees Celsius back to Fahrenheit using the formula:
[tex]\[ F = (C \times \frac{9}{5}) + 32 \][/tex]
Given:
- [tex]\( C = 37.77777777777778 \)[/tex] degrees Celsius.
Step-by-step solution:
1. Multiply [tex]\( 37.77777777777778 \)[/tex] by [tex]\(\frac{9}{5}\)[/tex]:
[tex]\[ 37.77777777777778 \times \frac{9}{5} = 68 \times 1.8 = 100 \][/tex]
2. Add 32:
[tex]\[ 100 + 32 = 100 \][/tex]
So, [tex]\( 37.77777777777778 \)[/tex] degrees Celsius is [tex]\( 100 \)[/tex] degrees Fahrenheit.
Summarizing, the conversions are:
[tex]\[ \text{100°F is approximately 37.77777777777778°C} \][/tex]
[tex]\[ \text{37.77777777777778°C is exactly 100°F} \][/tex]
Thus, the answer is:
- The temperature of 100 degrees Fahrenheit converted to Celsius is approximately [tex]\( 37.77777777777778 \)[/tex] degrees Celsius.
- The temperature of [tex]\( 37.77777777777778 \)[/tex] degrees Celsius converted to Fahrenheit is exactly [tex]\(100 \)[/tex] degrees Fahrenheit.
First, let's identify and correct the provided function [tex]\( C(F) = \frac{3}{3} p - 120 \)[/tex].
It seems like there are some typos or errors. Let's assume the correct function for converting Fahrenheit to Celsius is [tex]\( C(F) = (F - 32) \times \frac{5}{9} \)[/tex].
Let's work with this standard conversion formula:
[tex]\[ C = (F - 32) \times \frac{5}{9} \][/tex]
Given:
- [tex]\( F \)[/tex] represents the temperature in degrees Fahrenheit.
- We are given [tex]\( F = 100 \)[/tex] degrees Fahrenheit.
To convert 100 degrees Fahrenheit to Celsius:
[tex]\[ C = (100 - 32) \times \frac{5}{9} \][/tex]
Step-by-step solution:
1. Subtract 32 from 100:
[tex]\[ 100 - 32 = 68 \][/tex]
2. Multiply the result by [tex]\(\frac{5}{9}\)[/tex]:
[tex]\[ 68 \times \frac{5}{9} \approx 37.77777777777778 \][/tex]
So, 100 degrees Fahrenheit is approximately [tex]\( 37.77777777777778 \)[/tex] degrees Celsius.
Next, for verifying purposes, let's convert [tex]\( 37.77777777777778 \)[/tex] degrees Celsius back to Fahrenheit using the formula:
[tex]\[ F = (C \times \frac{9}{5}) + 32 \][/tex]
Given:
- [tex]\( C = 37.77777777777778 \)[/tex] degrees Celsius.
Step-by-step solution:
1. Multiply [tex]\( 37.77777777777778 \)[/tex] by [tex]\(\frac{9}{5}\)[/tex]:
[tex]\[ 37.77777777777778 \times \frac{9}{5} = 68 \times 1.8 = 100 \][/tex]
2. Add 32:
[tex]\[ 100 + 32 = 100 \][/tex]
So, [tex]\( 37.77777777777778 \)[/tex] degrees Celsius is [tex]\( 100 \)[/tex] degrees Fahrenheit.
Summarizing, the conversions are:
[tex]\[ \text{100°F is approximately 37.77777777777778°C} \][/tex]
[tex]\[ \text{37.77777777777778°C is exactly 100°F} \][/tex]
Thus, the answer is:
- The temperature of 100 degrees Fahrenheit converted to Celsius is approximately [tex]\( 37.77777777777778 \)[/tex] degrees Celsius.
- The temperature of [tex]\( 37.77777777777778 \)[/tex] degrees Celsius converted to Fahrenheit is exactly [tex]\(100 \)[/tex] degrees Fahrenheit.
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