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Answer :
Sure, let's go through the steps to solve the problem in detail.
### Part a
We need to convert Fahrenheit temperatures of [tex]\(212^{\circ}\)[/tex] and [tex]\(98.6^{\circ}\)[/tex] to Celsius.
The formula to convert Fahrenheit [tex]\(F\)[/tex] to Celsius [tex]\(C\)[/tex] is:
[tex]\[ C = \frac{5}{9}(F - 32) \][/tex]
1. For [tex]\(212^{\circ}F\)[/tex]:
[tex]\[ C = \frac{5}{9}(212 - 32) \][/tex]
[tex]\[ C = \frac{5}{9}(180) \][/tex]
[tex]\[ C = 100.0^{\circ}C \][/tex]
2. For [tex]\(98.6^{\circ}F\)[/tex]:
[tex]\[ C = \frac{5}{9}(98.6 - 32) \][/tex]
[tex]\[ C = \frac{5}{9}(66.6) \][/tex]
[tex]\[ C = 37.0^{\circ}C \][/tex]
So, the Celsius temperatures corresponding to [tex]\(212^{\circ}F\)[/tex] and [tex]\(98.6^{\circ}F\)[/tex] are [tex]\(100.0^{\circ}C\)[/tex] and [tex]\(37.0^{\circ}C\)[/tex] respectively.
### Part b
Now, we need to solve the equation [tex]\( C = \frac{5}{9}(F - 32) \)[/tex] for [tex]\(F\)[/tex] to obtain a rule for converting Celsius temperatures to Fahrenheit temperatures.
Starting with:
[tex]\[ C = \frac{5}{9}(F - 32) \][/tex]
1. Multiply both sides by 9 to get rid of the fraction:
[tex]\[ 9C = 5(F - 32) \][/tex]
2. Distribute the 5 on the right side:
[tex]\[ 9C = 5F - 160 \][/tex]
3. Add 160 to both sides:
[tex]\[ 5F = 9C + 160 \][/tex]
4. Finally, divide both sides by 5 to solve for [tex]\(F\)[/tex]:
[tex]\[ F = \frac{9C + 160}{5} \][/tex]
So, the formula to convert Celsius temperatures to Fahrenheit is:
[tex]\[ F = \frac{9C + 160}{5} \][/tex]
### Part c
We need to convert Celsius temperatures of [tex]\(-40^{\circ}\)[/tex] and [tex]\(2000^{\circ}\)[/tex] to Fahrenheit.
Using the formula we derived:
[tex]\[ F = \frac{9C + 160}{5} \][/tex]
1. For [tex]\(-40^{\circ}C\)[/tex]:
[tex]\[ F = \frac{9(-40) + 160}{5} \][/tex]
[tex]\[ F = \frac{-360 + 160}{5} \][/tex]
[tex]\[ F = \frac{-200}{5} \][/tex]
[tex]\[ F = -40.0^{\circ}F \][/tex]
2. For [tex]\(2000^{\circ}C\)[/tex]:
[tex]\[ F = \frac{9(2000) + 160}{5} \][/tex]
[tex]\[ F = \frac{18000 + 160}{5} \][/tex]
[tex]\[ F = \frac{18160}{5} \][/tex]
[tex]\[ F = 3632.0^{\circ}F \][/tex]
So, the Fahrenheit temperatures corresponding to [tex]\(-40^{\circ}C\)[/tex] and [tex]\(2000^{\circ}C\)[/tex] are [tex]\(-40.0^{\circ}F\)[/tex] and [tex]\(3632.0^{\circ}F\)[/tex] respectively.
### Part a
We need to convert Fahrenheit temperatures of [tex]\(212^{\circ}\)[/tex] and [tex]\(98.6^{\circ}\)[/tex] to Celsius.
The formula to convert Fahrenheit [tex]\(F\)[/tex] to Celsius [tex]\(C\)[/tex] is:
[tex]\[ C = \frac{5}{9}(F - 32) \][/tex]
1. For [tex]\(212^{\circ}F\)[/tex]:
[tex]\[ C = \frac{5}{9}(212 - 32) \][/tex]
[tex]\[ C = \frac{5}{9}(180) \][/tex]
[tex]\[ C = 100.0^{\circ}C \][/tex]
2. For [tex]\(98.6^{\circ}F\)[/tex]:
[tex]\[ C = \frac{5}{9}(98.6 - 32) \][/tex]
[tex]\[ C = \frac{5}{9}(66.6) \][/tex]
[tex]\[ C = 37.0^{\circ}C \][/tex]
So, the Celsius temperatures corresponding to [tex]\(212^{\circ}F\)[/tex] and [tex]\(98.6^{\circ}F\)[/tex] are [tex]\(100.0^{\circ}C\)[/tex] and [tex]\(37.0^{\circ}C\)[/tex] respectively.
### Part b
Now, we need to solve the equation [tex]\( C = \frac{5}{9}(F - 32) \)[/tex] for [tex]\(F\)[/tex] to obtain a rule for converting Celsius temperatures to Fahrenheit temperatures.
Starting with:
[tex]\[ C = \frac{5}{9}(F - 32) \][/tex]
1. Multiply both sides by 9 to get rid of the fraction:
[tex]\[ 9C = 5(F - 32) \][/tex]
2. Distribute the 5 on the right side:
[tex]\[ 9C = 5F - 160 \][/tex]
3. Add 160 to both sides:
[tex]\[ 5F = 9C + 160 \][/tex]
4. Finally, divide both sides by 5 to solve for [tex]\(F\)[/tex]:
[tex]\[ F = \frac{9C + 160}{5} \][/tex]
So, the formula to convert Celsius temperatures to Fahrenheit is:
[tex]\[ F = \frac{9C + 160}{5} \][/tex]
### Part c
We need to convert Celsius temperatures of [tex]\(-40^{\circ}\)[/tex] and [tex]\(2000^{\circ}\)[/tex] to Fahrenheit.
Using the formula we derived:
[tex]\[ F = \frac{9C + 160}{5} \][/tex]
1. For [tex]\(-40^{\circ}C\)[/tex]:
[tex]\[ F = \frac{9(-40) + 160}{5} \][/tex]
[tex]\[ F = \frac{-360 + 160}{5} \][/tex]
[tex]\[ F = \frac{-200}{5} \][/tex]
[tex]\[ F = -40.0^{\circ}F \][/tex]
2. For [tex]\(2000^{\circ}C\)[/tex]:
[tex]\[ F = \frac{9(2000) + 160}{5} \][/tex]
[tex]\[ F = \frac{18000 + 160}{5} \][/tex]
[tex]\[ F = \frac{18160}{5} \][/tex]
[tex]\[ F = 3632.0^{\circ}F \][/tex]
So, the Fahrenheit temperatures corresponding to [tex]\(-40^{\circ}C\)[/tex] and [tex]\(2000^{\circ}C\)[/tex] are [tex]\(-40.0^{\circ}F\)[/tex] and [tex]\(3632.0^{\circ}F\)[/tex] respectively.
Thank you for reading the article The Ruler Postulate suggests that there are many ways to assign coordinates to a line The Fahrenheit and Celsius temperature scales on a thermometer indicate. We hope the information provided is useful and helps you understand this topic better. Feel free to explore more helpful content on our website!
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Rewritten by : Jeany
