Answer :
- Converts 10°C to Fahrenheit: $F = \frac{9}{5}(10) + 32 = 50$.
- Converts 87°F to Celsius: $C = \frac{5}{9}(87 - 32) \approx 30.6$.
- Converts -5°C to Fahrenheit: $F = \frac{9}{5}(-5) + 32 = 23$.
- Converts 10°F to Celsius: $C = \frac{5}{9}(10 - 32) \approx -12.2$. The final answers are $\boxed{50, 30.6, 23, -12.2}$.
### Explanation
1. Understanding the Problem
We are given a table with Celsius and Fahrenheit temperatures, and we need to fill in the missing values using the conversion formulas. The formulas are:$$F = \frac{9}{5}C + 32$$and$$C = \frac{5}{9}(F - 32)$$where $F$ is the temperature in Fahrenheit and $C$ is the temperature in Celsius.
2. Converting Celsius to Fahrenheit (10°C)
First, we need to convert 10 degrees Celsius to Fahrenheit. Using the formula $F = \frac{9}{5}C + 32$, we have$$F = \frac{9}{5}(10) + 32 = 18 + 32 = 50$$So, 10 degrees Celsius is equal to 50 degrees Fahrenheit.
3. Converting Fahrenheit to Celsius (87°F)
Next, we need to convert 87 degrees Fahrenheit to Celsius. Using the formula $C = \frac{5}{9}(F - 32)$, we have$$C = \frac{5}{9}(87 - 32) = \frac{5}{9}(55) = \frac{275}{9} \approx 30.6$$So, 87 degrees Fahrenheit is approximately equal to 30.6 degrees Celsius.
4. Converting Celsius to Fahrenheit (-5°C)
Now, we need to convert -5 degrees Celsius to Fahrenheit. Using the formula $F = \frac{9}{5}C + 32$, we have$$F = \frac{9}{5}(-5) + 32 = -9 + 32 = 23$$So, -5 degrees Celsius is equal to 23 degrees Fahrenheit.
5. Converting Fahrenheit to Celsius (10°F)
Finally, we need to convert 10 degrees Fahrenheit to Celsius. Using the formula $C = \frac{5}{9}(F - 32)$, we have$$C = \frac{5}{9}(10 - 32) = \frac{5}{9}(-22) = -\frac{110}{9} \approx -12.2$$So, 10 degrees Fahrenheit is approximately equal to -12.2 degrees Celsius.
6. Final Answer
Therefore, the missing values in the table are: 50, 30.6, 23, and -12.2.
### Examples
Temperature conversion is used in many real-life situations, such as cooking, weather forecasting, and setting thermostats. For example, when following a recipe from a different country, you might need to convert the oven temperature from Celsius to Fahrenheit. Similarly, understanding temperature conversions helps you interpret weather reports and dress appropriately for the conditions. In scientific experiments, accurate temperature measurements and conversions are crucial for data analysis and reproducibility.
- Converts 87°F to Celsius: $C = \frac{5}{9}(87 - 32) \approx 30.6$.
- Converts -5°C to Fahrenheit: $F = \frac{9}{5}(-5) + 32 = 23$.
- Converts 10°F to Celsius: $C = \frac{5}{9}(10 - 32) \approx -12.2$. The final answers are $\boxed{50, 30.6, 23, -12.2}$.
### Explanation
1. Understanding the Problem
We are given a table with Celsius and Fahrenheit temperatures, and we need to fill in the missing values using the conversion formulas. The formulas are:$$F = \frac{9}{5}C + 32$$and$$C = \frac{5}{9}(F - 32)$$where $F$ is the temperature in Fahrenheit and $C$ is the temperature in Celsius.
2. Converting Celsius to Fahrenheit (10°C)
First, we need to convert 10 degrees Celsius to Fahrenheit. Using the formula $F = \frac{9}{5}C + 32$, we have$$F = \frac{9}{5}(10) + 32 = 18 + 32 = 50$$So, 10 degrees Celsius is equal to 50 degrees Fahrenheit.
3. Converting Fahrenheit to Celsius (87°F)
Next, we need to convert 87 degrees Fahrenheit to Celsius. Using the formula $C = \frac{5}{9}(F - 32)$, we have$$C = \frac{5}{9}(87 - 32) = \frac{5}{9}(55) = \frac{275}{9} \approx 30.6$$So, 87 degrees Fahrenheit is approximately equal to 30.6 degrees Celsius.
4. Converting Celsius to Fahrenheit (-5°C)
Now, we need to convert -5 degrees Celsius to Fahrenheit. Using the formula $F = \frac{9}{5}C + 32$, we have$$F = \frac{9}{5}(-5) + 32 = -9 + 32 = 23$$So, -5 degrees Celsius is equal to 23 degrees Fahrenheit.
5. Converting Fahrenheit to Celsius (10°F)
Finally, we need to convert 10 degrees Fahrenheit to Celsius. Using the formula $C = \frac{5}{9}(F - 32)$, we have$$C = \frac{5}{9}(10 - 32) = \frac{5}{9}(-22) = -\frac{110}{9} \approx -12.2$$So, 10 degrees Fahrenheit is approximately equal to -12.2 degrees Celsius.
6. Final Answer
Therefore, the missing values in the table are: 50, 30.6, 23, and -12.2.
### Examples
Temperature conversion is used in many real-life situations, such as cooking, weather forecasting, and setting thermostats. For example, when following a recipe from a different country, you might need to convert the oven temperature from Celsius to Fahrenheit. Similarly, understanding temperature conversions helps you interpret weather reports and dress appropriately for the conditions. In scientific experiments, accurate temperature measurements and conversions are crucial for data analysis and reproducibility.
