Let's fill out the given table with the equivalent temperature scales.
We have some known values and need to determine the missing ones.
### 1. Filling out the first row:
- Given Value: Celsius (°C) = 89
- Needed Values: Fahrenheit (°F) and Kelvin (K)
#### Converting Celsius to Fahrenheit:
The formula to convert Celsius to Fahrenheit is:
[tex]\[ °F = (°C \times \frac{9}{5}) + 32 \][/tex]
So for 89°C:
[tex]\[ °F = (89 \times \frac{9}{5}) + 32 \][/tex]
[tex]\[ °F = (89 \times 1.8) + 32 \][/tex]
[tex]\[ °F = 160.2 + 32 \][/tex]
[tex]\[ °F = 192.2 \][/tex]
#### Converting Celsius to Kelvin:
The formula to convert Celsius to Kelvin is:
[tex]\[ K = °C + 273.15 \][/tex]
So for 89°C:
[tex]\[ K = 89 + 273.15 \][/tex]
[tex]\[ K = 362.15 \][/tex]
So the filled out first row is:
[tex]\[ | 89 | 192.2 | 362.15 | \][/tex]
### 2. Filling out the second row:
- Needed Values: Celsius (°C) for given Fahrenheit (°F) of 56, and Kelvin (K) of 405
#### Converting Fahrenheit to Celsius:
The formula to convert Fahrenheit to Celsius is:
[tex]\[ °C = \frac{(°F - 32) \times 5}{9} \][/tex]
So for 56°F:
[tex]\[ °C = \frac{(56 - 32) \times 5}{9} \][/tex]
[tex]\[ °C = \frac{24 \times 5}{9} \][/tex]
[tex]\[ °C = \frac{120}{9} \][/tex]
[tex]\[ °C = 13.333 \approx 13.33 \][/tex]
#### Converting Kelvin to Celsius:
The formula to convert Kelvin to Celsius is:
[tex]\[ °C = K - 273.15 \][/tex]
So for 405 K:
[tex]\[ °C = 405 - 273.15 \][/tex]
[tex]\[ °C = 131.85 \][/tex]
So the filled out second row is:
[tex]\[ | 13.33 | 56 | 405 | \][/tex]
### Filled Table:
[tex]\[
\begin{tabular}{|c|c|c|}
\hline
{}^0 C & {}^0 F & K \\
\hline
89 & 192.2 & 362.15 \\
\hline
13.33 & 56 & 405 \\
\hline
\end{tabular}
\][/tex]
