Change each of the given temperature to the Fahrenheit and Reaumur scale : `30^@ C, 5^@ C and -20^@ C`.

Answer

To convert temperatures from Celsius to Fahrenheit and Reaumur scales, we will use the following formulas:

1. **Fahrenheit (°F)**:
\[ F = \frac{9}{5}C + 32 \]

2. **Reaumur (°Re)**:
\[ R = \frac{4}{5}C \]

Now, let's convert the given temperatures: \(30^\circ C\), \(5^\circ C\), and \(-20^\circ C\).

### Step 1: Convert \(30^\circ C\)

**Fahrenheit Conversion**:
\[ F = \frac{9}{5} \times 30 + 32 \]
\[ F = 54 + 32 = 86^\circ F \]

**Reaumur Conversion**:
\[ R = \frac{4}{5} \times 30 \]
\[ R = 24^\circ Re \]

### Step 2: Convert \(5^\circ C\)

**Fahrenheit Conversion**:
\[ F = \frac{9}{5} \times 5 + 32 \]
\[ F = 9 + 32 = 41^\circ F \]

**Reaumur Conversion**:
\[ R = \frac{4}{5} \times 5 \]
\[ R = 4^\circ Re \]

### Step 3: Convert \(-20^\circ C\)

**Fahrenheit Conversion**:
\[ F = \frac{9}{5} \times (-20) + 32 \]
\[ F = -36 + 32 = -4^\circ F \]

**Reaumur Conversion**:
\[ R = \frac{4}{5} \times (-20) \]
\[ R = -16^\circ Re \]

### Summary of Results:
- \(30^\circ C = 86^\circ F\) and \(24^\circ Re\)
- \(5^\circ C = 41^\circ F\) and \(4^\circ Re\)
- \(-20^\circ C = -4^\circ F\) and \(-16^\circ Re\)