Water frezes at `0^(@)C` and boils at `100^(@)C`. Write an inequality to show the range of temperature (t) for which water is a liquid.

Options

A. `tlt0^(@)C`
B. `0^(@)Cle tle 100^(@)C`
C. `tgt100^(@)C`
D. `0^(@)Clt t lt100^(@)C`

Answer

To determine the range of temperature (t) for which water is a liquid, we need to consider the freezing and boiling points of water.

1. **Identify the freezing and boiling points of water:**
- Water freezes at `0°C`.
- Water boils at `100°C`.

2. **Set up the inequality:**
- For water to be in a liquid state, the temperature must be greater than the freezing point and less than the boiling point.
- This can be expressed as:
\[ 0 < t < 100 \]

3. **Write the inequality in standard notation:**
- The inequality can be written as:
\[ t > 0 \quad \text{and} \quad t < 100 \]

4. **Combine the inequalities:**
- We can combine the two inequalities into a single compound inequality:
\[ 0 < t < 100 \]

Thus, the final inequality representing the range of temperature for which water is a liquid is:
\[ 0 < t < 100 \]