Matter is in a liquid state when its temperature is between its melting point and its boiling point. Suppose that some substance has a melting point of negative 46.81 degrees and a boiling point of 357.63 degrees . What is the range of temperatures in degrees Fahrenheit for which this substance is not in a liquid state? Express the range as an inequality and in interval notation.
-46.81 <= T <= 357.63
which interval is that?
To solve this problem, we need to convert the temperatures given from degrees Celsius to degrees Fahrenheit.
To convert from degrees Celsius to degrees Fahrenheit, we use the formula:
°F = (°C * 9/5) + 32
Let's start by converting the melting point from degrees Celsius to Fahrenheit:
Melting point (°F) = (-46.81 * 9/5) + 32 = -52.26 + 32 = -20.26 °F
Next, let's convert the boiling point from degrees Celsius to Fahrenheit:
Boiling point (°F) = (357.63 * 9/5) + 32 = 643.73 + 32 = 675.73 °F
Now we have the melting point in Fahrenheit as -20.26 °F and the boiling point in Fahrenheit as 675.73 °F.
The substance is not in a liquid state when the temperature is either below the melting point or above the boiling point.
Inequality notation:
Temperature (°F) < -20.26 or Temperature (°F) > 675.73
Interval notation:
(-∞, -20.26) U (675.73, ∞)
Therefore, the range of temperatures in degrees Fahrenheit for which this substance is not in a liquid state is (-∞, -20.26) U (675.73, ∞).