Math Problem Statement
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Part 1
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 45.67 degrees Upper C−45.67°C
and a boiling point of
310.21 degrees Upper C310.21°C.
What is the range of temperatures in degrees Fahrenheit for which this substance is not in a liquid state? (Hint:
Upper C equals five ninths left parenthesis Upper F minus 32 right parenthesisC=59(F−32))
Express the range as an inequality.
Question content area bottom
Part 1
Let x represent the temperature in degrees Fahrenheit. What is the range of temperatures for which this substance is not in a liquid state?
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Solution
The problem asks for the range of temperatures in degrees Fahrenheit for which the substance is not in a liquid state. The liquid state occurs when the temperature is between the melting point and the boiling point, so we need to find the temperatures outside this range.
Step 1: Convert the melting point from Celsius to Fahrenheit
The formula for converting Celsius to Fahrenheit is given as:
Solving for (Fahrenheit), we get:
Now, apply this formula to the melting point:
So, the melting point in Fahrenheit is approximately .
Step 2: Convert the boiling point from Celsius to Fahrenheit
Now, apply the same formula to the boiling point:
So, the boiling point in Fahrenheit is approximately .
Step 3: Determine the range for which the substance is not in a liquid state
The substance is not in a liquid state when the temperature is below the melting point or above the boiling point. Therefore, the range of temperatures where the substance is not in a liquid state is:
Thus, the inequality representing the range of temperatures in Fahrenheit for which the substance is not in a liquid state is:
Would you like more details or further clarification?
5 Related Questions:
- How do we convert temperatures from Fahrenheit to Celsius?
- What is the significance of the melting and boiling points in state changes of matter?
- Can a substance exist in both solid and liquid states at the melting point?
- How does pressure affect the melting and boiling points of substances?
- What are common substances with unusually high or low melting/boiling points?
Tip:
Always double-check temperature conversions, especially in scientific contexts, to avoid small errors impacting the final result.
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Math Problem Analysis
Mathematical Concepts
Temperature Conversion
Inequalities
Algebra
Formulas
C = (5/9)(F - 32)
F = (9/5)C + 32
Theorems
-
Suitable Grade Level
Grades 9-11
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