Math Problem Statement
Select all of the equations below in which t is inversely proportional to w.
Solution
To determine which equations show that is inversely proportional to , we need to understand what it means for two variables to be inversely proportional. Inverse proportionality between and means that , where is a constant. This can also be written as .
Let’s examine each equation:
- : This shows a direct proportionality, not an inverse one.
- : This is a linear equation with added to a constant, not inverse proportionality.
- : This is still direct proportionality because is proportional to , even though it's divided by 3.
- : This shows that is inversely proportional to , as it matches the form .
- : This is another linear equation and does not represent inverse proportionality.
Answer: The equation that shows is inversely proportional to is:
- .
Would you like more details or have any questions?
Here are some follow-up questions to consider:
- What is the difference between direct and inverse proportionality?
- Can you provide another example of an equation that shows inverse proportionality?
- How can we identify inverse proportionality from an equation?
- What are real-life examples of inverse proportionality?
- What happens to as increases in an inverse proportional relationship?
Tip: For two quantities to be inversely proportional, their product should always be a constant.
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Math Problem Analysis
Mathematical Concepts
Inverse Proportion
Direct Proportion
Algebra
Formulas
Inverse proportion: t = k / w, where k is a constant
Theorems
Inverse Proportion Theorem
Suitable Grade Level
Grades 7-9