Math Problem Statement
Solution
To solve this problem, let's go through the steps.
Step 1: Set up the relationship
Since is inversely proportional to , we can express this as: where is a constant.
Step 2: Find the constant
We know that when , . Substitute these values into the equation to find : Multiply both sides by 16:
Step 3: Rewrite the equation with the constant
Now that we know , the equation becomes:
Step 4: Find when
Substitute into the equation: Calculate : So the equation becomes: Dividing by is the same as multiplying by 4:
Final Answer
Would you like a further breakdown of these steps, or do you have any questions?
Here are five related questions that might interest you:
- How does inverse proportionality differ from direct proportionality?
- What happens to if is doubled in this inverse relationship?
- How can we interpret inverse proportionality graphically?
- How would the relationship change if were proportional to instead of ?
- Can this approach be used for other powers of , such as ?
Tip: Remember, when dealing with inverse proportionality, as increases, decreases, and vice versa.
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Math Problem Analysis
Mathematical Concepts
Inverse Proportion
Exponents
Algebra
Formulas
y = k / x^2
Theorems
-
Suitable Grade Level
Grades 8-10
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