Math Problem Statement
Solution
The problem in the image states that is directly proportional to the square root of , and asks you to complete the table.
We can express the relationship mathematically as: where is the constant of proportionality.
Step 1: Find
Using the values and from the table, we substitute these into the equation: Since , we find:
Step 2: Use to complete the table
Now that we know , we can use this to find the missing values for and the corresponding .
- When :
So the missing value for when is 54.
Thus, the completed table looks like this:
| | 1 | 36 |
| | 9 | 54 |
Would you like any further clarification on this solution? Here are five related questions you might find useful:
- What if were inversely proportional to the square root of ?
- How would the table change if were proportional to instead of ?
- Can you graph the relationship between and for this proportional relationship?
- What are other examples of directly proportional relationships in mathematics?
- How do you determine the constant of proportionality in any relationship?
Tip: Always ensure to substitute known values into the proportionality equation to find the constant before using it for other calculations.
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Math Problem Analysis
Mathematical Concepts
Direct Proportion
Square Roots
Formulas
b = k * sqrt(a)
Theorems
Direct Proportionality
Suitable Grade Level
Grades 8-10