Understanding the Operator '@' Logic
The question presents a pattern where an unknown operator '@' is used. We need to determine the rule governing this operator based on the given examples and then apply it to find the value of 7 @ 3.
Deriving the Calculation Rule
Let's analyze the first equation: 9 @ 1 = 82.
- Consider the operands A=9 and B=1.
- Testing the hypothesis that the operation is $A^2 + B$:
- $9^2 + 1 = 81 + 1 = 82$. This matches the given result.
Let's verify this rule with the second equation: 6 @ 2 = 38.
- Here, A=6 and B=2.
- Applying the rule $A^2 + B$:
- $6^2 + 2 = 36 + 2 = 38$. This also matches the given result.
Therefore, the rule for the operator '@' is established as: $A \text{ @ } B = A^2 + B$.
Calculating 7 @ 3
Now, we apply the confirmed rule $A \text{ @ } B = A^2 + B$ to find the value of 7 @ 3.
- Here, A=7 and B=3.
- $7^2 + 3 = 49 + 3 = 52$.
The value of 7 @ 3 is 52.
