Number Pattern Recognition
The question presents a sequence where a number maps to another number based on a specific mathematical pattern.
- Given: $11 \rightarrow 1331$
- Given: $12 \rightarrow 1728$
- To find: $13 \rightarrow ?$
Identifying the Pattern
Let's analyze the relationship between the input number ($n$) and the output number.
- For the first pair: $11^3 = 11 \times 11 \times 11 = 1331$. This matches the given output.
- For the second pair: $12^3 = 12 \times 12 \times 12 = 1728$. This also matches the given output.
The pattern is confirmed to be cubing the input number: $n \rightarrow n^3$.
Calculating the Result
To find the number corresponding to 13, we apply the identified pattern:
Calculate $13^3$:
$13^3 = 13 \times 13 \times 13$ $13^3 = 169 \times 13$ $13^3 = 2197$Conclusion
Following the pattern $n \rightarrow n^3$, the number 13 maps to 2197.
Similar Questions
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What is the simplified value of \(\dfrac{(0.05)^3 + (0.005)^3}{(0.25)^3 + (0.025)^3}\)?
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Important Questions from Cubes & Cube Roots
If \(x=3-3^{1/3}-3^{2/3}\), then what is \(x(x-3)(x-6)\) equal to?
What is the simplified value of \(\dfrac{(0.25)^3 + (0.05)^3}{(0.5)^3 + (0.1)^3}\)?
What is the simplified value of \(\dfrac{(0.05)^3 + (0.005)^3}{(0.25)^3 + (0.025)^3}\)?
A gardener organizes plants into rows to create a square formation but discovers that 15 plants are not included. If the total number of plants is 3984, then what is the number of plants in each row?
