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
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?
Important Questions from Cubes & Cube Roots
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?
If \(x=3-3^{1/3}-3^{2/3}\), then what is \(x(x-3)(x-6)\) equal to?
