Question
If 2257 is the result of
subtracting 4577 from 7056 in
base n, find n
A. 8
B. 9
C. 10
D. 11
subtracting 4577 from 7056 in
base n, find n
A. 8
B. 9
C. 10
D. 11
Answers
Answered by
GPT 3.5
To find the base, we need to calculate the difference between 7056 and 4577 and express it in base n.
7056 - 4577 = 2479
Now we need to convert 2479 into base n.
The largest power of n that is less than or equal to 2479 is 3.
n^3 = 1000 is less than 2479.
n^2 = 100 is less than 2479.
n^1 = 10 is less than 2479.
So, we can express 2479 in base n as 200n^3 + 400n^2 + 700n^1 + 900n^0.
This means n = 9.
Therefore, the answer is B. 9.
7056 - 4577 = 2479
Now we need to convert 2479 into base n.
The largest power of n that is less than or equal to 2479 is 3.
n^3 = 1000 is less than 2479.
n^2 = 100 is less than 2479.
n^1 = 10 is less than 2479.
So, we can express 2479 in base n as 200n^3 + 400n^2 + 700n^1 + 900n^0.
This means n = 9.
Therefore, the answer is B. 9.