First of all, the modular inverse of n modulo k can only exist if GCD(n, k) = 1.
We have
130 = 2 • 5 • 13
231 = 3 • 7 • 11
so n must be free of 2, 3, 5, 7, 11, and 13, which are the first six primes. It follows that n = 17 must the least integer that satisfies the conditions.
To verify the claim, we try to solve the system of congruences
Use the Euclidean algorithm to express 1 as a linear combination of 130 and 17:
130 = 7 • 17 + 11
17 = 1 • 11 + 6
11 = 1 • 6 + 5
6 = 1 • 5 + 1
⇒ 1 = 23 • 17 - 3 • 130
Then
23 • 17 - 3 • 130 ≡ 23 • 17 ≡ 1 (mod 130)
so that x = 23.
Repeat for 231 and 17:
231 = 13 • 17 + 10
17 = 1 • 10 + 7
10 = 1 • 7 + 3
7 = 2 • 3 + 1
⇒ 1 = 68 • 17 - 5 • 231
Then
68 • 17 - 5 • 231 ≡ = 68 • 17 ≡ 1 (mod 231)
so that y = 68.
Answer:
HI SORRY IM, SPEAK SPANISH... FROMN COLOMBIA
Step-by-step explanation:
HOLI MK NO SE HABLAR INGLES CHAU
Hello!
You have to find how many miles is 1 inch on the map
We can do this by doing 40 / 2 1/2 = 16
16 miles is equal to one inch
So we multiply this by 1 1/2
16 * 1 1/2 = 24
The answer is 24 miles
Hope this helps!
Answer:
The flag pole is 9 feet tall.
Step-by-step explanation:
It is asking you to slice off 40% of the bounce height in each subsequent bounce.
So you start with full height 1, that's n = 0 bounces. Then after n = 1 bounce the new height is .6. After the second bounce, n = 2, the height becomes .6 X .6 = .36. And after n = 3, we have .6 X .6 X .6 = .216
So by induction we see that h(n = 5) = .6^n = .6^5 = 0.07776 = .078 of its original height or H = .078*200 = 15.6 ft. after five bounces. ANS. 16.0 if rounded to the nearest tenth
:)
