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.
Step-by-step explanation:
present temprature outside=10 degree
temp drops every hour= 5 dgree
let number of hours=h
10 9 8 7 6 5 4 3 2 1 0 hours
--l----l----l----l-----l----l-----l-----l-----l----l----l----l----l-----------
-40-35 -30 -25 -20-15 -10 -5 0 5 10 degrees
it will take 10 hours
for the temperature below -40 degree
h=10
Answer:
Step-by-step explanation:
Did you find the answer
Answer:
one third or 0.333333...
Step-by-step explanation:
a rational number is a number that can be written as a ratio between two numbers. they an be repeating like 1/3 or terminating like 1.36.
Answer:
The change in volume is estimated to be 17.20 
Step-by-step explanation:
The linearization or linear approximation of a function 
is given by:
where 
is the total differential of the function evaluated in the given point.
For the given function, the linearization is:
Taking 
inches and 
inches and evaluating the partial derivatives we obtain:
substituting the values and taking 
and 
inches we have:
Therefore the change in volume is estimated to be 17.20
