a. The moduli are coprime, so you can apply the Chinese remainder theorem directly. Let
- Taken mod 3, the last two terms vanish, and
so we need to multiply by the inverse of 2 modulo 3 to end up with a remainder of 1. Since 
, we multiply the first term by 2.
- Taken mod 4, the first and last terms vanish, and
. Multiply by the inverse of 3 modulo 4 (which is 3 because 
), then by 2 to ensure the proper remainder is left.
- Taken mod 5, the first two terms vanish, and
. Multiply by the inverse of 2 modulo 5 (3, since 
) and again by 3.
By the CRT, we have
i.e. any number 
(where 
is an integer) satisifes the system.
b. The moduli are not coprime, so we need to check for possible contradictions. If 
and 
, then we need to have 
. This basically amounts to checking that if , then we should also have 
.
The last congruence conflicts with the previous one modulo 3, so there is no solution to this system.
Answer:
Step-by-step explanation:
The circumference of a circle can be found by multiplying pi ( π = 3.14 ) by the diameter of the circle.
Answer:
Step-by-step explanation:
By geometric mean property:
Answer:
72
Step-by-step explanation:
just times 6 by 12 to get the answer
Answer: P = 25n + 35
Step-by-step explanation:
The perimeter of a rectangle is twice the sum of length and width.
P = 2(l +w)
P = 2((8.5n+9) + (4n +8.5))
P = 2(12.5n +17.5)
P = 25n + 35
