(a) Suppose we let
Modulo 7, we're left with
, but we want a remainder of 2, so multiply 4 by 7 to assure that that remainder vanishes. So now
and
, but modulo 11, we have
. But we want the remainder to be 4, so multiply the first term by 11 to guarantee this. So we write
but now, we get a remainder of 1 modulo 7 and 6 modulo 11. To fix the first case, multiply the first term by 2. For the second case, first find the inverse of 6 modulo 11. We have
, and
, so the inverse is 2. Multiply the second term by 2, so that the second term's remainder modulo 11 becomes 1. Then multiply by 4, so that now
We have
(b) This is done similarly. Modulo 3, we want a remainder of 2, so we can start with
Then taken modulo 4, we need to multiply the first term by 2 and the third term by 4 to ensure the remainder becomes 3. The second term can be left alone.
Now taken modulo 5, we can multiply the first two terms by 5 and the third term by the inverse of
. We have
, so we multiply by 3.
Now
which means the smallest positive solution for the system would be
.
Answer:
y+6=-1/2(x-3)
Step-by-step explanation:
Point slope form: y-y1=m(x-x1)
Given that:
m=-1/2 and point (3, -6), you just add these numbers into the equation, and this gives:
y+6=-1/2(x-3)
Hope this helped!
Have a nice day!
The net force acting on the crate is the sum of all the forces acting in the different directions on the crate, which is 176 N to the left.
<h3>What is net force?</h3>
The net force is defined as the sum of all the forces acting on an object.
From the figure given that,
Upward force = 440 N
Downward force = - 440 N
Rightward force = 176 N
Leftward Force = - 352 N
The net vertical force acting on the crate = Upward force + Downward force
= 440 N + (-440 N)
= 0 N
The net horizontal force acting on the crate = Rightward force + Leftward force
=176 N + (- 352 N)
= - 176 N
Hence, the net force acting on the crate is - 176 N, which is 176 N to the left.
To learn more about the net force from the given link:
brainly.com/question/24855755
#SPJ4