M partly varies as N and is partly constant. When M=2,N=3,when M=4,N=2.find M when N=1
M = kN + c
when M=2, N=3
---> 2 = 3k + c
when M=4, N=2
---> 4 = 2k + c
subtract the two equations:
-2 = k
sub into one of them to find c,
rewrite M = kn + c, replace N with 1 to find M
I want to search for partial variation
October 27,2021
To find the value of M when N=1, we need to understand the relationship between M and N based on the given information.
We are told that M partly varies as N and is partly constant. Let's break it down:
1. When M=2, N=3
2. When M=4, N=2
From these examples, we can observe that as N decreases, M increases. This suggests that there is a direct or positive relationship between M and 1/N.
Let's calculate 1/N for both scenarios:
1st scenario: when M=2 and N=3:
1/3 = 0.3333...
2nd scenario: when M=4 and N=2:
1/2 = 0.5
Now, we can examine the relationship between M and 1/N in terms of a constant, C:
When N=3, 1/N = 1/3 = 0.3333...
When M=2, M = C + (0.3333...)
Similarly, when N=2, 1/N = 1/2 = 0.5
When M=4, M = C + (0.5)
Since we are looking for the value of M when N=1, we need to calculate 1/N for this scenario as well:
When N=1, 1/N = 1/1 = 1
Now, we can find M using the equation derived above:
M = C + (0.3333...) (from the first scenario)
M = C + (0.5) (from the second scenario)
M = C + (1) (from the scenario with N=1)
As M is partly constant, we can assume that C remains the same throughout. Therefore, from the equations, we can conclude that:
0.3333... = 0.5 = 1 = C
Therefore, C = 1.
Now, substituting C=1 into the equations, we can find the value of M when N=1:
M = C + (1) = 1 + (1) = 2
So, when N=1, M=2.