Answer:a)m =K n
b)m = 32
c)n=15
Step-by-step explanation:
M varies directly as n can be expressed mathematically as
m ∝ n
Introducing the constant of proportionality, K, we have that
m =K n
Now when m=14 and n=7, K becomes
14=K X 7
K=14/7 = 2
b) find m when n=16
m =K n
m = 2 x 16=32
c) find n when m=30
m =K n
30=2 x n
n=30/2 =15
Expression is formed using numbers, variables, and mathematical operations. The value of m, when the value of n is 16 is 32.
In mathematics, an expression is defined as a set of numbers, variables, and mathematical operations formed according to rules dependent on the context.
As we know that the value of m is directly varying with n, therefore, we can write the relationship as,
[tex]m \propto n[/tex]
Now, in order to remove the proportionality, we will add a constant,
[tex]m = kn[/tex]
As the value of m and n is given as 14 and 7, substitute the values in order to get the value of the constant k,
[tex]m = kn\\14 = k(7)\\\dfrac{14}{7} = k\\k=2[/tex]
We know the value of the constant k is 2, therefore, the equation can be written as,
[tex]m=2n[/tex]
Substitute the value of n as 16, to get the value of m,
[tex]m=2n\\m=2(16)\\m=32[/tex]
Hence, the value of m, when the value of n is 16 is 32.
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