Answer:
[tex]\dfrac{10}{3}.[/tex]
Step-by-step explanation:
It is given that M varies directly as n and inversely as the square of p. So,
[tex]M\propto \dfrac{n}{p^2}[/tex]
[tex]M=\dfrac{kn}{p^2}[/tex]
where, k is constant of proportionality.
It is given that M= 10 when n=8 and p = 2.
Substitute M= 10, n=8 and p = 2 in the above equation.
[tex]10=\dfrac{k8}{2^2}[/tex]
[tex]10=\dfrac{k8}{4}[/tex]
[tex]10=2k[/tex]
Divide both sides by 2.
[tex]5=k[/tex]
The value of k is 5.
So, requied equation is
[tex]M=\dfrac{5n}{p^2}[/tex]
Now, substitute n=6 and p=3 in the above equation.
[tex]M=\dfrac{5(6)}{(3)^2}[/tex]
[tex]M=\dfrac{30}{9}[/tex]
[tex]M=\dfrac{10}{3}[/tex]
Therefore, the required value of M is [tex]\dfrac{10}{3}.[/tex]
