If M varies directly as N and inversely as the root of P. Given that M = 3, N = 5 and P = 25. Find the value of P when M = 2 and N = 6.
Answer Details
The problem tells us that "M varies directly as N and inversely as the root of P". This means that M is directly proportional to N and inversely proportional to the square root of P, which can be written mathematically as:
M = k(N / sqrt(P))
where k is a constant of proportionality. We can solve for k by using the given values of M, N, and P.
When M = 3, N = 5, and P = 25, we can plug these values into the equation above and solve for k:
3 = k(5 / sqrt(25))
3 = k(5 / 5)
3 = k
So, we have found that k = 3.
Now, we can use this value of k to find P when M = 2 and N = 6. We can rearrange the equation above to solve for P:
M = k(N / sqrt(P))
sqrt(P) = k(N / M)
P = (k(N / M))^2
Plugging in k = 3, N = 6, and M = 2, we get:
P = (3(6 / 2))^2
P = 9(3)^2
P = 81
Therefore, the value of P when M = 2 and N = 6 is 81. So, option D is the correct answer.