p varies directly as the square of m inversely as n. if p =200 when m=5 and n=1/2 find p when m=6 and n=2
m.vavies directly as n and inversily as the square.of p.if m=3,when n=2 and p=1,find m in times of n and p
Please answer the above question
To find the value of p when m = 6 and n = 2, we need to understand the relationship between p, m, and n from the given information.
The statement "p varies directly as the square of m inversely as n" can be mathematically expressed as:
p = k * (m^2) / n
Here, k is the constant of variation.
To find the value of k, we can substitute the given values of p, m, and n when p = 200, m = 5, and n = 1/2:
200 = k * (5^2) / (1/2)
200 = k * 25 / (1/2)
200 = k * 50
k = 200 / 50
k = 4
Now that we have the value of k, we can substitute the given values of m and n when m = 6 and n = 2 into the equation:
p = 4 * (6^2) / 2
p = 4 * 36 / 2
p = 4 * 18
p = 72
Therefore, when m = 6 and n = 2, the value of p is 72.