# M varies directly with n and inversely with the square of p.?

Question:m varies directly with n and inversely with the square of p. If m=4.0 and n=3.2 when p= 1.1, find n when m=2.0 and p=1.6

ok, so I thought this would go something like this:

m=kxm/p^2
m=kn/p^2
4.0=k(3.2)k/1.1^2
4.0=3.2k/1.21
1.21x4.0=1.21x3.2k/1.21
4.84=3.2k
k=4.84/3.2
m=4.84/3.2
m=4.84/3.2 x n/p^2

When m=2.0 and p=1.6 find n.
How do I find n with the equation:
m=4.84/3.2 x n/p^2
?
Am I even doing it right?
Point me in the right direction!
I would know how to do it if I were finding m, but not n because it's on the right side of the equation!

Well, you got the equation right, m = kn/p^2, so I'm assuming you understand how proportionality works.

Initially you're given m = 4.0, n = 3.2, and p = 1.1, because you have to determine the constant, k. So let's start by determining the constant, k:

m = kn/p^2 => 4.0 = k(3.2) / (1.1)^2 => 4.0 = 3.2k / 1.21
=> 4.84 = 3.2k => k = 1.5125.

So the constant, k is 1.5125.
Now, you're told to determine n, if m = 2.0, and p = 1.6. Now you also happen to know that k = 1.5125 since k never changes - it's a constant. So let's determine n:

m = kn/p^2 => 2.0 = 1.5125(n) / (1.6)^2
=> 2.0 = 1.5125n / 2.56 => 5.12 = 1.5125n
=> n = 3.385

Therefore, n = 3.4.

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