L varies directly as the cube of M and inversely as the square root of n. If L =108 when m=3 and n= 4. Find N when L is 4000 and M is 10

Pls help me with this

L = kM^3/√N

that means L√N/M^3 = k, which is constant
so you want N such that
4000√N/1000 = 108√4/3^3
√N = 108*2/27 * 1000/4000 = 2
N = 4
makes sense, since 108/27 = 4000/1000
They could have chosen a better set of values, I think

Did you know?

Did you know that the relationship between two variables L and M can be described by a mathematical equation? In this case, L varies directly with the cube of M and inversely with the square root of n. This means that as M increases or decreases, L will change accordingly, and as n increases or decreases, L will change inversely. To illustrate this, let's take an example: when M equals 3 and n equals 4, L is equal to 108. Now, if we want to find out what n is when L reaches 4000 and M is 10, we can use the given equation to solve for it. This equation shows that L is directly proportional to the cube of M and inversely proportional to the square root of n. By plugging in the values of M, L, and the initial values of n and solving the equation, we can find the missing value of n when L is 4000 and M is 10.