M varies inversely with the square root of n and m=18 when n=144
To solve this problem, let's first write down the formula for inverse variation:
M = k/n^0.5
where k is the constant of variation.
We can now plug in the values given:
18 = k/144^0.5
Simplifying the equation:
18 = k/12
Multiplying both sides by 12:
k = 216
Now we have the constant of variation, k. We can use this to find M when a different value of n is given.
M = 216/n^0.5
To find the equation that relates M and n, we can use the formula for inverse variation:
M = k / √n
where k is the constant of variation.
To find the value of k, we can substitute the given values of M and n:
18 = k / √144
To simplify the equation, we know that √144 is equal to 12:
18 = k / 12
To solve for k, we can multiply both sides of the equation by 12:
216 = k
Now that we have the value of k, we can substitute it back into the equation for inverse variation:
M = 216 / √n
So the equation that relates M and n is M = 216 / √n.
To solve this problem, we can begin by setting up the inverse variation equation. In inverse variation, we have a constant that relates the two variables. Let's call this constant k.
The inverse variation equation can be written as:
m = k / sqrt(n)
Given that m = 18 when n = 144, we can substitute these values into the equation:
18 = k / sqrt(144)
Now, we need to solve for the constant k. We know that the square root of 144 is 12, so we can simplify the equation further:
18 = k / 12
To solve for k, we can multiply both sides of the equation by 12:
18 * 12 = k
Simplifying the left side of the equation:
216 = k
So, the constant k is equal to 216.
Now that we have found the constant, we can write the inverse variation equation as:
m = 216 / sqrt(n)
This equation allows us to find the value of m for any given value of n.