M varies directly as n and inversely as p. if M=3, when n=2,and p=1, find M in terms of n and p

m = kn/p

3 = k*2/1 --> k = 3/2

m = 3n / 2p

Well, let's use a little math and sprinkle in some humor to solve this problem!

First, we know that M varies directly as n and inversely as p. So, we can say that M = k(n/p), where k represents some constant.

To find the value of k, we can use the given information. When n = 2 and p = 1, M = 3. So, let's plug those values in: 3 = k(2/1). Simplifying this, we get 3 = 2k. Dividing both sides by 2, we find that k = 3/2.

Now that we have our value of k, we can substitute it back into the equation. M = (3/2)(n/p). And voila, we have M in terms of n and p!

To find M in terms of n and p, we need to express the direct and inverse relationships in a mathematical form.

We are given that M varies directly as n, which means we can write a proportionality equation as M = k * n, where k is the constant of proportionality.

We are also given that M varies inversely as p, which means we can write another equation as M = k / p.

Combining these two equations, we have:
M = k * n = k / p

Now we can solve for the constant of proportionality k.

Substitute the given values into the equation when M = 3, n = 2, and p = 1:

3 = k * 2 / 1
3 = 2k

Divide both sides by 2:
k = 3/2

Now that we have the value of k, we can substitute it back into the equation for M in terms of n and p:

M = (3/2) * n / p

Therefore, M = (3/2) * (n/p) is the expression for M in terms of n and p.

To find the equation that relates M, n, and p, we can use the concept of direct and inverse variation.

The statement "M varies directly as n" means that M is directly proportional to n. This can be represented as:
M ∝ n

Similarly, the statement "M varies inversely as p" means that M is inversely proportional to p. This can be represented as:
M ∝ 1/p

Combining these two proportionality statements, we can write the equation as:
M ∝ n/p

To find the constant of variation (k), we need to substitute the given values of M, n, and p and solve for k.

Given:
M = 3
n = 2
p = 1

Using the value of M and the equation M ∝ n/p, we can write:
3 = k * (2/1)

Simplifying the equation:
3 = 2k

Dividing both sides of the equation by 2, we get:
k = 3/2 = 1.5

Now that we have the constant of variation (k), we can write the final equation that relates M, n, and p:
M = k * (n/p)

Substituting the value of k into the equation:
M = 1.5 * (n/p)

Therefore, the equation representing M in terms of n and p is:
M = 1.5 * (n/p)

If M varies directly as R, what is the equation of variation if M = 3 and R = 1?