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m varies directly as n and inversely as the square of p. Given that m=3 when n=2 and p=1. Write down an equation connecting m,n and p.

m = k (n/p^2)

for the given:
3 = k(2/1)
k = 3/2

so , m = (3/2)n/p^2

Did you know?

Did you know that in the world of mathematics, there is a concept called direct and inverse variation that helps us understand relationships between quantities? In this case, we have a situation where a variable, m, varies directly with another variable, n, and inversely with the square of a third variable, p. Here's an interesting fact: When m equals 3, n equals 2, and p equals 1. These values allow us to form an equation that connects m, n, and p based on the given variation. This equation would be m = k * (n / p^2), where k represents the constant of variation. Understanding these connections between variables can help us analyze and predict how changes in one quantity might affect the other quantities involved. It's truly fascinating how mathematics can unveil hidden relationships in the world around us!