Final answer:
The general formula for the variable m that varies jointly with the inverse of the square of b and directly with the cube of b simplifies to m = k*b, where k is the constant of proportionality.
Step-by-step explanation:
The question asks for the general formula to describe a variable m that varies jointly with the inverse of the square of b and directly with the cube of b. To represent this relationship mathematically, we use a constant of proportionality k. The variation can be denoted as m = k*(1/b^2)*b^3, which simplifies to m = k*b. Hence, the variational equation shows that m is directly proportional to b, altered by a constant k.
It is important to notice that when we multiply the inverse of the square of b (1/b^2) with the cube of b (b^3), the exponents add up algebraically (since one exponent is negative), resulting in b^(3-2) = b^1, which is simply b. This relationship is based on the laws of exponents, which allow us to simplify exponential expressions.