a varies directly as the cube of b and inversely as the product of c and d
a = kb^3/(cd)
To get a solution
To express the relationship using variables, we can say:
a ∝ b^3 and a ∝ 1/(c*d)
To find the equation that combines these relationships, we need to introduce a constant of proportionality, k:
a = k * (b^3) * (1/(c*d))
Simplifying further:
a = (k * b^3) / (c*d)
This is the equation that represents the direct variation of a with the cube of b and the inverse variation of a with the product of c and d.
To find the relationship between the variables a, b, c, and d, we can use the following mathematical expression:
a = k * (b^3) / (c * d)
In this equation, k represents the constant of variation. It is multiplied by the cube of b and divided by the product of c and d. Therefore, the equation shows that a varies directly as the cube of b and inversely as the product of c and d.
If you have specific values for b, c, d, and a, you can rearrange the formula to solve for the constant of variation, k. Alternatively, if you have the value of k, you can substitute the given values of b, c, and d to find the value of a.