Rewrite the connecting the variable using a constant of variation,k.

Z varies as the cub root of m
r varies inversely as the square root of q.
s is inversely proportional to t square
x is proportional to (v-1) all square

The variable Z is directly proportional to the cube root of m, which can be written as Z = k * ∛m.

The variable r is inversely proportional to the square root of q, which can be written as r = k / √q.

The variable s is inversely proportional to the square of t, which can be written as s = k / t^2.

The variable x is directly proportional to the square of (v-1), which can be written as x = k * (v-1)^2.

To rewrite the statements using a constant of variation, k, we can use the following formulas:

1. Z = k * ∛m

This equation represents that Z varies directly with the cube root of m, with k as the constant of variation.

2. r = k / √q

This equation indicates that r varies inversely with the square root of q, with k as the constant of variation.

3. s = k / t²

This equation shows that s is inversely proportional to the square of t, with k as the constant of variation.

4. x = k * (v - 1)²

This equation states that x is directly proportional to the square of (v - 1), with k as the constant of variation.