Write an equation that expresses the statement (Use k as the constant of proportionality.)
1- T varies directly as x.
2- w is jointly proportional to y and z
3- x is proportional to s and inversely proportional to t.
4- A is proportional to the square of t and inversely proportional to the cube of y

In math, a proportional relationship between a quantity y and a quantity x that has a constant of proportionality k is represented by the equation y = kx.

Given,

Here we have to find the equation that expresses the statement by using the k as the constant of proportionality.

Here we know that the value of the constant of proportionality is k.

Then the equation for the statement are,

1- T varies directly as x. And it can be written based on the constant proportionality,

=> T = kx

2- w is jointly proportional to y and z

Then the statement is written as,

=> w = k x y x z

=> w = kyz

3- x is proportional to s and inversely proportional to t.

Here we have to use the inverse proportional to write the statement,

=> x = k x s x 1/t

=> x = ks/t

4- A is proportional to the square of t and inversely proportional to the cube of y

Here first we have to take the square on t, then we get t² and then have to take cube on y, then we get y³,

then the equation is written as,

=> A = kt²/y³

To know more about Proportionality here.

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