x propto y and y propto z ^ 2 How does x vary with z?

Answer 1

Since y is proportional to z^2, we can write y = k(z^2), where k is a constant of proportionality.

Similarly, if x is proportional to y, then we can write x = m(y), where m is a constant of proportionality.

Substituting the value of y from the first equation into the second equation, we get:
x = m(k(z^2))

Rearranging the equation, we can write it as:
x = (m*k)(z^2)

This shows that x is proportional to z^2. Therefore, x varies with z^2.