Let's start by looking at the original function q:

q = 5e / (4x(z^2))

Now, let's apply the changes to e, x, and q:

- e is quadrupled, so the new value of e is 4e.
- x is doubled, so the new value of x is 2x.
- q is multiplied by a factor of 0.2222222222222222, so the new value of q is 0.2222222222222222q.

Let's substitute these new values into the original function:

0.2222222222222222q = 5(4e) / (4(2x)(z^2))

Now, let's simplify the equation:

0.2222222222222222q = 20e / (8x(z^2))

We can simplify this further by dividing both the numerator and the denominator by 4:

0.2222222222222222q = 5e / (2x(z^2))

Now, let's compare this new equation with the original equation:

Original: q = 5e / (4x(z^2))
New: 0.2222222222222222q = 5e / (2x(z^2))

We can see that the only change on the right side of the equation is the denominator's x term, which has been halved (from 4x to 2x). The e term and the z term have not changed in the new equation. Since the question asks by what factor z was changed, we can see that z was not changed at all, because the (z^2) term remains the same in both the original and the new equation.

Therefore, z was not changed; it remains the same. The factor by which z was changed is 1 (no change).
원래 함수 q를 살펴보는 것으로 시작하겠습니다:

q = 5e / (4x(z^2))

이제 e, x, q에 변경 사항을 적용해 보겠습니다:

- e는 4배가 되었으므로 e의 새 값은 4e입니다.
- x는 2배가 되었으므로 x의 새 값은 2x입니다.
- q는 0.222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222