During a science project, Pedro created a system that is governed by the following equation:
$$f(x) = \frac{1}{32}x^{2}a\ -\frac{1}{2}xz +3$$
In this system, \(a\) and \(z\) are constants that are adjusted manually by him, while \(x\) is the primary variable he wants to change. During his experimental tests, he found that the system can be very unstable, only for a few values of \(x\) for different \(a\) and \(z\) the system becomes stable. Can you help him find an equation that given \(a\) and \(z\) he can easily find the value of \(x\)?
- \(x = \frac{16z}{2a}\)
- \(x = \frac{16za}{2}\)
- \(x = \frac{2az}{16}\)
- \(x = \frac{16a}{2z}\)
- None of the above.
Original idea by: Pedro Henrique Di Francia Rosso
