Find all possible integer values of $n$ such that the following system of equations has a solution for $z$: \begin{align*} z^n &= 1, \\ \left(z + \frac{1}{z}\right)^n &= 1. \end{align*}

What is the pattern in the values as the exponents increase?

Suppose that f(0) = −3 and f '(x) ≤ 8 for all values of x. how large can f(4) possibly be? solution we are given that f is differentiable (and therefore continuous) everywhere. in particular, we can apply the mean value theorem on the interval [0, 4] . there exists a number c such that

Ahovercraft takes off from a platform. its height (in meters), xx seconds after takeoff, is modeled by: h(x)=-2x^2+20x+48h(x)=−2x 2 +20x+48 what is the maximum height that the hovercraft will reach?