1. Using the formula $P = 2\pi\sqrt{\frac{L}{32}}$, what is the period $P$ in seconds of a pendulum with a length $L$ of 8 feet? Your answer may include $\pi$. The period is ___ seconds.
2. An electrical circuit has a voltage of 90 volts and a power of 270 watts. Using the formula $V = \sqrt{PR}$, what is the resistance $R$ in ohms?
3. An electrical circuit has a power of 80 watts and a resistance of 20 ohms. Using the formula $V = \sqrt{PR}$, the voltage $V$ is ___ volts.
4. A pendulum has a period of 6 seconds. Using the formula $P = 2\pi\sqrt{\frac{L}{32}}$, what is its length $L$ in feet?
5. An electrical circuit has a voltage of 60 volts and a resistance of 15 ohms. Using the formula $V = \sqrt{PR}$, the power $P$ is ___ watts.
6. Solve the equation $2\sqrt[3]{x} + 15 = 5$. $x = \_\_\_$
7. Solve for $x$: $\sqrt[3]{2x - 5} - 1 = 2$. The solution is $x = \_\_\_.$
8. Solve the equation $2 = 8 - 3\sqrt[3]{x^3 + 1}$.