Express the point \( \left(9, \frac{\pi}{3}\right) \) in cartesian coordinates

Find the following product, and write the product in rectangular form, using exact values. \( \left[8\left(\cos 90^{\circ}+i \sin 90^{\circ}\right)\right]\left[3\left(\cos 30^{\circ}+i \sin 30^{\circ}\right)\right] \) \( \left[8\left(\cos 90^{\circ}+i \sin 90^{\circ}\right)\right]\left[3\left(\cos 30^{\circ}+i \sin 30^{\circ}\right)\right]=\square \) \( ( \) Type your answer in the form \( \mathrm{a}+\mathrm{bi} \).

Follow the seven step strategy to graph the following rational function. \( f(x)=\frac{6 x}{x-3} \) Find the horizontal asymptote(s). Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The equation(s) of the horizontal asymptote(s) is/are (Type an equation. Use a comma to separate answers as needed.) B. There is no horizontal asymptote.

Find the standard form of the equation of the hyperbola satisfying the given conditions. Foci at \( (0,-8) \) and \( (0,8) \); vertices at \( (0,3) \) and \( (0,-3) \)

2- Work out composite functions \( f \circ g \) and \( g \circ f \) for each of the following pairs of functions. \( \begin{array}{ll}\text { (a) } f(x)=x-1 \text { and } g(x)=x^{3} & \text { (b) } f(x)=\sqrt{x} \text { and } g(x)=x-2\end{array} \)

Find the magnitude and positive direction angle of the vector \( \langle 2,-2 \sqrt{3}\rangle \). The magnitude of the vector is (Simplify your answer.)