Find the cube roots of 27 cis \( 300^{\circ} \). Graph each cube root as a vector in the complex plane. Choose the correct cube roots below. A. \( 3 \operatorname{cis} 40^{\circ}, 3 \operatorname{cis} 160^{\circ}, 3 \operatorname{cis} 280^{\circ} \) B. 27 cis \( 70^{\circ}, 27 \operatorname{cis} 190^{\circ}, 27 \operatorname{cis} 310^{\circ} \) C. 27 cis \( 10^{\circ}, 27 \operatorname{cis} 130^{\circ}, 27 \operatorname{cis} 250^{\circ} \) D. \( 3 \operatorname{cis} 100^{\circ}, 3 \operatorname{cis} 220^{\circ}, 3 \operatorname{cis} 340^{\circ} \)

Use the given functions to answer the question. \( \begin{array}{l}f(x)=2^{x} \\ g(x)=x-3 \\ \text { What is the domain of } \frac{f(x)}{g(x)}=\frac{2^{x}}{x-3} \text { ? } \\ \text { A. the set of all real numbers } \\ \text { B. the set of all real numbers greater than } 0 \\ \text { D. the set of all real numbers not equal to } 0 \\ \text { E. the set of all real numbers not equal to } 3\end{array} \) B. thers greater than 3

3. A desintegração de certa substância é descrita pela lei \( M(t)=256(4)^{-0,125 t} \), em que 256 g é a massa inicial dessa substância, \( t \) representa o tempo, em horas e \( M(t) \) a massa, em gramas dessa substância no instante \( t \). Quanto tempo leva para que uma amostra seja reduzida a 32g.

Write the vector v in the form \( \mathrm{ai}+\mathrm{bj} \), given its magnitude \( \|\mathrm{v}\| \) and the angle \( \alpha \) it makes with the positive \( x \)-axis, \[ \alpha v=45^{\circ} \] \( \mathrm{v}=\square \) (Simplify your answer. Type an exact answer using radicals as needed. Type your answer in the form ai + bj.)

Find \( \|\mathbf{v}\| \). \( \begin{array}{l}\mathbf{v}=9 \mathbf{i}-12 \mathbf{j} \\ \|\mathbf{v}\|=\square \text { (Type an exact answer, using radicals as needed. Simplify your answer.) }\end{array} \)

Determine la forma polar del complejo \( z=-3-\sqrt{3} i \)