Find the domain of the function. \[ g(x)=\ln (x+8) \] The domain of \( g \) is (Type your answer in interval notation.)

Write the complex number in trigonometric form \( r(\cos \theta+i \sin \theta) \), with \( \theta \) in the interval \( \left[0^{\circ}, 360^{\circ}\right) \). \[ \begin{array}{l}1+i\end{array} \] \( \begin{array}{l}1+i=\square\left(\cos \square^{\circ}+i \sin \square^{\circ}\right) \\ \text { (Type the value for } r \text { as an exact answer, using radicals as needed. Type the value for } \theta \text { as an integer or } \\ \text { as needed.) }\end{array} \)

The exponential model \( \mathrm{A}=612.2 e^{0.014 t} \) describes the population, A, of a country in millions, \( t \) years after 2003. Use the model to determine when the population of the country will be 724 million. The population of the country will be 724 million in (Round to the nearest year as needed.)

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 \( \mathrm{a}+\mathrm{bi} \).

Write the complex number in trigonometric form \( r(\cos \theta+i \sin \theta) \), with \( \theta \) in the interval \( \left[0^{\circ}, 360^{\circ}\right) \). \[ -3 \sqrt{3}+3 i \] \( -3 \sqrt{3}+3 i=\square\left(\cos \square^{\circ}+i \sin \square^{\circ}\right) \) (Type the value for \( r \) as an exact answer, using radicals as needed. Type the value for \( \theta \) as an intege as needed.)

Find the standard form of the equation of the hyperbola satisfying the given conditions. Foci at \( (-7,0) \) and \( (7,0) \); vertices at \( (3,0) \) and \( (-3,0) \)