\( y=f(x)=(\frac{5}{9})^{x} \)

Find the outer measure of \( x \) for \( \{-5 \leq x \leq 3\} \cup\{-2 \leq x<7\} \)

Find the direction angle of \( v \) for the following vector. \( v=2 i-4 j \) What is the direction angle of \( v \) ? TRound to one decimal place as needed.)

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.)

The formula \( A=24.2 e^{0.0766 t} \) models the population of a US state, \( A \), in millions, \( t \) years after 2000 . a. What was the fopulation of the state in 2000 ? b. When will the population of the state reach 31.4 million? a. In 2000 , the population of the state was \( \square \) million. b. The population of the state will reach 31.4 million in the year \( \square \). (Round to the nearest year as needed.)

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