21. Sketch the curve \[ y=5-(x-1)^{2} \] and state the coordinates of the turning point.

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.)

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 32 g .

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.)

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

\( \frac{\log x-\sqrt{x^{2}-3 x+2}}{\sqrt{x^{2}-4}} \) For Domain