The amount of particulate matter left in solution during a filtering process is given by the equation \( P(x)=1,000(2)^{-0.4 n} \), where \( n \) is the number of filtering steps. Find the amounts left for \( n=0 \) and \( n=5 \). (Round to the nearest whole number.) A. \( 2,000,251 \) B B. \( 1,000,4,000 \) O C. \( 1,000,251 \) O D. \( 1,000,32 \)

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.)

257. Funksiýalaryň grafigini guruñ: \( \begin{array}{ll}\text { a) } y=x^{2}+6 x ; & \text { c) } y=0,5 x^{2}-4 \\ \text { b) } y=-\frac{1}{2} x^{2}+2 ; & \text { d) } y=\frac{1}{2} x^{2}-3 x\end{array} \)

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.)

Постройте график функции и укажите для нее область определения и значения \( x \), при которых \( y>0 \). а) \( у=3 \mathrm{x}^{-3} \);

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