8. Consider the polar curve given by the equation \( r=2 \sin (\theta) \) a) \( (7 \mathrm{pts}) \) The point \( \left(\sqrt{2}, \frac{\pi}{4}\right) \) is a point on this polar curve. Determine the \( x y \)-coordinates of this point. b) (8pts) Represent this curve as a parametric curve (with parameter \( \theta \) ).

Where is there a discontinuity / are there discontinuities (holes or asymptotes) in the rational function \( f(x)=\frac{x^{2}+3 x+2}{x^{2}-4} ? \) \( x= \) 0 \( x= \) 2 \( x= \) -2 \( x=2 \) -2 \( x=0 \) \( 2,-2 \) \( x \)

The number of U.S. travelers to other countries during the period from 1990 through 2009 can be modeled by the polynomial function \( P(x)=-0.00530 x^{3}+0.1366 x^{2}+1.250 x+46.49 \) where \( x=0 \) represents \( 1990, x=1 \) represents 1991 , and so on and \( P(x) \) is in millions. Use this function to approximate the number of \( U \).S. travelers to other countries in each given year. (a) 1990 (b) 2000 (c) 2009 (a) In 1990 , the number of U.S. travelers to other countries was approximately \( \square \) million. (Simplify your answer. Type an integer or decimal rounded to the nearest tenth as needed.) (b) In 2000, the number of U.S. travelers to other countries was approximately \( \square \) million. (Simplify your answer. Type an integer or decimal rounded to the nearest tenth as needed.) (c) In 2009, the number of U.S. travelers to other countries was approximately \( \square \) million. (Simplify your answer. Type an integer or decimal rounded to the nearest tenth as needed.)

What is the direction of a vector with a horizontal component of 2 and a vertical component of -4 ?

The size of a certain insect population is given by \( \mathrm{P}(\mathrm{t})=400 e^{.03 \mathrm{t}} \), where t is measured in days. At what time will the population equal 1600 ?

Argumen dari \( 1-i \sqrt{3} \) adalah...