Part 2 of 3 an antique table increases in value according to the function \( v(x)=650(1.03)^{x} \) dollars, where \( x \) is the number of years after 1980 . a. How much was the table worth in 1980 ? b. If the pattern indicated by the function remains valid, what was the value of the table in 2005 ? 1 c. Use a table or a graph to estimate the year when this table will reach double its 1980 value. a. The table was worth \( \$ 650 \) in 1980. (Round to the nearest cent as needed.) b. The value of the table was \( \$ \square \) in 2005 . (Round to the nearest cent as needed.)

Find an equation for the hyperbola described. Graph the equation. Center at \( (-1,-7) ; \) focus at \( (-1,-10) ; \) vertex at \( (-1,-9) \) Write an equation for the hyperbola. \( \square-\square=1 \) (Type exact answers for each term, using fractions as needed.)

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 magnitude of a vector with a horizontal component of 5 and a vertical component of \( 12 ? \)

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