3. En el presente problema trabajamos con restricciones de funciones. Sea la función \( \quad f: \mathbb{R} \rightarrow \mathbb{R}, \quad f(x)=15+21 \cos \left(\frac{2 \pi}{20}(x-12)\right) \). Sea la función restricción \( g=\left.f\right|_{[32,52]} \). La imagen de la función \( g \) es rango \( (g)=[A, B] \). (a) Encuentre el valor de \( A \). (b) Encuentre el valor de \( B \). La imagen inversa de 15 satisface \( g^{-1}(15)=\{C, D\} \) con \( C<D \). (c) Encuentre el valor de \( C \). (d) Encuentre el valor de \( D \). Considere la función restricción \( h=\left.f\right|_{[32, E]} \), donde \( E \) es una con- stante a ser determinada.

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

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.)

The function \( f(t)=60,000(2)^{\frac{1}{40}} \) gives the number of bacteria in a population \( t \) minutes after an initial observation. How much time, in minutes, does it take for the number of bacteria in the population to double?

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

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