Contexto: Este lipo de preguntas se desarrollan en torno a un (1) enunciado y cuatro (4) opciones de respuesta. Solo una (1) de estas opciones responde correctamente a la pregunta. Considerando los vectores \( \vec{a}=(2,-3,5) \) y \( \vec{b}=(-1,4,2) \), selecrione la opción que representa correctamente el producto escalar \( \vec{a} \cdot \vec{b} \).

6) O domínio da função dada por \( \mathrm{f}(\mathrm{x})= \) é a) \( \{x \in R \mid-2 \leq x \leq 3\} \). b) \( \{x \in R \mid-2 \leq x<3\} \). c) \( \{x \in R \mid 2 \leq x<3\} \). d) \( \{x \in R \mid-2 \leq x \leq 3\} \). e) \( \{x \in R \mid x \neq 3\} \).

The exponential model \( \mathrm{A}=474.2 e^{0.006 t} \) describes the population, A , of a country in millions, \( t \) years after 2003 . Use the model to determine the population of the country in 2003 . The population of the country in 2003 was \( \square \) million.

Find the standard form of the equation of the hyperbola satisfying the given conditions. Foci at \( (-7,0) \) and \( (7,0) \); vertices at \( (3,0) \) and \( (-3,0) \)

Follow the seven step strategy to graph the following rational function. \( f(x)=\frac{6 x}{x-2} \) To graph the function, first determine the symmetry of the graph of f . Choose the correct answer below. y-axis symmetry origin symmetry neither \( y \)-axis symmetry nor origin symmetry What is the \( y \)-intercept? Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The \( y \)-intercept is (Type an integer or a simplified fraction.)

Suppose that the functions \( f \) and \( g \) are defined as follows. \[ \begin{array}{l}f(x)=\sqrt{5 x+3} \\ g(x)=3 x^{2}+1\end{array} \] Find \( f+g \) and \( f \cdot g \). Then, give their domains using interval notation.