Topic
Q:
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 \( \vec{a} \cdot \vec{b} \).
Q:
For the line through \( \left(\frac{1}{3}, \frac{1}{8}\right) \) and \( \left(-\frac{7}{6}, \frac{5}{8}\right) \), find the parametrization of \( y(t) \) if \( x(t)=\frac{1}{3}-\frac{3}{2} t \).
(Use symbolic notation and fractions where needed.)
Q:
For the line through \( (-9,15) \) with slope 9 find the parametrization of \( y(t) \) with given \( x(t)=-9+t \).
Use symbolic notation and fractions where needed.)
Q:
The population in a certain city was 54,000 in 2000 , and its future size is predicted to be \( P(t)=54,000 e^{0.017 t} \), where \( t \) is
the number of years after 2000 .
Complete parts a through d below.
a. Does this model indicate that the population is increasing or decreasing?
b. Use this function to estimate the population of the city in 2002 .
(Round to the nearest whole number as needed.)
Q:
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.)
Q:
Analyze the graph of the function.
\( \mathrm{R}(\mathrm{x})=\frac{8 \mathrm{x}+8}{9 \mathrm{x}+27} \)
A. \( \mathrm{x}=-3 \)
(Use a comma to separate answers as needed. Type an integer or a fraction.)
B. There is no vertical asymptote.
(c) What is the equation of the horizontal or oblique asymptote of \( \mathrm{R}(\mathrm{x}) \) ? Select the correct choice below and fill in any answer boxes within your choice.
A. \( \mathrm{y}=\square \) (Simplify your answer.)
B. There is no horizontal or oblique asymptote.
Q:
Analyze the graph of the function.
\( R(x)=\frac{x+5}{x(x+14)} \)
(a) What is the domain of \( R(x) \) ?
A. \( \{x \mid x \neq 0 \) and \( x \neq-14 \) and \( x \neq-5\} \)
B. \( \{x \mid x \neq 0 \) and \( x \neq-14\} \)
C. \( \{x \mid x \neq 0 \) and \( x \neq-5\} \)
D. All real numbers
Q:
Sketch the graph of \( y = \log_{10}(x) \) and identify its intercepts.
Q:
Construa o gráfico de \( f(x)=\left\{\begin{array}{l}x-1 \text {, se } x>2 \\ 2-x, \text { se } x<2\end{array}\right. \)
Q:
8. Consider the polar curve given by the equation \( r=2 \sin (\theta) \)
a) (7pts) The point \( \left(\sqrt{2}, \frac{\pi}{4}\right) \) is a point on this polar curve. Determine the \( x \) )-coordinates of this point.
b) (8pts) Represent this curve as a parametric curve (with parameter \( \theta \) ).
c) (8pts) Set up, but do not evaluate, an integral which represents the area enclosed by this curve.
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