Topic
Q:
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 \( (-3,0) \)
Q:
Find the standard form of the equation of the hyperbola satisfying the given conditions.
Foci at \( (0,-8) \) and \( (0,8) \); vertices at \( (0,3) \) and \( (0,-3) \)
Q:
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.
Q:
Use transformations of the absolute value function,
\( \mathrm{f}(\mathrm{x})=|\mathrm{x}| \), to graph the function \( g(x)=-|\mathrm{x}-3|-5 \).
...
\( \square \) A. Horizontal shift
\( \square \) B. Vertical stretch/shrink
\( \square \) C. Horizontal stretch/shrink
\( \square \) D. Vertical shift
\( \square \) E. Reflection about the \( x \)-axis
\( \square \) F. Reflection about the \( y \)-axis
Q:
A farmer decides to enclose a rectangular garden using the side of a barn as one side of the rectangle. What are the maximum dimensions that can be enclosed with 80 ft of fence?
What is the maximum area of this garden?
Select the correct choice below and fill in the answer box(s) to complete your choice.
A. The area is maximized when both sides are \( \square \mathrm{nt} \). The area is maximized when the longer side is \( \square \mathrm{ft} \) and the shorter side is
The maximum area that the farmer can enclose with 80 ft of fence is \( \square \mathrm{sq} \mathrm{ft} \)
Q:
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) \( \{x \in R \mid x \neq 3\} \).
Q:
Use the given function to complete parts (a) through (e) below.
\( f(x)=x^{4}-36 x^{2} \)
d) Determine the symmetry of the graph.
Odd; origin symmetry
Even; \( y \)-axis symmetry
Neither
Q:
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.)
Q:
What is the dot product of vector \( h \)
with a magnitude of 5 and vector \( i \)
with a magnitude of 8 if the angle
between the vectors is \( \frac{\pi}{6} \) radians?
(Round your answer to the nearest
hundredth.)
Q:
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.
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