, and 
, give exact values
for:
-
.
Answer:
.
-
.
Answer:
.
-
.
Answer:
.
-
.
Answer:
.
and
.
Answer: The angle is approximately 
.
, Find
values for a, b, c, and d.
|
Answer: The values are:
- a=-2.
- b=3.
-
. - d=-1.
Answer: Let x be the number of
Doberman pinschers, and y be the number of German shepherds. The system of inequalities is:
between 
and 
that satisfy 
. Write you answers in the
degree-minute-second format.
Answer: The angles are 
, and 
.
Answer:
.
- Convert z to its trigonometric form.
Answer:
- Using DeMoivre's theorem, write
as a complex number
in standard form (a + bi).
Answer:
- Use DeMoivre's theorem to solve the equation
Write your solutions in standard form.
Answer: The answers are:
Show all steps.
Answer:
, and
.
- Eliminate the parameter and obtain a rectangular equation for
the graph described by x and y above.
Answer: The equation is:
- Using you observations from the problem above, find a set of
parametric equations for the ellipse with vertices at (4,7) and
(4,-3), and foci at (4,5) and (4,-1).
Answer: The set of parametric equations is
. Include
three cycles (periods) and label each asymptote.
Answer:
|
Answer: The formula for finding the sum of an infinite
geometric sequence is 
. In this case a=7 and r=-3/7; thus the sum of the given
sequence is 
on the
interval 
.
Answer: There are four solutions:
- In how many ways can the 4 be chosen?
Answer: The 4 employees can be chosen in 495 different ways. - In how many ways can 4 of the 12 employees be chosen to be
placed in 4 different jobs, if they are all well qualified for any of
the 4 positions?
Answer: The 4 employees can be chosen in 11880 different ways.
, and 
,
find exact values for the following:
-
.
Answer:
.
-
.
Answer:
.
-
.
Answer:
.
Answer: The nth term has the form
at the point (-1,1).
Answer: The equation of the tangent line is
.
.
Answer: The unit vector is
.
Answer:
- When n=1, the formula is valid, because
- Assuming that
You must show that
To do this, write the following:
Combining the results from the two parts, it is concluded by mathematical induction that the formula is valid for every positive integer.