- If , and , give exact values
- Find the angle between the vectors and
Answer: The angle is approximately .
- Using the given sketch of the function , Find
values for a, b, c, and d.
Answer: The values are:
- A kennel raises Doberman pinschers and German shepherds. The kennel can
raise no more than 40 dogs and wishes to have no more than 24 Doberman
pinschers. The cost of raising a Doberman pinscher is $50, the cost
of raising a German shepherd is $30, and the kennel can invest no
more than $1500 for this purpose. Find a system of inequalities
which describes the number of Doberman pinschers and German shepherds
that can be raised by the kennel.
Answer: Let x be the number of
Doberman pinschers, and y be the number of German shepherds. The system of inequalities is:
- Find all angles between and
that satisfy . Write you answers in the
Answer: The angles are , and .
- Find the partial fraction decomposition of
- Let .
- Verify the identity
Show all steps.
- Consider the parametric equations , and
- Sketch the graph of
three cycles (periods) and label each asymptote.
- Find the sum of the sequence given below. Show your work:
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
- Find the all exact solutions for on the
Answer: There are four solutions:
- A manager must select 4 employees for promotion: 12 employees
- If , and ,
find exact values for the following:
- Write an expression for the nth term of the sequence. (Assume
n begins with 1.)
Answer: The nth term has the form
- Find the equation of the tangent line to the parabola given by
at the point (-1,1).
Answer: The equation of the tangent line is
- Find a unit vector in the direction of v= .
Answer: The unit vector is
- Use mathematical induction to prove the given formula for every
positive integer n:
- 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.