- If , and , give exact values
- Find the angle between the vectors and
- Using the given sketch of the function ,
find the values for a, b, c, and d.
- 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.
- Find all angles between and
that satisfy . Write your answers in the
- Find the partial fraction decomposition of
- Let .
- Verify the identity
Show all steps.
- Consider the parametric equations , and
- Eliminate the parameter and obtain a rectangular equation for
the graph described by x and y above.
- 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).
- Sketch the graph of .
Include three cycles (periods) and label each asymptote.
- Find the sum of the sequence given below. Show your work:
- Find the all exact solutions for on the
- A manager must select 4 employees for promotion: 12 employees
- In how many ways can the 4 be chosen?
- 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?
- If , and ,
find exact values for the following:
- Write an expression for the nth term of the sequence. (Assume
n begins with 1.)
- Find the equation of the tangent line to the parabola given by
at the point (-1,1).
- Find a unit vector in the direction of v= .
- Use mathematical induction to prove the given formula for every
positive integer n:
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