Extra Credit Problems
Second Six Weeks

 Instructions:
  1.  Problems may be submitted any time during the six weeks, but they MUST be turned by the due date.
        (Due Date:  October 30, 2007)
  2.  Your work must accompany each problem and the problem must be stated or printed out.
        No credit will be given for just an answer.
  3.  Parts of problems are worth anywhere from 1 - 3 points depending on level of difficulty.
       Credit is given only for correct work and answers. The whole part must be correct to
       receive credit.
  4.  You may do as many or as few problems as you desire. Try to keep them in order.

Problems:

1.   Two trains leave Kansas City at the same time. Train A is traveling due north at 55 mph,
      Train B is traveling west at the rate of 65 mph. Find the distance between the two trains two
      hours later and the bearing of Train B from Train A.

2.   A tree is 18 ft from a house. From the top of the tree, the angle of depression to the base of
      the house is 41o, and the angle of elevation to the top of the house is 26o. Find the height of
      the house.

3.  Consider a commuter bus company that charges $2.00 per ride and receives about 1200 fares
     daily. It is estimated that for every $0.20 the fare is lowered, an additional 200 riders will take
     the bus. Find the fare that will maximize the bus company's revenue.

4.  A cylinder is generated by rotating a rectangle with perimeter 12 inches about one of its sides.
     a. Express the volume of the cylinder as a function of x.
     b. Give the domain of this function.
     c. Find the approximate value of x that maximizes the volume.
     d. Give the approximate maximum volume.

5.  Find a polynomial whose roots are double those of   y = x3 - 7x2 - 5x + 2.

6.  What happens to the roots of a polynomial when the coefficients are reversed?

7.  A cone with a height of 10 cm and a radius of 5 cm will increase in volume by 20% when the
       radius is increased and the height remains the same.  Find the increase in the radius.

8.  Graph      without a calculator.
                            

9.  Graph   without a calculator.
                      

12.  Analyze and graph , identifying all local maximum and minimum points
       and asymptotes.   Calculator output is not acceptable.

13.  Find the maximum volume of a cylinder inscribed in a sphere with radius 10.

14.  Solve for x:  |x - 2| - |x + 3|  >  |2x + 7|

15.      Find   function



16.  Graph 
        Find the domain, range, and zeros.

17.  Find the domain of f(g(x))  and the domain of g(f(x))  when