Math 1507

Quiz Dec 2, 1997
Name: _______________

Open Books and notes. You ahave 30 minutes. Please show all work. 
This test consists of three riddles. One by Maria Callas, one by Birgit Nilsson, and one by Joan Sutherland

Problem 1  Maria Callas's riddle is  whether:
                      x^2 + 6x - 4 y^2 + 16 y  = 11
is a hyperbola, parabola or an ellipse. Which is it? What is the center?  What are the foci (or focus and directrix)? Draw a picture.

(((x  +  3)^2)/4   -  (y  - 2)^2   -  1) 4 
       // ExpandAll

Problem 2 (10 points) Birgit Nilssons riddle: Three cars A, B, and C are in a race. There poisitions are
given by f(t), g(t) and h(t). They start at the same place
at the same time with the same velocities:
f(0) = g(0) = h(0) ,
f'(0) = g'(0) = h'(0).

Car A is decelerating, f ''(t) <= 0, Moreover f ''(t) is decreasing. 
Car B starts out with the same velocity as A, and continues on with
constant velocity.
Car C  starts out with the same postition and velocity and acceleration
as A, f(0) = h(0), f'(0) = h'(0), f ''(0) = h''(0), but C continues on
with constant acceleration h''(t) = f ''(0).

Can we conclude what the order of cars  is at time t = 2? 
If so why. If not why not?

Problem 3: (10 points)  Joan Sutherland's riddle: Appoximate  cos(31 degrees) by the tanget line approximation centered  at 30 degrees.  Warning: Radians!