Are there any connections between culture and math (not necessarily your culture, but any). Explain why or why not.

Part 1:  A tower is 120 meters tall.  A cable is attached from the top of the tower to a point on the ground that is 50 meters from the base of the tower.  How long is the cable?  (Drawing a picture might help.)  Be sure to explain your work and show details.

Part 2:  Suppose the cable described in part 1 is removed and a new cable is attached from the top of the tower to a point on the ground closer to the base of the tower.  You are told the cable is 110 meters long.  Is there something wrong with this?  Explain what you are thinking about the proposed length of the cable for part 2.  (This part of the problem does not necessarily require computation.)  

5. [4] TRUE OR FALSE: a. If a homogeneous system of linear equations has more equations than unknowns then it is necessarily going to have infinitely many solutions. Answer: b. For any invertible matrix A. we have det A'' = (det A)"' (Hint: use the properties of determinants seen in class) Answer: