Hello again, archistrategos214!
3) A waterway whose crosssection is a parabola is being designed for a theme park boat ride.
It has a depth of 12 ft and a width of 6 ft at the surface.
Rectangular crosssectioned boats are to be used, and they sink to a depth of 4 ft.
What should be the proper width of the boat to facilitate easy passage? Code:

*  *+*  *(3,12)
  
*   4 *
*  x  x  *
*+*
*  * :y
*  * :
          *       +  

The parabola has the equation: .$\displaystyle y \,=\,ax^2$
The point $\displaystyle (3,12)$ is on the parabola.
. . We have: .$\displaystyle 12 \:=\:a\cdot3^2\quad\Rightarrow\quad a = 2$
The parabola is: .$\displaystyle y \,=\,2x^2$
Since the boats sink to 4 feet, then: .$\displaystyle 12  y = 4$
. . Then: .$\displaystyle 12  2x^2\:=\:4\quad\Rightarrow\quad x \,=\,2$
Therefore, the boatrs should be $\displaystyle 2x = 4$ feet wide at most.