Expert: Scott A Wilson - 1/5/2010

Question
My daughter has a homework assigment that is asking her to create equivalent expressions and prove those expressions using inputting and outputting.  I have now idea what this means.  I understand that equivalent equations approximate each other in value.  How do I begin to understand this so I can help her?  The question involves the design of a swimming pool.  She is being asked to create equivalent espressions/equations for the area of the pool then to prove that they are equivalent by inputting and 0outputting.  For example:  width of pool 25 ft, lenght of deep end is X while length of shallow end is 6 ft.  I believe one equation for the area of the pool would be (x+6)25=A.  Help!

Answer
I will assume that 25 is the distance from the shallow end to the deep end of the pool.
I will give the pool a depth D and a length L with the shallow end at L=0.
This makes the deep end at L=25 with depth X.

The slope of the pool bottom can be found by taking the difference in length over
the difference in depth.  That is, D = 6 + (X-6)L/25.

Again, D is the depth at some point L, L is how far from the shallow end (between  and 25),
and X is the depth at the deep end,

As can be seen, when the shallow end is looked at, L=0, so D = 6.
When the deep end is looked at, L=25, so D = 6 + (X-6)25/25 = 6 + (X-6) = 6 + X - 6 = X.

Note that D is the distance below the surface, so on a graph,
D would be how far below the horizontal axis.