00:01
So we have a three -part problem here, and we're working on this trough of water that evaporates.
00:08
So on part a, our job is to express width w as a function of h.
00:15
And we know that our width begins at 4 feet, and our height h begins at 2 feet.
00:24
And since it will decrease proportionately, we have a proportion here where we get 4h equals 2w.
00:34
So solving for w, we will get w equals 2 times h.
00:43
So the width is double the height.
00:46
So this is our first part.
00:50
Now in the second part, we want to express volume v as a function of h.
00:59
So we know that volume is 3 times w times h.
01:05
So to do v of h, we need to write it only in terms of h.
01:10
So we'll take our expression that we got in part a and substitute it in for w so that we write everything in terms of h.
01:18
So we get 3 times 2 w times h here.
01:24
And so this simplifies to v of h equals 6h squared...