00:01
Hi there, so for this problem, we have the situation that is shown in here.
00:06
So we're also given that the volume rate of change for this is 0 .7 in units of cubic feet per minute.
00:18
So the question is, how fast is the water level rising with the depth of the deepest point? let's label this as age, is equal to 5 feet.
00:36
Okay, you need to run your answer to five decimal places.
00:40
So first of all, we know that we need to write the volume expression for this.
00:46
That will be the width, and this times the area of the trapezoid.
01:00
That is just simply equal to.
01:03
So we have 20 for the feet wide, this times 1 divided by 2, and this times 12 plus the height of this, which is age plus 12, and this plus 8 times the height divided by 3, and all of this times the height.
01:34
So with that, we can simplify themes, and we will find that the volume for this is just simply 240 times the height plus 100, 110 times the height squared divided by 3.
01:58
Now with this, we need to derive this with respect to the height...