00:01
So in this question, they say that the altitude of a triangle is increasing at a rate of 3 centimeters per minute, while the area of the triangle is increasing at a rate of 4 square centimeters per minute.
00:14
At what rate is the base of the triangle changing when the altitude is 7 centimeters, and the area is 89 square centimeters? so i have a triangle, and i have the base of that triangle.
00:32
Triangle, which is changing in length, and i have the height of the triangle, which is changing as well.
00:42
They said that the altitude of the triangle was increasing in a rate of three centimeters per minute.
00:51
My altitude is my height, so my height is increasing at three centimeters per minute.
00:59
I have been given that my dhdt is 3 centimeters per minute.
01:06
Now they also said that my area was increasing at the rate of 4 square centimeters per minute.
01:16
In other words, my dadt is equal to 4 square centimeters per minute.
01:25
And i want to know what is the rate of change of the base? so i want to know what is dbdt when my altitude, when my height is 7, and my area is 89.
01:46
Now, how am i going to relate the h, the a, and the b without their derivatives this time? i can say that my area is equal to one -a -half base times height.
02:03
And now i'm going to take the derivative of each side with respect to t.
02:10
So the derivative of the left side with respect to t, that's d -a -d -t.
02:17
On the right side, to take my derivative, one -half is a constant multiple.
02:25
That's going to come along.
02:27
My derivative of b times h, that requires the chain.
02:33
I'm going to have b times d -h d -t plus a...