Solving related rates mr kelly and mr sullivan are riding...

Solving Related Rates Mr. Kelly and Mr. Sullivan are riding bikes on two different streets, both approaching the same intersection. They are going to converge at right angles to each other. Mr. Kelly is 150 meters from the intersection, moving at 450 meters per minute. Mr. Sullivan is 200 meters from the intersection, moving at 600 meters per minute. At what rate is the distance between the cyclists decreasing? The radius r of a sphere is increasing at a constant rate of 0.02 centimeters per second. The volume of a sphere with radius r can be modeled by V = (4/3)πr^3. At the time when the radius of the sphere is 8 centimeters, what is the rate of increase of its volume? Round/truncate your answer to three decimal places.

Transcript

00:04 Now here we have mr.

00:06 Kelly and mr.

00:08 Sullivan, right? now, these two are riding backs on two different streets, right? so suppose you have a street here and you're another street here, and these two streets at right angles and across the intersection, right, the cross is here.

00:20 And they are approaching the same intersection, approaching this intersection, right? so suppose kelly is approaching here, right? this is kelly.

00:28 Now, kelly is 1 to 50 meters away from across, over from the section at the moment, and is approaching at 450 meter per second, not per minute actually, okay, approaching the intersection.

00:45 And the other one, i mean the mr.

00:48 Civilian actually is 200 meters away from the intersection and his proportion this way at speed, which is 600, 600 meter per minute, okay? so you ask, how, i mean, you asked basically how this distance is changing, right? so let me show it better, how this distance, which is s, right, as a function of t, how this distance would actually change, right? and how fast would this distance change, right? so you see that, suppose this is x and this is y, and the s is given by square of x squared plus y squared, right? and if you take the derivative of s, that's given by x over, actually x plus y, over square, of x plus y, okay? and xx dot, extra plus y, y, dot.

01:39 I forgot this dot.

01:40 X dot of course, according to the question is, you know, 4, 150, and y dot, of course, is 600, right? so this is going to be given by x according to the question is 150, right? and x dot, actually, is 450, and plus y in this question is 200 and times of y dot, which is 600, and divided, of course, by a school of this squared, i forgot.

02:04 X is 150 squared and plus 200 squared, right? so that would be what you found...

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