November 30th, 2008, 07:14 AM  #1 
Newbie Joined: Nov 2008 Posts: 12 Thanks: 0  Related Rates Help Please
I'm not asking these because I'm trying to cheat on my homework, I have a test coming up and I need to understand how to do these. 1. The minute hand of a certain clock is 4 in. long. Starting from the moment when the hand is pointing straight up, how fast is the area of the sector that is swept out by the hand increasing at any instant during the next revolution of the hand? 2. Oil spilled from a ruptured tanker spreads in a circle whose area increases at a constant rate of 6 mi ^2/hr. How fast is the radius of the spill increasing when the area is 9 mi^2? Thanks for any help you could give me 
November 30th, 2008, 07:24 AM  #2 
Senior Member Joined: Jul 2008 Posts: 895 Thanks: 0  Re: Related Rates Help Please
This is the internet. There is no way for anyone to really know if this is or is not homework, regardless of what is seen in print [I'm tall, young, dark skinned, good looking, and rich, and you have to believe me because I said so.] A base guideline is that it is still "homework" until you have shown that you can at least start these problems ...one at a time. You could list forty as easily as four. It's simply a matter of showing your own goodwill if you wish. If someone simply gives you a full solution with no dialogue or consideration of your own effort, then you are no further ahead than you are now, having already seen some in your text and the classroom. It only shows that they can still do it easily, not you. So, if you can show what you have at least tried for just the first one .... 
November 30th, 2008, 07:27 AM  #3 
Newbie Joined: Nov 2008 Posts: 12 Thanks: 0  Re: Related Rates Help Please
I have done work but I can't really show it on here because I don't know how to do all the math symbols

November 30th, 2008, 07:36 AM  #4  
Senior Member Joined: Jul 2008 Posts: 895 Thanks: 0  Re: Related Rates Help Please Quote:
OK, let's start with #1. Quote:
Let's assume at the start. So, at 5 minutes after he has started to walk, you should have a point of his location [where on the yaxis], the woman still being 500' due east of his starting point. You can then extend in the diagram, his position increasing by "s", and hers due south by (5/4)s [can you see why?] You can then form a right triangle containing for one side the distance East of the woman [500], the northerly distance between them [1200 + s + (5/4)s], and can then find the direct distance between them, using Pythagoras, in terms of th one variable, "s". The 1200 is from your first calculation of his location when she starts to walk. You can then apply your knowledge of calculus to find the rate of change of that distance in terms of ds/dt [which is given.]  
November 30th, 2008, 07:40 AM  #5  
Newbie Joined: Nov 2008 Posts: 12 Thanks: 0  Re: Related Rates Help Please Quote:
 
November 30th, 2008, 07:54 AM  #6  
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Quote:
Now, we are given the area is 9. So, plug that in for A and solve for r. That is the radius when the area is 9. Differentiate the area equation w.r.t time, plug in the knowns and solve for dr/dt. You have dA/dt and r. All you need to plug in and find dr/dt. Does that help?.  
November 30th, 2008, 08:00 AM  #7 
Newbie Joined: Nov 2008 Posts: 12 Thanks: 0  Re: Related Rates Help Please
Yes it does, thank you!

November 30th, 2008, 08:02 AM  #8  
Senior Member Joined: Jul 2008 Posts: 895 Thanks: 0  Re: Related Rates Help Please Quote:
 
November 30th, 2008, 08:03 AM  #9  
Guest Joined: Posts: n/a Thanks:  Re: Related Rates Help Please Quote:
The area of a sector of a circle is The radius remains constant since that is the length of the hand (4 inches). . Do you see why?.  
November 30th, 2008, 08:23 AM  #10  
Newbie Joined: Nov 2008 Posts: 12 Thanks: 0  Re: Related Rates Help Please Quote:
Thanks for helping!  

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