Related rates and derivatives word problem. Need help clearing a few things up.

Hey all, thanks in advance for any help you can offer.

I have completed most of the problem here, I just need some help in the right direction! Most of this problem will be trig, but I posted this in the calculus forum because it is calculus level. I will go ahead and post the whole problem in the form of an image to make things easier, with my questions at the bottom.

http://i.imgur.com/Ko20L.png

My questions are from 46.1.2 and on. I have determined that the radius at the top of the cup is twelve, and I used the concept of similar triangles to express r as h.

Could somebody please look this over?:

http://i.imgur.com/BlZfo.png

**Is this correct so far?**

Now is where my questions come in. 46.1.3 is driving me crazy. **How do I find dh/dt? ** Here is my work so far:

http://i.imgur.com/yWA15.png

__Is what I found for dv/dt correct? If it is, how do I go about finding dh/dt? __

Thanks for any help you can offer, and sorry for the wall of text!

-dan

Re: Related rates and derivatives word problem. Need help clearing a few things up.

Quote:

Originally Posted by

**dan147** My questions are from 46.1.2 and on. I have determined that the radius at the top of the cup is twelve, and I used the concept of similar triangles to express r as h.

The radius of the top of the cup is not twelve. Why are you assuming that the angle is ?

Re: Related rates and derivatives word problem. Need help clearing a few things up.

Because they didn't give me enough information. How do I get the angle?

Re: Related rates and derivatives word problem. Need help clearing a few things up.

Re: Related rates and derivatives word problem. Need help clearing a few things up.

Whoops! You sir are absolutely right! I found that 3 = r. Is the rest of this right?

http://i.imgur.com/g6otJ.png

Re: Related rates and derivatives word problem. Need help clearing a few things up.

Quote:

Originally Posted by

**dan147** I found that 3 = r. Is the rest of this right?

Well, I don't think you calculated correctly. But again, you really don't need to find the angle. As the problem states, we have similar triangles. So

This is our "relation equation," as the problem calls it.

Re: Related rates and derivatives word problem. Need help clearing a few things up.

Ok, I think I am starting to get it. Thank you! How does this look?

http://i.imgur.com/SDJHw.png

Now we get down to derivatives. How do I get dh/dt? I think this is correct for dv/dt, except for missing information:

http://i.imgur.com/aLOHE.png

Thank you so much!

Re: Related rates and derivatives word problem. Need help clearing a few things up.

Re: Related rates and derivatives word problem. Need help clearing a few things up.

Ok, I feel like I am really close. How do I get h? This doesn't seem right...

http://i.imgur.com/5PAv8.png

Re: Related rates and derivatives word problem. Need help clearing a few things up.

Re: Related rates and derivatives word problem. Need help clearing a few things up.

How does this look? The final answer doesn't really look right to me...

http://i.imgur.com/QqcSZ.png

Re: Related rates and derivatives word problem. Need help clearing a few things up.

Quote:

Originally Posted by

**dan147** How does this look? The final answer doesn't really look right to me...

That's what I got. So at that particular moment, the depth of the slushy is decreasing by about 0.010 cm/s.

Re: Related rates and derivatives word problem. Need help clearing a few things up.

What a problem! Thank you so much for your help, I really appreciate it. I thanked each one of your posts.