anonymous
  • anonymous
Need help with a related rates calculus problem! I'll type it!
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
anonymous
  • anonymous
A candy company needs a custom box for their truffles. The box they've chosen is in the shape of a cylinder with a hemisphere of the same radius on top. The total volume of the box is V= 1/2(4r^2pi/3) + r^2pi(y-r), where y is the height of the box and r is the radius. Originally the candy box was designed to have a height of 6 inches and a radius of 2, but the shipper suggests that the boxes be made slightly shorter. You now need to adjust the radius so that the height is reduced to 5.75 but the volume remains constant. A. Find the value of dr/dy at the point r =2, r = 6. Help with process
anonymous
  • anonymous
Just need help getting started.
Hero
  • Hero
mertsj would be surprised if I solved this

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anonymous
  • anonymous
Why is that? I really don't understand how dy/dr can be taken on that formula. I'll write it out nicer if you like.
anonymous
  • anonymous
\[1/2(4\pi r^2\div 3)+\pi r^2(y-r)=V\]
Hero
  • Hero
Okay, I got it
anonymous
  • anonymous
Thanks a lot. Let me know if you need anything else.
Hero
  • Hero
r = 2, y = 6, right?
anonymous
  • anonymous
Yes.
anonymous
  • anonymous
Later they ask you to use your dr/dy to change the radius to 5.75.
Hero
  • Hero
-3/11 = dr/dy
anonymous
  • anonymous
Hero, thank you, but this is free response and I needed help with the process.
anonymous
  • anonymous
Can anyone help me with the process?
Hero
  • Hero
Maybe. Do you know how to take the derivative of Volume?
anonymous
  • anonymous
Yes. Typically though, it is d/dt. That is what is tripping me up. This time it is dr/dy. What changes?
Hero
  • Hero
derivative of the radius with respect to y, rather than t
anonymous
  • anonymous
So, when you end up taking the derivative of an 'y' values, you get dr/dy? ex. dr/dy(2y^2) = 4y dr/dy?
anonymous
  • anonymous
I suppose my question is this: What happens mathematically when you take the derivative of radius in respect to height?
Hero
  • Hero
Well, it doesn't exactly work like that but you're on the right track. If you have an expression with y and you take the derivative of r with respect to y, you take the derivative normally, then tack on the dr/dy
anonymous
  • anonymous
Okay. That _doesn't_ happen with 'r' terms though.
Hero
  • Hero
You take the derivative with r as normal. The derivative of r with respect to y only applies to the y variable
anonymous
  • anonymous
Thank you! That's what I needed to know.
Hero
  • Hero
Tell mertsj that I helped you. When you get the answer, let me know. I probably shouldn't have told you so early.
Hero
  • Hero
You do realize that finding dr/dy is only the first part. The second part is, you have to replace y = 5.75 to find r while keeping the volume constant
anonymous
  • anonymous
Honestly, I don't know how to tell him if he's not online, but if I see him chatting I will; I'm fairly new here. I will let you know when I get the answer. Thank you, and yes, I figured that part out. It was the implicit stuff that was killing me.
Hero
  • Hero
:D Okay, glad to help you.
anonymous
  • anonymous
And thank you for your time :)
Hero
  • Hero
Actually, we can go to a site called vyew
Hero
  • Hero
Then I can watch you do the steps
anonymous
  • anonymous
Uhh, is that...video chat? Because I think I'll pass for the afternoon, thanks.
anonymous
  • anonymous
I'm very close to the answer, just give me another minute or two.
Hero
  • Hero
It's not video chat. Why does everyone automatically assume video chat?
anonymous
  • anonymous
Might have to do with the 'watch' part.
Hero
  • Hero
It's just a site with an online whiteboard
Hero
  • Hero
http://vyew.com/room#/418625/Open_Study
anonymous
  • anonymous
Okay. I've got a tablet. My handwriting should be decent.
Hero
  • Hero
Yes, your handwriting was very nice. I figured you must have a tablet
anonymous
  • anonymous
Sorry, man. Let me keep working and see if I can figure out what I did wrong. I don't know why my microphone wouldn't work.
Hero
  • Hero
Well, I think it would be better if you worked on the mic, but okay
anonymous
  • anonymous
I can keep trying.
anonymous
  • anonymous
I got -1/5 this time. I'm checking wolframalpha.
Hero
  • Hero
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