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anonymous

  • 4 years ago

Need help with a related rates calculus problem! I'll type it!

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  1. anonymous
    • 4 years ago
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    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

  2. anonymous
    • 4 years ago
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    Just need help getting started.

  3. Hero
    • 4 years ago
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    mertsj would be surprised if I solved this

  4. anonymous
    • 4 years ago
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    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.

  5. anonymous
    • 4 years ago
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    \[1/2(4\pi r^2\div 3)+\pi r^2(y-r)=V\]

  6. Hero
    • 4 years ago
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    Okay, I got it

  7. anonymous
    • 4 years ago
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    Thanks a lot. Let me know if you need anything else.

  8. Hero
    • 4 years ago
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    r = 2, y = 6, right?

  9. anonymous
    • 4 years ago
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    Yes.

  10. anonymous
    • 4 years ago
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    Later they ask you to use your dr/dy to change the radius to 5.75.

  11. Hero
    • 4 years ago
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    -3/11 = dr/dy

  12. anonymous
    • 4 years ago
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    Hero, thank you, but this is free response and I needed help with the process.

  13. anonymous
    • 4 years ago
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    Can anyone help me with the process?

  14. Hero
    • 4 years ago
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    Maybe. Do you know how to take the derivative of Volume?

  15. anonymous
    • 4 years ago
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    Yes. Typically though, it is d/dt. That is what is tripping me up. This time it is dr/dy. What changes?

  16. Hero
    • 4 years ago
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    derivative of the radius with respect to y, rather than t

  17. anonymous
    • 4 years ago
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    So, when you end up taking the derivative of an 'y' values, you get dr/dy? ex. dr/dy(2y^2) = 4y dr/dy?

  18. anonymous
    • 4 years ago
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    I suppose my question is this: What happens mathematically when you take the derivative of radius in respect to height?

  19. Hero
    • 4 years ago
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    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

  20. anonymous
    • 4 years ago
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    Okay. That _doesn't_ happen with 'r' terms though.

  21. Hero
    • 4 years ago
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    You take the derivative with r as normal. The derivative of r with respect to y only applies to the y variable

  22. anonymous
    • 4 years ago
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    Thank you! That's what I needed to know.

  23. Hero
    • 4 years ago
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    Tell mertsj that I helped you. When you get the answer, let me know. I probably shouldn't have told you so early.

  24. Hero
    • 4 years ago
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    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

  25. anonymous
    • 4 years ago
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    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.

  26. Hero
    • 4 years ago
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    :D Okay, glad to help you.

  27. anonymous
    • 4 years ago
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    And thank you for your time :)

  28. Hero
    • 4 years ago
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    Actually, we can go to a site called vyew

  29. Hero
    • 4 years ago
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    Then I can watch you do the steps

  30. anonymous
    • 4 years ago
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    Uhh, is that...video chat? Because I think I'll pass for the afternoon, thanks.

  31. anonymous
    • 4 years ago
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    I'm very close to the answer, just give me another minute or two.

  32. Hero
    • 4 years ago
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    It's not video chat. Why does everyone automatically assume video chat?

  33. anonymous
    • 4 years ago
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    Might have to do with the 'watch' part.

  34. Hero
    • 4 years ago
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    It's just a site with an online whiteboard

  35. Hero
    • 4 years ago
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    http://vyew.com/room#/418625/Open_Study

  36. anonymous
    • 4 years ago
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    Okay. I've got a tablet. My handwriting should be decent.

  37. Hero
    • 4 years ago
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    Yes, your handwriting was very nice. I figured you must have a tablet

  38. anonymous
    • 4 years ago
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    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.

  39. Hero
    • 4 years ago
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    Well, I think it would be better if you worked on the mic, but okay

  40. anonymous
    • 4 years ago
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    I can keep trying.

  41. anonymous
    • 4 years ago
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    I got -1/5 this time. I'm checking wolframalpha.

  42. Hero
    • 4 years ago
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spraguer (Moderator)
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is replying to Can someone tell me what button the professor is hitting...

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