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Math Help - implicit differentiation

  1. #1
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    implicit differentiation

    so, i'm supposed to be using implicit differentiation here. i've got a picture of a dude pulling a boat up to a dock by a rope. it's a right triangle. he's holding the rope 4 feet above the dock

    a boat is being pulled toward a dock. if the rope is being pulled in at 3 feet per second, how fast is the distance between the dock and the boat decreasing when it is 30 feet from the dock?

    i mean i know how to do implicit differentiation, i just can't figure out how to get the initial equation. at least not without using the sqrt of 916 which i doubt i'm supposed to do

    this is what i got:

    x=4, y=30

    x^2+y^2=z^2

    2x+2yy'=2z
    8+60y'=2(sqrt916)
    60y'=2(sqrt916)-8
    y'=(2(sqrt916)-8)/60
    y'=.8755163967

    and it's supposed to be -3.03 feet per second

    so i need help, please! (first post, btw)
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  2. #2
    MHF Contributor Calculus26's Avatar
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    See attachment
    Attached Thumbnails Attached Thumbnails implicit differentiation-relrates.jpg  
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  3. #3
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    Quote Originally Posted by Calculus26 View Post
    See attachment
    fantastic. thanks
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  4. #4
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    Re: implicit differentiation

    How did u get the 90.9.
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