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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fantastic. thanks