implicit differentiation

• Nov 18th 2009, 02:32 PM
propjohn
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)
• Nov 18th 2009, 02:49 PM
Calculus26
See attachment
• Nov 18th 2009, 02:57 PM
propjohn
Quote:

Originally Posted by Calculus26
See attachment

fantastic. thanks
• Apr 5th 2013, 03:23 PM
Iluggy06
Re: implicit differentiation
How did u get the 90.9.