🚀 Related Rates Boat problem ! ! ! ! ! - vTomb

🚀 Related Rates Boat problem ! ! ! ! !

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RELATED RATES PLAYLIST: https://goo.gl/85bbsG
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In this video you will learn how to find the rate of change of the length of the boat cable by using Pythagorean Theorem and implicit differentiation.

A barge, whose deck is 10 feet below the level of the dock, is being drawn in by means of a cable attached to the deck and passing through a ring on the dock. When the barge is 24 feet away and approaching the dock at 3/4 feet per second, how fast is the cable being pulled in? (Neglect any sag in the cable.)

0:20 Drawing picture - labeling known points, quantities and variables
1:53 Relating rate of change with given info and understanding negative/positive signs
4:03 Understanding what to look for - using Pythagorean Theorem to find an equation
4:59 Differentiating both sides implicitly with respect to time t
5:31 Determining which components we know and which need to be found in the differentiated equation - finding unknown component/variable and plugging in everything into the differentiated equation
7:47 Solving for rate of change dD/dt - rate of change of the length of the boat cable
8:53 Understanding negative answer - putting the result into words

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