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Calculate Equal-Area Slope of Longest Water Course

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I need some assistance in getting started in developing a python script to determine the Equal-Area Slope for the Longest Water Course of a catchment. The Longest Water Course is represented as a 3D Polyline. I need to determine the Equal-Area Slope of the each 3D polyline within a feature class.

The formula to derive the Equal-Area Slope is attached below as two jpegs. I'm battling to figure out how to extract the necessary information from each polyline and store it in either python lists or python dictionaries that I can then use within the formulas to determine the Equal-Area slope and then add the result back into the Longest Water Course feature class within a new field.

Any assistance in getting the following going will be appreciated.

Regards
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Name:	EqualAreaSlope01.JPG‎
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Name:	EqualAreaSlope02.JPG‎
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