007A Sample Midterm 2, Problem 5 Detailed Solution
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A kite 30 (meters) above the ground moves horizontally at a speed of 6 (m/s). At what rate is the length of the string increasing when 50 (meters) of the string has been let out?
Background Information: 

The Pythagorean Theorem 
For a right triangle with side lengths where is the length of the 
hypotenuse, we have 
Step 1: 

From the diagram, we have by the Pythagorean Theorem. 
Taking derivatives, we get 

Step 2: 

If then 
So, we have 
Solving for we get 
Final Answer: 
