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:  
9AF 5 GP.png
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:  

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