Word Problems/Derivatives

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Question
What is the answer to this word problem? Trigonometry can be used to assist in getting the answer, but derivatives or differentiation must be used.

A 20 foot ladder is leaning against a house when its base starts to slide away. By the time the base is 12 feet from the house, the base is moving at 2 feet/second? How fast is the ladder sliding down the wall at that moment?

Answer
Ladder
Ladder  
By the Pythagorean Theorem,
y = 20-x
When x = 12 ft:
 the horizontal rate of change is dx/dt = 2 feet per second.
 y = 16 ft

Differentiate y with respect to time.
dy/dt = 0 - dx/dt
2ydy/dt = -2xdx/dt
dy/dt = (-x/y)dx/dt

x=12, y=16, dx/dt=2 ft/sec:
dy/dx = (-12/16)2 = -1.5
The ladder slides down the wall at 1.5 feet per second.

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Janet Yang

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Word problems are my favorite type of math questions! I would not feel comfortable answering questions that require specialized knowledge (Physics, Statistics, etc.) because I have not studied these in depth.

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I tutor students (fifth through twelfth grades) and am a Top Contributor on Yahoo!Answers with over 24,000 math solutions.

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Co-author of An Outline of Scientific Writing: For Researchers With English as a Foreign Language.

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I have a Bachelor's degree in Applied Mathematics from the University of California at Berkeley, and a Master of Business Administration degree from The Wharton School.

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George White Elementary School. Homework Help program at the Ridgewood Public Library, Ridgewood, NJ. Individual students.

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