Lesson #59 Related Rates

Quote of the Day: 
"There are two ways to do great mathematics. The first is
 to be smarter than everybody else. The second way is to be 
 stupider than everybody else -- but persistent." 
      -- Raoul Bott

Objectives:
The student will solve related rates problems.
       
1. Collect homework.  

2. Review the Strategy for solving related rates problems
  (1) Draw and label a diagram.
  (2) Write down what you wish to solve for (express it in
      terms of a variable). e.g., dh/dt
  (3) Identify other variables in the problem.
  (4) Write equations that relate the variables.
  (5) Use substitution to obtain one equation involving the 
      known quantities.
  (6) Take the derivative of each side with respect to 
      time.
  (7) Solve for the desired rate.
  (8) Make numerical substitutions.


3. Go over Kite Problem from previous day (if not finished):
     A kite is at an altitude of 75 feet and moving
     horizontally at 12 ft/sec.  How fast is the string 
     being paid out when the kite is 100 feet away 
     (measured along the string)?

     Answer is 7.94 ft/sec

4. Example:
     Water runs into an inverted conical tank that is 10 
     feet high and 10 feet across at a rate of 2 cubic feet 
     per minute.  How fast is the water rising when the 
     water level is 6 feet deep?

    Solution:
       
       

5. Assignment: 
    p. 274 (13, 20a, 21, 26) 
        Worksheet "How Far Can You Watch?"        

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