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. Bell Ringer.
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. 222 (16, 24, 25, 27, 30)
Worksheet "How Fast Can You Watch?"
Worksheet "Frank S. Key" Problem (PDF File)
Worksheet "Frank S. Key" Problem (Word DOCUMENT)
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