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Warm-Up: January 7, 2013

Warm-Up: January 7, 2013. Write a differential formula that estimates the change in volume of a sphere when the radius changes from r to r+dr. Homework Questions?. Quiz Results: 4.1-4.3. 7 questions, 3 points each 21 points possible. Quiz Questions. Related Rates. Section 4.6.

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Warm-Up: January 7, 2013

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  1. Warm-Up: January 7, 2013 • Write a differential formula that estimates the change in volume of a sphere when the radius changes from r to r+dr.

  2. Homework Questions?

  3. Quiz Results: 4.1-4.3 • 7 questions, 3 points each • 21 points possible

  4. Quiz Questions

  5. Related Rates Section 4.6

  6. What are related rates? • A rate is a ratio of the change in one variable to the change in another variable. • Typically the second variable is time, t. • Related rates are two (or more) rates that can be related in a single equation.

  7. Example 1 – p. 238 #16 • Sand falls from a conveyor belt at the rate of 10 m3/min onto the top of a conical pile. The height of the pile is always three-eights of the base diameter. How fast are the (a) height and (b) radius changing when the pile is 4 m high? Give your answers in cm/min.

  8. Example 1 – p. 238 #16

  9. Related Rate Problems • Draw a picture and name the variables and constants. • Write down the numerical information. • Write down what we are asked to find. • Write a single equation that relates the variables. • Differentiate with respect to t. • Evaluate.

  10. Assignments • Read Section 4.6 (pages 232-236) • Page 237 Exercises #1-13 odd • Page 237 Exercises #15-25 odd • Page 237 Exercises #27-35 odd

  11. Warm-Up: January 8, 2013 • A spherical balloon is being inflated. The air pump delivers a constant 12 cm3/s. How fast is the radius increasing when the radius is 8 cm?

  12. Continuing 4.6 notes

  13. Example 2 – p. 239 #22 • A balloon is rising vertically above a level, straight road at a constant rate of 1 ft/sec. Just when the balloon is 65 ft above the ground, a bicycle moving at a constant rate of 17 ft/sec passes under it. How fast is the distance between the bicycle and balloon increasing 3 sec later?

  14. Example 2 – p. 239 #22

  15. Assignments • Read Section 4.6 (pages 232-236) • Page 237 Exercises #1-13 odd • Page 237 Exercises #15-25 odd • Page 237 Exercises #27-35 odd

  16. January 9, 2013 • You have all of class to work on your 4.6 assignments. • Stay in your assigned seat until after Mr. Szwast has checked your homework.

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