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Analysis

Analysis. October 27, 2015 Happy Tuesday!. One-Minute Question. Write the equation of the curve on the board. Homework??. Questions?. A Deer Problem.

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Analysis

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  1. Analysis October 27, 2015 Happy Tuesday!

  2. One-Minute Question • Write the equation of the curve on the board.

  3. Homework?? • Questions?

  4. A Deer Problem • To avoid a hunter a deer runs in a sinusoidal path that crosses a stream. At time = 2 sec., the deer is 30 feet to the north of the stream and at time = 20 sec., the deer is 10 feet to the south of the stream. If these are maximum distances from the stream that runs east-west, write an equation of the deer’s path.

  5. Extensions • . Where is the deer at t = 0 seconds? • . Where is the deer at t = 13 seconds? • . What are the first 3 times at which the deer will cross the stream?

  6. Answers An equation is: y = 20cos((π/18)(x – 2)) + 10 • . At t = 0 seconds, the deer is 28.79’ north of the stream. • . At t = 13 seconds, he is 3.16’ north of the stream.

  7. Answers To find where he crosses the stream algebraically, let 20cos((π/18)(x – 2)) + 10 = 0 • So 20cos((π/18)(x – 2)) = -10 • cos((π/18)(x – 2)) = -1/2 • cos-1(cos((π/18)(x – 2)) = cos-1(-1/2) • (π/18)(x – 2) = ±2π/3 + 2πk • x – 2 = ±12 + 36k **** Why is 36 right? • X = 14 + 36k or x = -10 + 36k so… • X = {14, 26, 50} so at t = 14, t = 26 and t = 50, the deer crosses the stream.

  8. Another Example • A water wheel 14 feet in diameter is rotating counterclockwise. You start a stopwatch and observe a point P on the rim of the wheel. At t = 2 seconds, P is at its highest, 13 feet above the water. At t = 7 seconds, P is at its maximum depth below the water.

  9. Questions: • . Write an equation of the motion. • . At what time does the wheel first emerge from the water? • . Where is P at time = 6 seconds?

  10. Questions: • . Y = 7cos (π/5(x – 2)) + 6 • . The wheel first emerges from the water at t = 7.861 seconds. • . At time = 6 seconds, P is.3369’ above the water.

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