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Homework, Page 562

Homework, Page 562. 1. Homework, Page 562. 5. Homework, Page 562. Let A = (2, –1), B = (3, 1), C = (–4, 2), and D = (1, –5). Find the component form and magnitude of the vector. 9. Homework, Page 562. 13. Homework, Page 562. Convert the polar coordinates to rectangular coordinates.

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Homework, Page 562

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  1. Homework, Page 562 1.

  2. Homework, Page 562 5.

  3. Homework, Page 562 Let A = (2, –1), B = (3, 1), C = (–4, 2), and D = (1, –5). Find the component form and magnitude of the vector. 9.

  4. Homework, Page 562 13.

  5. Homework, Page 562 Convert the polar coordinates to rectangular coordinates. 17.

  6. Homework, Page 562 Rectangular coordinates of point P are given. Find all polar coordinates of P that satisfy: (a) 0 ≤θ≤2π (b) –π≤θ≤π (c) 0 ≤ θ≤ 4π 21.

  7. Homework, Page 562 Eliminate the parameter t and identify the graph. 25.

  8. Homework, Page 562 Eliminate the parameter t and identify the graph. 29.

  9. Homework, Page 562 Refer to the complex number shown in the figure. 33. If z1 = a + bi, find a, b, and |z1|.

  10. Homework, Page 562 Write the complex number in standard form. 37.

  11. Homework, Page 562 Write the complex number in trigonometric form where 0 ≤ θ≤ 2π. Then write three other possible trigonometric forms for the number. 41.

  12. Homework, Page 562 Use DeMoivre’s Theorem to find the indicated power of the complex number. Write the answer in (a) trigonometric form and (b) standard form. 45.

  13. Homework, Page 562 Find and graph the nth roots of the complex number for the specified value of n. 49. Continued on next slide.

  14. Homework, Page 562 49. Cont’d

  15. Homework, Page 562 49. Continued

  16. Homework, Page 562 Decide whether the graph of the polar function appears among the four. 53. b.

  17. Homework, Page 562 Decide whether the graph of the polar function appears among the four. 57. Not shown.

  18. Homework, Page 562 Convert the polar equation to rectangular form and identify the graph. 61.

  19. Homework, Page 562 Convert the rectangular equation to polar form and graph the polar equation. 65.

  20. Homework, Page 562 Analyze the graph of the polar curve. 69. Domain: All real numbers Range: –3≤ r ≤ 7 Continuity: Continuous Symmetry: Symmetric about the y-axis. Boundedness: Bounded Maximum r-value: 7 Asymptotes: None

  21. Homework, Page 562 73.

  22. Homework, Page 562 73.

  23. Homework, Page 562 77. A 3,000-lb car is parked on a street that makes an angle of 16º With the horizontal. (a) Find the force required to keep the car from rolling down the hill. (b) Find the component of the force perpendicular to the ground.

  24. Homework, Page 562 81. The lowest point on a Ferris wheel of radius 40-ft is 10-ft above the ground, and the center is on the y-axis. Find the parametric equation for Henry’s position as a function of time t in seconds, if his starting position (t = 0) is the point (0, 10) and the wheel turns at a rate of one revolution every 15 sec.

  25. Homework, Page 562 85. Diego releases a baseball 3.5-ft above the ground with an initial velocity of 66-fps at an angle of 12º with the horizontal. How many seconds after the ball is thrown will it hit the ground? How far from Diego will the ball be when it hits the ground? The ball hits the ground about 1.06 secs after it is thrown, 68.431 ft from Diego.

  26. Homework, Page 562 89. A 60-ft radius Ferris wheel turns counterclockwise one revolution every 12 sec. Sam stands at a point 80 ft to the left of the bottom (6 o’clock) of the wheel. At the instant Kathy is at 3 o’clock, Sam throws a ball with an initial velocity of 100 fps and an angle of 70º with the horizontal. He releases the ball at the same height as the bottom of the Ferris wheel. Find the minimum distance between the ball and Kathy.

  27. Homework, Page 562 89. Continued Minimum distance between the ball and Kathy is about 17.654 feet

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