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Comprehensive Review of Mathematical Concepts and Applications

This document covers a detailed review of various mathematical concepts including equations, trigonometry, area calculations, and graphing functions. It includes step-by-step solutions for equations, the analysis of polar curves, and real-world applications such as area and population growth models. The review is organized into multiple parts, each focusing on specific mathematical problems and concepts. Students can use this review as a guide for preparing for examinations or to strengthen their understanding of key topics.

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Comprehensive Review of Mathematical Concepts and Applications

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  1. #7-9 on the board! Final Review Part 1

  2. Final Review Part 1 continued • 10. y = ±√(x-8) • 11. 500,000 meters squared • 12. On the board

  3. Final Review Part 1 continued

  4. Final Review Part 2

  5. Final Review Part 2 Continued • 11. 1 • 12. 1/2 • 13. -2 • 14. 0 • 15. -3√2 -2√3 • 16. -3√3/2 • 17. • SinӨ=5/13 cscӨ=13/5 secӨ=-13/12 • tanӨ=-5/12 cotӨ=-12/5 20) To be drawn on the board

  6. #1-6 to be done on the board. 7. 5.29rad, 4.13 rad 8. 67.98, 292.02 degrees 9. pi/2, 3pi/2, 0 10. 30, 330 degrees 11) b =11.05 units, A = 35 degrees, a = 36.50 units. 12) A=26.38 degrees, B = 36.34 degrees, C = 117.28 degrees. Final Review Part 3

  7. 13. a=23.38 units, B = 29.44 degrees, C = 100.56 degrees 14. No Triangle 15. B1= 70.44 degrees, C1 = 51.56 degrees, c1 = 4.17 units. B2 = 109.56 degrees C2 = 12.44 degrees c2 = 1.14 units 16. B = 38.02 degrees C = 1.98 degrees c = 2.58 units 17. 22.45 units squared 18. 28.19 units squared 19. 19.453 KM 20. 138.8 miles Final Review part 3 Continued

  8. 1. 1/8 2. 10200 3. a) 0.8888 b) 8/9 4. Arithmetic d =-7 5. Not Arithmetic 6. 200, 20, 2, 0.2, 0.02, 0.002 7. 1301.01 8-10) to be drawn on the document camera. 11) (0, 3) 12) (-3, 11pi/4) (-3, -5pi/4) (3, 7pi/4) (3, -pi/4) Final Review Part 4

  9. Final Review Part 4 continued 13. • 14. A. Limacon-looped B. Symmetric over polar axis

  10. 2. Initial Population 3. y=15.13sin(0.09x-1.08)+16.50, How far off the ground the ride is raised. 4. y = 5.57(1.04)^x, 66.64 5. Max length = 8, Petals = 8, The number in front of the trig function is the max petal length. The number infront of theta is even so 4*2 = number of petals. 6. Graph to be drawn on board. Moves right 2 and up 3. Final Review Part 5

  11. 7. 10.36, 5% decrease of insulin per minute. 8. The power function best fits the data, because the coefficient of correlation of the power function is closest to 1. 34.69 9. [-42, 7), [-4, 16), 4 10. x = 75 yds, Area = 15000 yds squared, L= 150 yds, w = 100 yds. 11. $2,460.75, 8.4 years, 7.3% 12. 36mg Final Review Part 5 Continued

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