Find the solutions of each equation on the interval [0, 2). 3 3 sin ( +...

 

Transcribed Image Text:

Find the solutions of each equation on the interval [0, 2). 3 3 sin ( + x) + sin( 3 + x) - (SHOW WORK) --2 Directions: Answer the questions below. Make sure to show your work and justify all your answers. 2. The following table shows the estimated populations and annual growth rates for four countries in the year 2000. Find the expected population of each country in 2025, assuming their annual growth rates remain steady. Country Australia China Mexico Zaire (SHOW WORK) Population in 2000 19,169,000 1,261,832,000 100,350,000 51,965,000 Growth Rate 0.6% 0.9% 1.8% 3.1% 5. Astronomers classify stars according to their brightness by assigning them a stellar "magnitude." The higher the magnitude the dimmer the star. The dimmest stars visible to the naked eye have stellar magnitudes of 6. The table below shows the relative brightness of different stellar magnitudes. Stellar Magnitude Relative Brightness 1 2 100 40 3 16 4 5 6 6.3 2.5 1 a. Find an equation that gives the relative brightness in terms of stellar magnitude. b. Use this equation to find the relative brightness of a star with magnitude 9. (SHOW WORK) 6. A restaurant offers a lunch special in which a customer can select from one of the 7 appetizers, one of the 10 entrees, and one of the 6 desserts. How many different lunch specials are possible? (SHOW WORK) Divide using long division. 7. -3x5-22x4-13x+39x +14x 6 x+6x-3x -5 (SHOW WORK) Condense each expression. 8. 5log,x-log, (8-x) 9. A gear of radius 6.1 cm turns at 11 revolutions per second. What is the linear velocity of the gear in meters per second? (SHOW WORK) Directions: Answer the questions below. Make sure to show your work and justify all your answers. Use the graph to determine the domain and range of the relation, and state whether the relation is a function. 10. A tan 9x -tan 5x 11. Simplify 1 + tan 9x tan 5x (SHOW WORK) Find each f(c) using synthetic substitution. 12.f(x) = 5x + 10x+ + 3x + 8x - 6x-3; c = 3 (SHOW WORK) 13. Suppose is an angle in the standard position whose terminal side is in Quadrant I and sin 8= 84 of the five remaining trigonometric functions of 0. 85- Find the exact values 14. A truck driver travels at 59 miles per hour. The truck tires have a diameter of 30 inches. What is the angular velocity of the wheels in revolutions per minute (rpm)? (SHOW WORK) Directions: Answer the questions below. Make sure to show your work and justify all your answers. 15. Determine the zeros for and the end behavior of f(x) = x(x-4) (x+2). 16. Verify sin(180- 8) = sin e (SHOW WORK) 17. The hourly temperature at Portland, Oregon, on a particular day is recorded below. 1 A.M. 46 1 P.M. 72 2 3 4 5 8 9 10 44 43 41 40 43 46 52 2 3 4 5 6 7 8 9 10 11 74 75 75 77 75 74 70 62 55 51 6 7 40 41 ||||||| 11 65 12 Noon 69 12 Midnight 48 a. Find the amplitude of a sinusoidal function that models this temperature variation. (77 -40)/2 = 37/2 = 18.5. b. Find the vertical shift of a sinusoidal function that models this temperature variation. c. What is the period of a sinusoidal function that models this temperature variation? d. Use t = 0 at 5 P.M. to write a sinusoidal function that models this temp. variation. e. What is the model's temperature at 10 A.M.? Compare this to the actual value? Find the solutions of each equation on the interval [0, 2). 3 3 sin ( + x) + sin( 3 + x) - (SHOW WORK) --2 Directions: Answer the questions below. Make sure to show your work and justify all your answers. 2. The following table shows the estimated populations and annual growth rates for four countries in the year 2000. Find the expected population of each country in 2025, assuming their annual growth rates remain steady. Country Australia China Mexico Zaire (SHOW WORK) Population in 2000 19,169,000 1,261,832,000 100,350,000 51,965,000 Growth Rate 0.6% 0.9% 1.8% 3.1% 5. Astronomers classify stars according to their brightness by assigning them a stellar "magnitude." The higher the magnitude the dimmer the star. The dimmest stars visible to the naked eye have stellar magnitudes of 6. The table below shows the relative brightness of different stellar magnitudes. Stellar Magnitude Relative Brightness 1 2 100 40 3 16 4 5 6 6.3 2.5 1 a. Find an equation that gives the relative brightness in terms of stellar magnitude. b. Use this equation to find the relative brightness of a star with magnitude 9. (SHOW WORK) 6. A restaurant offers a lunch special in which a customer can select from one of the 7 appetizers, one of the 10 entrees, and one of the 6 desserts. How many different lunch specials are possible? (SHOW WORK) Divide using long division. 7. -3x5-22x4-13x+39x +14x 6 x+6x-3x -5 (SHOW WORK) Condense each expression. 8. 5log,x-log, (8-x) 9. A gear of radius 6.1 cm turns at 11 revolutions per second. What is the linear velocity of the gear in meters per second? (SHOW WORK) Directions: Answer the questions below. Make sure to show your work and justify all your answers. Use the graph to determine the domain and range of the relation, and state whether the relation is a function. 10. A tan 9x -tan 5x 11. Simplify 1 + tan 9x tan 5x (SHOW WORK) Find each f(c) using synthetic substitution. 12.f(x) = 5x + 10x+ + 3x + 8x - 6x-3; c = 3 (SHOW WORK) 13. Suppose is an angle in the standard position whose terminal side is in Quadrant I and sin 8= 84 of the five remaining trigonometric functions of 0. 85- Find the exact values 14. A truck driver travels at 59 miles per hour. The truck tires have a diameter of 30 inches. What is the angular velocity of the wheels in revolutions per minute (rpm)? (SHOW WORK) Directions: Answer the questions below. Make sure to show your work and justify all your answers. 15. Determine the zeros for and the end behavior of f(x) = x(x-4) (x+2). 16. Verify sin(180- 8) = sin e (SHOW WORK) 17. The hourly temperature at Portland, Oregon, on a particular day is recorded below. 1 A.M. 46 1 P.M. 72 2 3 4 5 8 9 10 44 43 41 40 43 46 52 2 3 4 5 6 7 8 9 10 11 74 75 75 77 75 74 70 62 55 51 6 7 40 41 ||||||| 11 65 12 Noon 69 12 Midnight 48 a. Find the amplitude of a sinusoidal function that models this temperature variation. (77 -40)/2 = 37/2 = 18.5. b. Find the vertical shift of a sinusoidal function that models this temperature variation. c. What is the period of a sinusoidal function that models this temperature variation? d. Use t = 0 at 5 P.M. to write a sinusoidal function that models this temp. variation. e. What is the model's temperature at 10 A.M.? Compare this to the actual value?