Find the solutions of each equation on the interval [0, 2π). - Essay Prowess

Find the solutions of each equation on the interval [0, 2π).

Find the solutions of each equation on the interval [0, 2π).

Find the solutions of each equation on the interval [0, 2π).
1.  (SHOW WORK)                  
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 Population in 2000 Growth Rate Australia 19,169,000 0.6% China 1,261,832,000 0.9% Mexico 100,350,000 1.8% Zaire 51,965,000 3.1%


3. Solve . (SHOW WORK)              
Estimate and classify the critical points for the graph of the function.
  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 1 2 3 4 5 6 Relative Brightness 100 40 16 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.  (SHOW WORK)              
Condense each expression.
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)                  
Use the graph to determine the domain and range of the relation, and state whether the relation is a function.
        11. Simplify . (SHOW WORK)                  
Find each f(c) using synthetic substitution.
12. f(x) =5x5 + 10x4 + 3x3 + 8x2 – 6x – 3; c = 3 (SHOW WORK)              
13. Suppose θ is an angle in the standard position whose terminal side is in Quadrant I and . Find the exact values of the five remaining trigonometric functions of θ.        
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)          
15. Determine the zeros for and the end behavior of f(x) = x(x – 4)(x + 2)4.          
16. Verify . (SHOW WORK)                                      
17. The hourly temperature at Portland, Oregon, on a particular day is recorded below.
  1 A.M. 2 3 4 5 6 7 8 9 10 11 12 Noon 46° 44° 43° 41° 40° 40° 41° 43° 46° 52° 65° 69° 1 P.M. 2 3 4 5 6 7 8 9 10 11 12 Midnight 72° 74° 75° 75° 77° 75° 74° 70° 62° 55° 51° 48°
a. Find the amplitude of a sinusoidal function that models this temperature variation.
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 intersections and unions of the following given sets.
18. Ten students from a school appear in one or more subjects for an inter school quiz competition as shown in the table given below.

  General Knowledge Math Science Acel Barek Carlin Acton Bay Acton Anael Max Anael Max Kai Kai Carl Anael Dario Dario Carlin Barek
Let G represents the set of students appearing for General Knowledge, M represents the set of students appearing for Math, and S represents the set of students appearing for Science.
Find and .            
19. Heather invests $4,900 in an account with a 3.5% interest rate, making no other deposits or withdrawals. What will Heather’s account balance be after 5 years if the interest is compounded 2 times each year? (SHOW WORK)          
20. Find the area of the triangle with a = 19, b = 14, c = 19. Round to the nearest tenth. (SHOW WORK)
Word Questions Section
1. Roland’s Boat Tours sells deluxe and economy seats for each tour it conducts. In order to complete a tour, at least 1 economy seats must be sold and at least 6 deluxe seats must be sold. The maximum number of passengers allowed on each boat is 30 Roland’s Boat Tours makes $40 profit for each economy seat sold and $35 profit for each deluxe seat sold. What is the maximum profit from one tour? (Show work)          
2. The senior class is having a fundraiser to help pay for the senior trip. Selling a box of chocolates yields a profit of $2.45, while selling a box of cookies yields a profit of $2.70. The demand for cookies is at least twice that of chocolates, but the amount of cookies produced must be no more than 550 boxes plus 3 times the number of chocolates produced. Assuming that the senior class can sell every box that they order, how many boxes of each should they order to maximize profit if they cannot order more than 1950 boxes combined? (Show work)          
3. A projectile is fired from ground level with an initial velocity of 35 m/s at an angle of 35° with the horizontal. How long will it take for the projectile to reach the ground? (Show work)            
4. A discus is thrown from a height of 4 feet with an initial velocity of 65 ft/s at an angle of 44° with the horizontal. How long will it take for the discus to reach the ground? (Show work)              
5. A rock is tossed from a height of 2 meters at an initial velocity of 30 m/s at an angle of 20° with the ground. Write parametric equations to represent the path of the rock. (Show work)  
6. An airplane is taking off headed due north with an air speed of 173 miles per hour at an angle of 18° relative to the horizontal. The wind is blowing with a velocity of 42 miles per hour at an angle of S47°E. Find a vector that represents the resultant velocity of the plane relative to the point of takeoff. Let i point east, j point north, and k point up.
(Show work)        
7. A 2600-pound truck is stopped at a red light on a hill with an incline of 25°. Ignoring the force of friction, what force is required to keep the truck from rolling down the hill?
 (Show work)    
8. While doing bicep curls, Tamara applies 155 Newtons of force to lift the dumbbell. Her forearm is 0.366 meters long and she begins the bicep curl with her elbow bent at a 15° angle below the horizontal, in the direction of the positive x-axis. Determine the magnitude of the torque about her elbow. (Show work)          
9. Jenny is sitting on a sled on the side of a hill inclined at 15°. What force is required to keep the sled from sliding down the hill if the combined weight of Jenny and the sled is 90 pounds? (Show work)              
10. Anne is pushing a wheelbarrow filled with mulch to place in her garden. She is pushing the wheelbarrow with a force of 70 N at an angle of 50° with the horizontal. How much work in joules is Anne doing when she pushes the wheelbarrow 25 meters? (Show work)          
11. A baseball player running forward at 3 meters per second throws a ball with a velocity of 20 meters per second at an angle of 20o with the horizontal. What is the resultant speed and direction of the throw? (Show work)          
12. Write 18(cos169° + isin169°) in rectangular form. Round numerical entries in the answer to two decimal places. (Show work)          
13. Find the rectangular coordinates of . (Show work)          
14. Find the distance between (7, ) and (5, ) on the polar plane. (Show work)            
15. A music concert is organized at a memorial auditorium. The first row of the auditorium has 16 seats, the second row has 24 seats, the third row has 32 seats, and so on, increasing by 8 seats each row for a total of 50 rows. Find the number of people that can be accommodated in the sixteenth row. (Show work)          
16. Makya was conducting a physics experiment. He rolled a ball down a ramp and calculated the distance covered by the ball at different times. The ball rolled a distance of 1 foot during the first second, 3 feet during the next second, and so on. If the distances the ball rolled down the ramp each second form an arithmetic sequence, determine the distance the ball rolled down during the fifteenth second. (Show work)          
For each statement, write the null and alternative hypotheses. State which hypothesis represents the claim.
17. John claims that he can list the birth dates of more than 15 students of his class.
The chirp rates n (in number of chirps per minute) of snowy tree crickets and the air temperature T (in degree Fahrenheit) are shown in the table below.
  n 33 54 72 95 112 136 T 45 50 55 65 70 75
18. Use the regression capabilities of a graphing calculator to find the least squares regression line for the data.            
19. A company’s marginal cost function is where x is the number of units. Find the total cost of producing units 144 to 625. (Show work)            
20. A technician can test video player chips at the rate of chips per hour (for ), where t is the number of hours after 9:00 am. How many chips can be tested between 11:00 a.m. to 3:00 p.m.? (Assume for 9:00 a.m.) (Show work)