CA Review Calculator COMPLETE ON A SEPARATE SHEET OF PAPER. c) Suppose the price tag were $5.00, how many pony tail holders would you get?

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1 CA Review Calculator Name # COMPLETE ON A SEPARATE SHEET OF PAPER Precalculus Date Period 1. Grocer s Mart sells the following pony tail holders: 15 holders for $ holders for $ holders for $3.00 a) Define the variables and use the regression capabilities of a graphing utility to write a quadratic equation for the data. b) If the store sold 100 holders, how much do you think they would cost? c) Suppose the price tag were $5.00, how many pony tail holders would you get? d) The price-intercept is the price when the package contains zero holders. What does the priceintercept equal in this model? Why do you think that it is greater than zero? e) Graph the curve in a suitable domain (label the axes). f) State the vertex and explain its meaning. 2. I own a lawn mower (it s a very expensive one) that I purchased new 3 years ago for $2,000. The mower depreciates at a rate of 8%, continuously. a) Define the variables and write an exponential equation that represents the data. b) Use the equation to find the mower s current value. c) When will the mower be worth $250? d) Will the mower ever be worth $0? (Justify your answer mathematically) 3. I have a cardboard paper that I need to make a box from. Its dimensions are 22 X 18 with equal squares cut out of the corners. a) Write a polynomial equation that expresses the volume of the box as a function of x. b) If we want the volume to be 500 cubic inches, what are the possible values of x? c) Using your result from b, state the possible new dimensions of the box.

2 4. My husband owns a chocolate fountain that has a 500 liter capacity. Yum! It contains 25 liters of a 40% milk chocolate flavor. He adds x liters of a 90% chocolate solution. a) Write the concentration, C, of the chocolate solution as a function of x. Show your work. b) Sketch the graph and explain what the concentration of chocolate appears to approach as the tank is filled to its maximum. c) Suppose the fountain could hold an infinite amount of chocolate, what would the maximum concentration level be? d) If we only want the concentration level to be 60%, how much of the 90% solution do we add to the original 25 liters? 5. A wheel has a diameter of 8 inches. It can travel at 25 miles per hour. a) Find the rotational speed of the wheel in revolutions per minute. b) What should the radius of the wheel be to achieve a speed of 30 miles per hour if the angular velocity is now 1700 revolutions per minute? 6. You go up in a ferris wheel that is 3 feet off the ground. The diameter of the wheel is 108 feet. It takes you 38 seconds to get to the top after they get the last car filled and they start the ride. You make a full revolution every 2 minutes. a) Write the equation of the sinusoid. b) How high will you be after 5 ¾ minutes? c) When will you be 80 feet off of the ground and going down for the 10 th time? C º 47 feet 39 feet A B Find AB.

3 8. Find the distance between City A (N 32º ) and City B (N 49º 38 9 ). Assume the earth is a sphere of radius 4000 miles and the cities are on the same meridian. 9. An airplane has an airspeed of 750 miles per hour at a bearing of N 40 E. If the wind velocity is 30 miles per hour from the southeast. Find the groundspeed and direction of the plane. 10. Verify: 1 cot x csc x sec x cos x 11. Verify: 1 1 cos csc cot sin 12. Write an equivalent expression for functions greater than 1. 4 cos x that does not contain powers of trigonometric 13. Simplify: 3 i Find the sixth roots of Find the cube roots of 1 3i. 16. Graph two full cycles of: y 1 3cos 2x and identify the amplitude, period, phase shift, and vertical shift. In addition, rewrite the function in terms of sine.

4 17. Graph two full cycles: y csc x º 39º 2.35 miles Find the altitude of the triangle. 20. One day in the middle of summer, the high tide occurred at 5:22 a.m. You saw a scientist measuring the depth of the water from a small pier and you asked her, Hey, what is the depth of the water? The very intelligent scientist yelled, 22 feet! You quickly jotted the time and depth down, knowing that you may be able to do some calculations later in the day. Knowing that the depth of the water is a sinusoidal function with a period of ½ a lunar day (which is approximately 12 hours and 24 minutes) at 11:34 a.m. you found the scientist making a castle in the sand and ordered her to measure the depth at the same exact location she had earlier in the morning. She measured and found the depth to be 14.5 feet. You decided to create a sinusoidal function of time. a. Write the sinusoidal equation to represent the situation. b. What was the approximate depth at 2:00 a.m. and 9:30 p.m.? c. What is the first time on that day that the water is at a depth of 15 feet?

5 21. Bouncing Spring Problem: A weight attached to the end of a long spring is bouncing up and down. As it bounces, its distance from the floor varies sinusoidally with time. You start a stopwatch. When the stopwatch reads 0.4 seconds, the weight first reaches a high point 58 cm above the floor. The next low point, 38 cm above the floor, occurs at 1.6 seconds. a. Sketch a graph of this sinusoidal function. b. Write the particular equation expressing distance from the floor in terms of the number of seconds the stopwatch reads. c. Predict the distance from the floor when the stopwatch reads 16.7 seconds. d. What was the distance from the floor when you started the stopwatch? 22. Find the distance between City A (S 42º ) and City B (N 13º 51 7 ). Assume the earth is a sphere of radius 6378 km and the cities are on the same meridian. 23. Two little rabbits are on the ground in the hot Arizona desert. They are 1850 cm from one another when a humming bird hovers at a point above both of them. The angles of elevation from the rabbits to the owl are 42º and 47º. How high above the ground is the humming bird? Draw a picture of the problem to help you. 24. Three boats are at sea: Missy One, (M1), Missy Two (M2), and Missy Three (M3). The crew of M1 can see both M2 and M3. The angle between the line of sight to M2 and the line of sight to M3 is 45º. If the distance between M1 and M2 is 2 miles and the distance between M1 and M3 is 4 miles, what is the distance between M2 and M3? 25. Flights 104 and 217 are both approaching O Hare International Airport from directions directly opposite one another at an altitude of 2.5 miles. The pilot on flight 104 reports and angle of depression of 17º47 to the tower, and the pilot on flight 217 reports an angle of depression of 12º39 to the tower. Calculate the distance between the planes. 26. Matt measures the angle of elevation of the peak of a mountain as 35º. Susie, who is 1200 feet closer on a straight level path, measures the angle of elevation as 42º. How high is the mountain? 27. An airplanes velocity with no wind is 580 km/h with a bearing of N60ºE. The wind at the altitude of the plane has a velocity of 60 km/h and is coming from the northwest. What is the true speed and bearing of the plane?