1. Beth could do p problems in 2 hours and Mollie could do x problems in h hours. How long would they have to work together to finish 400 problems? 2. Use cofactors to evaluate: 3. Find the area of this triangle. 2 41 0 1-2 -1 7 0 -3 4. Find the four fourth roots of -3 + 4i and express the roots in polar coordinates. 5. Express log74 in terms of natural logarithms. Do not find a numerical answer. 7. Find the middle term of (3x - 2y). 9. Solve the following equations given that 0 x < 2n: (a) cosx - sin x = -1 6. (a) Find the pH of a liquid if the concentration of H* is 4.1 x 10-5 mole per liter. (b) The pH of a solution is 3.7. What is the concentration of hydrogen ions (H+) in moles per liter of the solution? - (b) 1 + 3 tan 2x = 0 10. The general form of the equation of an ellipse is 4r + 9 - 64x + 72y + 364 = 0. Write the equation in standard form and give the coordinates of the center, the length of the major axis, and the length of the minor axis. Then graph the ellipse. 13. Find A + B, A B, and 24 where A and B are defined as follows: A = 8. Use a calculator to compute: 11. The general form of the equation of a hyperbola is 16x 2+32x + 2y 1 = 0. Write the equation of this hyperbola in standard form and give the coordinates of the center, the coordinates of the vertices, and the equations of the asymptotes. Then graph the hyperbola. - 1/1 (x ). - 6m 12. Rene and Britta had $500 to buy Buffalo Boys tickets. Goodey Tickets, Inc. was selling tickets for d dollars. Since they arrived at the box office at 6 A.M. they got a discount of x dollars for each ticket. How many Buffalo Boys tickets could they buy? 19. Sketch the graph of y = 2 + 3 sin 20. Write the equations of these trigonometric functions: 65 1444 -270-180-90 90 180 270 14. Expand as the sum of the individual logarithms, each of whose argument is linear: logs 15. Find the sum of this infinite geometric series: 6 6 6 6 + + 4 8 2 16. Sketch the graph of each of the following: (a) y = 2 + 2 sec 8 (b) y = -1 + cot 17. Solve forx: log (x + 3) - log (2x - 3) = 2log 2 ... 18. Show: (6) 10 m 42300/4800 5400 1 -3-4 (9) B - [39] 10 (251/+243) 25xy5 1 + cos 2x csc x sin 2x 12+ 9+--- 6- = COS X 90 180 270 360 450 540