1. Write the equation below in its equivalent exponential form. 2. Write the first four terms of the sequence whose general term is given below: a = 4(3n 1) 3. Use the addition method to solve the system below: 4x + 27y = 27 8x 3y = -3 4. In the right triangle ABC below, C is the right angle, and two sides are given. Find sin ? of the given angle. The sin of an angle in a right triangle is equal to the ratio of the opposite side to the hypotenuse. 5. Find the reference angle for 6. Find the area of a triangle with these measurements: C = 100º, = 1 yard, and = 8 yards. Round your answer to the nearest square unit. 7. Solve the right triangle in the figure below in which A = 51.9º and c = 51.2. Round lengths to one decimal place, and express angles to the nearest tenth of a degree. 8. Plot the complex number -3 + 6i. 9. Write the expression below as the cosine of an angle, knowing that the expression is the right side of the formula for with particular values for ? and ?. 10. Solve the equation below on the interval . 11. Find the exact value of the expression 12. Find the rectangular coordinates of the point whose pola
r coordinates are (3, -270º) 13. Complete the identity below: 14. Using the vectors given below, find 15. If the sequence below is a geometric sequence, find the common ratio. 16. Graph the solution set of the system of inequalities below. 17. Find the maximum and minimum values of the given objective function of a linear programming problem. The figure illustrates the graph of the feasible points. Objective function: z = 5x + 8y 18. Use Gauss-Jordan elimination to solve the system x y + 3z = 0, 2x + 2y z = 9, and x + 5y 10z = 4 19. Find the product of the matrices and . 20. Compute the determinant 21. Write an equation for the ellipse with vertices (2, 2), (4, 2), (3, -1) and (3, 5). 22. Find the foci of the hyperbola 23. What is the standard form equation of a parabola with directrix = -2 and focus (2, 0)? 24. Eliminate the parameter from the parametric equations and 25. Determine what kind of conic is represented by the equation 26. Estimate the following limit using a table: 27. Use properties of limits to compute the following limit exactly. 28. Use the limit definition to compute f(x) if f(x) = 6x 9.