1. Write the equation below in its equivalent exponential form. lo...

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1. Write the equation below in its equivalent exponential form. logg 25 = x 2. Write the first four terms of the sequence whose general term is given below. an=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 0 of the given angle. B 8 C 3 A 5. Find the reference angle for 571 5w 6. Find the area of a triangle with these measurements: C = 100°, a = 1 yard, and b = 8 yards. Round your answer to the nearest square unit. 7. Solve the right triangle in the figure below in which A = 51.9° and C = 51.2. Round lengths to one decimal place and express angles to the nearest tenth of a degree. B c a A b C 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 cos(a - ß) with particular values for a and B. cos (155°) cos (35°) + sin (155°) sin (35°) 10. Solve the equation below on the interval [0, 2m). cos2x= 2 3 11. Find the exact value of the expression sin-1(-0.5). 12. Find the rectangular coordinates of a point whose polar coordinates are (3, -270°). 13. Complete the identity below. = tan²x 14. Using the vectors given below, find u . V. u = 13i-7j and V = -6i + 7j 15. If the sequence below is a geometric sequence, find the common ratio. 4 8 16 32 64 3 3 3 3 , 3 16. Graph the solution set of the system of inequalities below. y < -X + 8 y>8x-3 - 17. Find the maximum and minimum values of the given objective function of a linear programming problem. The figure below illustrates the graph of the feasible points. Objective function: Z = 5x + 8y y (0.9) (9,9) (0,3) (9, 3) + + x (3.0) 18. Use Gauss-Jordan elimination to solve the system X - y + 3z = 0, 2x + 2y - Z = 9, and + 5y - 10z = 4. 1 2 6 1 19. Find the product of the matrices -8 3 and -1 8 . 4 0 6 2 - 1 20. Compute the determinant 0 3 -3 9 -1 7 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 (x-3)3_(y+2) 1 = 1 23. What is the standard form equation of a parabola with directrix X = -2 and focus (2,0)? 24. Eliminate parameter parametric equations 1-1-1+ and y = cos t - sin the from the t. 25. Determine what kind of conic is represented by the equation r 26. Estimate the following limit using a table. x = X + 2 4 27. Use properties of limits to compute the following limit exactly. lim = x->0 28. Use the limit definition to compute f'(x)

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