project 5 pre calc

Take this test as you would take a test in class. After you are finished, check your work against the answers given in the back of the book. In Exercises 1-6, use the given information to solve the triangle. If two solutions exist, find both solutions. 1. A = 36", B = 98", c = 16 2. a = 4, b = 8, c = 10 3. A = 35", b = 8, c = 12 4. A = 25%, b = 28, a = 18 5. B = 130%, c = 10.1, b = 5.2 6. A = 150%, b = 4.8, a = 9.4 7. Find the length of the pond shown at the right. 3. A triangular parcel of land has borders of lengths 55 meters, 85 meters, and 100 meters. Find the area of the parcel of land. 565 0 9. Find the component form and magnitude of the vector w that has initial point 480 ft (-8, - 12) and terminal point (4. 1). In Exercises 10-13, find (a) 2v + u, (b) u - 3v, and (c) 5u - v. 10. u = (0, -4), v = (-2, -8) 11. u = (-2, -3), v = (-1, -10) Figure for 7 12. u = i - j, v = 61 + 9j 13. u = 2i + 3j, v= -i - 2j 14. Find a unit vector in the direction of v = 7i + 4j. 15. Find the component form of the vector v with v = 12, in the same direction as u = (3, -5). 16. Forces with magnitudes of 250 pounds and 130 pounds act on an object at angles of 45" and -60", respectively, with the positive r-axis. Find the direction and magnitude of the resultant of these forces. 17. Find the dot product of u = (-9, 4) and v = (1, 3). 18. Find the angle between the vectors u = 7i + 2j and v = -4j. 19. Are the vectors u = (6, -4) and v = (2. -3) orthogonal? Explain. 20. Find the projection of u = (6, 7) onto v = (-5, -1). Then write u as the sum of two orthogonal vectors. 21. Write the complex number z = -2 + 2/ in trigonometric form. 22. Write the complex number 100(cos 240" + i sin 240") in standard form. In Exercises 23 and 24, use DeMoivre's Theorem to find the indicated power of the complex number. Write the result in standard form. 23. 3(cos " + i sin 24. (3 -3/)6 25. Find the fourth roots of 128(1 + V/3/). 26. Find all solutions of the equation x4 - 625/ = 0 and represent the solutions graphically