uiz 3 MATH 108 Trigonometry and Analytical Geometry Name _______________ Dr. Chowdhury Fall 2016 Date ____________________ INSTRUCTIONS The quiz is worth 50 points. There are 5 multiple choice (4 points) and 5 long answers (6 points, with work) 1.)This quiz is open book and open notes, and you may take as long as you like on it provided that you submit the quiz no later than the due date posted in our course schedule of the syllabus. You may refer to your textbook, notes, and online classroom materials, but you may not consult anyone. 2.) You must show all of your work for the long answers to receive full credit. If you do not show work, you may earn only partial or no credit at the discretion of the professor.Showing work for the other questions is not mandatory, but recommended so that if needed I can see where your mistakes were made. 3.) Please type or handwrite your answers on the provided answer sheet. You must show your written work for #6-10 only on the answer sheet. Be sure to include your name in the document. Review instructions for submitting your quiz in the Unit Quizzes Module. 4.) Finally, be sure to sign the honor statement. Without this your quiz may be invalidated. If you have any questions, please contact me by e-mail. MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Describe the graph of the polar equation. 1) 9r cos + r sin = 3 A) Line with slope 3 and y-intercept (0, 9) C) Parabola with vertex (9, 3) opening upward B) Line with slope -9 and y-intercept (0, 3) D) Vertical line passing through (9, 0) Use the figure provided to find the requested expression. 2) Vectors u, v, and w are determined by the sides of ABC below: Find an expression for v in terms of u and w. A) w - u B) u + w C) -u - w 1 D) u - w Calculate the unit vector u = (cos )i + (sin )j for the given direction angle. 3) = 4 A) 1 3 i+ j 2 2 B) 2 2 i+ j 2 2 C) 2 2 ij 2 2 D) 3 1 i+ j 2 2 Match the given equation with one of the graphs. 4) 2x2 + 4y2 - 24x + 24y + 100 = 0 A) B) C) D) Tell whether the given equation describes a parabola, an ellipse, or a hyperbola. 7 5) r = 1 - sin A) Hyperbola B) Ellipse C) Parabola SHORT ANSWER. You must show all your work to receive full credit. Find the center and the radius of the circle. 6) x2 + y2 + 18x - 10y + 106 = 64 Solve. 7) A sign board has an area of 204 m 2 . The length of the diagonal is 2 433 m. What are the dimensions of the sign? Solve the problem. 8) A cross-section of an irrigation canal is a parabola. If the surface of the water is 45 feet wide and the canal is 39 feet deep at the center, how deep is it 1 feet from the edge? Solve. 9) The roof of a building is in the shape of the hyperbola y2 - x2 = 55, where x and y are in meters. Refer to the figure and determine the height h of the outside walls. A=3 m 10) A railroad tunnel is shaped like a semi-ellipse. The height of the tunnel at the center is 25 ft and the vertical clearance must be 20 ft at a point 12 ft from the center. Find an equation for the ellipse. 3