percal quiz
QUIZ 5 Professor: Ms. Chowdhury MATH 115 Fall 2018 Name___________________________________ Date ________________ INSTRUCTIONS
The quiz is worth 55 points. There are 20 multiple choice (2 points) and 5 (3 points) short answer problems.
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.
You must show all of your work for the short 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.
Please type your answers on the table provided in the answer sheet, then create a separate document containing your work. Scanned handwritten work is also acceptable. Be sure to include your name in the document. Review instructions for submitting your quiz in the Unit Quizzes Module.
If you have any questions, please contact me by e-mail.
Be sure to sign and date the honor statement also found on the answer sheet, or your quiz will not be valid.
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
A vector v has initial point P1 and terminal point P2. Write v in terms of ai + bj.
1) P1 = (6, 1); P2 = (-3, -3)
A) v = 4i + 9j B) v = 9i + 4j C) v = -4i - 9j D) v = -9i - 4j
Draw a sketch to represent the vector. Refer to the vectors pictured here.
2) b + c
A) B)
Find the angle between the given vectors.
3) u = i - j, v = 4i + 6j
A) 11.3° B) 101.3° C) 106.1° D) -11.3°
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Find the area of the triangle having the given measurements. Round to the nearest square unit.
4) C = 100°, a = 3 yards, b = 4 yards
A) 98 square yards B) 6 square yards C) 1 square yards D) 24 square yards
Find the magnitude v of the vector.
5) v = 5i - 4j
A) 3 B) 1 C) 41 D) 9
Find the specified vector or scalar.
6) u = -6i - 2j, v = 11i + 7j; Find u - v.
A) -17i - 9j B) -18i + 5j C) 5i + 5j D) -19i + 5j
7) v = 3i + 5j; Find -8v .
A) 32 B) 8 34 C) -8 34 D) 32i
Find the unit vector having the same direction as v.
8) v = -8j
A) u = -j B) u = 64j C) u = - 1 8 j D) u = -8j
9) v = -4i - 3j
A) u = - 5 4 i -
5 3 j B) u =
3 5
i + 4 5 j C) u = -
4 5 i -
3 5 j D) u = -20i - 15j
Perform the indicated operation.
10) u = 4i + j, v = -8i - 8j, w = i - 6j; Find v - (u - w).
A) -11i + 15j B) -11i - 15j C) -3i - 13j D) -13i - 3j
Solve the equation on the interval [0, 2 ).
11) -tan2 x sin x = -tan2 x
A) , 2 , 2 B) , 2 C) 0, D)
0, , 2
Solve the equation on the interval [0, 2 ).
12) 2 cos2 x + sin x - 2 = 0
A) 3 , 2
3 B) 0, ,
6 , 5
6 C) 6 , 5
6 D) 2 , 3
2 ,
3 , 2
3
13) cos2 x + 2 cos x + 1 = 0
A) 4 , 7
4 B) C) 2 , 3
2 D) 2
2
14) cos x = sin x
A) 34 , 7
2 B) 3 4
, 5 4 C) 4
, 7 4 D) 4
, 5 4
Solve the problem.
15) A force is given by the vector F = 3i + 6j. The force moves an object along a straight line from the point (5, 7) to the point (19, 18). Find the work done if the distance is measured in feet and the force is measured in pounds.
A) -108 foot-pounds B) -24 foot-pounds C) 117 foot-pounds D) 108 foot-pounds
Solve the triangle. Round lengths to the nearest tenth and angle measures to the nearest degree.
16)
8 5
4
A) A = 30.8°, B = 125.1°, C = 24.1° B) A = 125.1°, B = 24.1°, C = 30.8°
C) A = 30.8°, B = 24.1°, C = 125.1° D) A = 125.1°, B = 30.8°, C = 24.1°
Two sides and an angle (SSA) of a triangle are given. Determine whether the given measurements produce one triangle, two triangles, or no triangle at all. Solve each triangle that results. Round lengths to the nearest tenth and angle measures to the nearest degree.
17) B = 102°, b = 5, a = 23
A) A = 50°, C = 27°, c = 30 B) A = 52°, C = 27°, c = 32
C) A = 51°, C = 27°, c = 28 D) no triangle
18) A = 30°, a = 4, b = 8
A) B = 60°, C = 90°, c = 6.9 B) B = 60°, C = 60°, c = 6.9
C) B = 90°, C = 60°, c = 6.9 D) no triangle
Use the given vectors to find the specified scalar.
19) u = 9i + 7j and v = 11i - 7j; Find u · v.
A) -49 B) 148 C) 50 D) 99
Write a vector v in terms of i and j whose magnitude v and direction angle are given.
20) v = 7, = 225°
A) v = - 7 2 2
i - 7 2 2
j B) v = - 7 2
i - 7 3 2
j
C) v = 7 2 2
i + 7 2 2
j D) v = - 7 3 2
i - 7 2
j
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SHORT ANSWER. You must show all your work to receive full credit.
Solve the problem.
21) The magnitude and direction of two forces acting on an object are 35 pounds, N45°E, and 55 pounds, S30°E, respectively. Find the magnitude, to the nearest hundredth of a pound, and the direction angle, to the nearest tenth of a degree, of the resultant force.
22) Two airplanes leave an airport at the same time, one going northwest (bearing 135°) at 419 mph and the other going east at 347 mph. How far apart are the planes after 4 hours (to the nearest mile)?
23) To find the distance AB across a river, a distance BC of 1018 m is laid off on one side of the river. It is found that B = 109.8° and C = 14.3°. Find AB. Round to the nearest meter.
24) Find the work done by a force of 7 pounds acting in the direction of 42° to the horizontal in moving an object 4 feet from (0, 0) to (4, 0).
25) The distance from home plate to dead center field in Sun Devil Stadium is 410 feet. A baseball diamond is a square with a distance from home plate to first base of 90 feet. How far is it from first base to dead center field?
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