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Unformatted text preview: MA 166 Exam 1 01 Spring 2011 NAME
10—DIGIT PUID
REC. INSTR. ______.________ REC. TIME LECTURER INSTRUCTIONS: 1. There are 7 different test pages (including this cover page). Make sure you have a
complete test. 2. Fill in the above items in print. Also write your name at the top of pages 2—7. 3. Do any necessary work for each problem on the space provided or on the back of
the pages of this test booklet. Circle your answers in this test booklet. N0 partial
credit will be given, but if you show your work on the test booklet, it may be used in borderline cases.
4. No books, notes, calculators or any electronic devices may be used on this exam. 5. Each problem has its own points assigned. The maximum possible score is 100 points. 6. Using a #2 pencil, ﬁll in each of the following items on your answer sheet: (a) On the top left side, write your name (last name, ﬁrst name), and ﬁll in the little
circles. (b) On the bottom left side, under SECTION NUMBER, put 0 in the ﬁrst column
and then enter the 3—digit section number. For example, for section 016 write 0016. Fill in the little circles. (c) On the bottom, under TEST/QUIZ NUMBER, write 01 and ﬁll in the little
circles. ' (d) On the bottom, under STUDENT IDENTIFICATION NUMBER, write in your
10—digit PUID, and ﬁll in the little circles. ' (e) Using a #2 pencil, put your answers to questions 1—12 on your answer sheet by
ﬁlling in the circle of the letter of your response. ‘Double check that you have ﬁlled
in the circles you intended. If more than one circle is ﬁlled in for any question,
your response will be considered incorrect. Use a #2 pencil. 7. After you have ﬁnished the exam, hand in your answer sheet _an_d your test booklet to
your recitation instructor. MA 166 Examl 01 Spring 2011 Name:_____________ Page 2/7 (6 pts) 1. The equation of the sphere that passes through the origin with center (1,2,3) is:
A. (x~—1)2+(y2)2+(z—3)2=6
B. (m—1)2+(y—2)2+(z—3)2=14
C. x2+y2+22=14
D. ($+1)2+ (y+2)2+ (2+3)2 :6
E. ($+1)2+ (y+2)2+ (z+3)2 = 14 (8 pts) 2. For What values of b are the vectors (—6, b, 2) and (b, ()2, b) orthogonal?
A. 0,1 and ~1
B. 0,3 and —3
C. 0,2 and —2
D. 2x/2 and ~2x/2
E. 1 and 2 MA 166 Examl 01 Spring 2011 Name: Page 3/7 (8 pts) 3. The vector projection pro jab of a vector b = (5, 0) onto another vector a = (3, ~11) (8 NS) 18: A. §
5
5
' 3(3) _4>
E
5 (5,0) <39 _4> 3
55(5) 0) 3
— 41 4. A sled is pulled 100 In along a horizontal path by a force of 30 N acting at an angle of 30 degree above the horizontal. The work done by the force is A.
B.
C.
D.
E. 1500 J
150 L
150W? J
150%3' J
mom/37 J MA 166 Exam 1 01 Spring 2011 Name: ______________ Page 4/7
(8 pts) 5. Which of the following is a vector orthogonal to the plane through the points P(2, 1, 5),
Q(—1,3,4), R(3,0,6)?
A. 2i + 3j + 2k
B. i ~j + k
C. —2i — 3j + k
D. 2i + 4j + 2k
E. 3i +j — 3k (8 pts) 6. Find the values of a: such that the vectors a = (1, 0, cc), b = (2, as, 1),
c = (6,1,5) are coplanar, that is to to say, they lie on a plane. A. 4 and 1/8
B. 3 and 2 C. 1/6 and 1
D. 1/2 and —1
E. 0 and 2 MA 166 Examl 01 Spring 2011 Name: Page 5/7 (8 pts) 7. Find the area of the region enclosed by the curves :1: 2 4y —— 3/2 and a: 2 2y —— 3. A.
B.
C.
D. 64/5
32/3
16 15/7 E. 8/3 (8 pts) 8. Find the formula for the volume of the solid obtained by rotating the region bounded
by the curves 3/ = 6—3”, y = 1 and :1: 2: 4 about the line y = 2 A. (10 pts) 9. Find the volurne of the solid obtained by rotating about the yaXis the region bounded byy=3sc2—x3 andyzO. scam? W/6
8W/5
16W/5
243n/20
243w/10 (10 pts) MA 166 Examl 01 Spring 2011 Name:__________ Page 6/7 10. Consider the following tank in the shape of a triangular prism.
The top is a rectangle with sides W 2: 3m and L 2 10m. Each vertical cross section
is an inverted triangle with height 6m (and with base of length 3m). It is completely filled with water with density 1000kgm”3. Find the work done nec
essary to pump all the water just out of the tank. (Warning: Carry out the computation setting the gravitational acceleration
g to be lOms‘2.) A. 18 x 105J
36 x 105J
2 x 104J
. 9 x MW
18 X 104J F1150?“ MA 166 Examl 01 Spring 2011 Name:____________ Page 7/7 (8 pts) 11. Find the following indeﬁnite integral /sin_l(593)dx A. :03 332153: + C B. m2 si5n 5:1: + 2:1: (32058 52: + C C. 002 Sign 52: + 25002053551: + 13—5sin 593+ O
D. :02 si5n5m + 21:20:51: _ 12753m5m+0
E. $3 cgs 53: + 902 8151152: + C (10 pts) 12. Evaluate the following integral
\/§ M1 (g) l ...
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