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Unformatted text preview: MA 162 Exam 1 1. What does the pair of equations :1: : 2, y : 7 represent in R3? 7 2. Find the radius of the sphere m2+y2+z2—2m+4y—62:7. 3. Let a=2i+5j—kandb=4i+2j. Find la—b. A.
B.
C.
D.
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a cone. two planes. geese MA 162 Exam 1 Spring 2008 4. Find a unit vector with direction opposite that of < 2, 4, —4 >. 5. Let a=< 1,2,3>andb:< 2,—1,1>. Findaxb. 6. Let a=i+ 2j +k and b :j +k. Find projab, A 94,4) ' ¢ﬁ’¢ﬁ”%ﬁ
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7. Let a=< 4,2,3> andb=< —2,1,2>. Find ab.
A. 11
B. < 2,3, 5 >
C. 0
D.
E [\DIOJOO 8. Let a : i+ 2j + k and b : 2i — 2j + k. Find cos 0, where 6 is the angle between a
and b. 9. The area. between the curves y : $2 + 2x and y = .733 and between a: = 0 and x : 2 is 8 A 2
'§ 4 y=w2+2m 13' g
5 c. _ y=m3 3 D .8. ' 3 a; 10
E. ~— 2 3 MA 162 Exam 1 Spring 2008 10. The area between the curves y2 : :c —— 1 and y : a: — 3 is A /_1((y+3)—(y2+1))dy U3
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{Q 11. What is the distance between the points (w,:1:2) and (:13, a: + 1) for no > 2?
A. x2 — :10 — 1
B. m + 1 — x2 C. Cannot be determined. 2 12. The region bounded by y = 1 — :3 and y = 0 is rotated about the ay—axis. Find the volume of the solid generated.
A. —7r B. ——7r MA 162 Exam 1 Spring 2008 13. The region bounded by a: : 1/2 and a: z 2 is rotated about the line at : 3. Using the
method of cylindrical shells, the volume of the solid generated is A. /02 27r (3331/2 — 533/2) d$ B. /2 27r (6131/2 ~ 2x3/2> d3: 2 27? (3 — :13) da
2 0
C.
0 D. / 27r mar—2:132) dzc
0 2
E. / 27r (3:1: —:132) do:
0 14. A person slides a block of ice 20 feet along a horizontal floor by pulling with a force
of 10 lbs at an angle of 45° to the ﬂoor. How much work is done by the person? A. @ ft—lbs \/§
B. 200 ft—lbs C. 100 ft—lbs D. :1—09 ft—lbs x/E E. @ ft—lbs ﬁ 15. A water trough with triangular cross—section (see ﬁgure) is 2 feet high, 4 feet wide
at the top and 10 feet long, and is full of water (62.5 lbs/ft3). Find the work done pumping all the water to the top of the tank.
A. (62.5)(30) ft—lbs
) B. (62.5)(25 ft—lbs v C. (62.5) (43—0) ft—lbs
( 7—) ft—lbs O D. (62.5) 3
E. (62.5) ft—lbs V MA 162 Exam 1 7r/6
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0 ‘ 7r/2
17. / sin3 :1: 0082 :13 da: 2
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 Fall '11
 PETERCOOK
 Geometry, Let A=, ft—lbs

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