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162E1-S2008

# 162E1-S2008 - MA 162 Exam 1 1 What does the pair of...

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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. E. acne? sees“ €11.50??? Spring 2008 a point. a line. a plane. 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 C <;£_:i.£;> ' Vﬁ”¢ﬁ”¢ﬁ 12—4 13' <3’g’7> E. <:,:_2,2> 3 3 3 A. <—5,—5,5> <LL—1> <5,5,—5> .<——L—4,1> EUQW <—L~z3> MA 162 Exam 1 Spring 2008 7. Let a=< 4,2,3> andb=< —2,1,2>. Find a-b. 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 /‘\ /‘\ (Q [\3 + '—l v I A {Q + DD V V g. {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 16. / wsinm dx: 0 ‘ 7r/2 17. / sin3 :1: 0082 :13 da: 2 0 ?> P3 Spring 2008 1 \/§ ———7r 2 12 LEW 2 2 x/éjr 2 12 3 £+1 2 12 1 3 2 6 4 15 2 15 —2 15 —4 15 1 3 ...
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