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Sol-162E1-S2008

Sol-162E1-S2008 - MA 162 Exam 1 Spring 2008 1 What does the...

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Unformatted text preview: MA 162 Exam 1 Spring 2008 1. What does the pair of equations a: = 2, y r: 7 represent in R3? A. a point. Idwgmﬁm Big 2 VLFHWqEQAW a line. W is 6‘ 0414' . aplane. D. a cone. E. two planes. 2. Find the radius of the sphere m2+y2+22—2x+4y—6z=7. 07"” 1)+(}frqj+i) +(fvlmil : :7 :3 c m MA 162 Exam 1 Spring 2008 4. Find a unit vector With direction opposite that of < 2, 4, —4 >. .<2,4,—4> [<24 W7 W+HVF=AL111> 3 «Emma ~2 —4 4 TIGVTTVE> ,_1 Doll 0‘31““ u <3in “11; 101;: ODIN V H /1\ WI” | WI!" wlﬁ . \/ \/ (5 a .o w /\/\/\/\ V 11,4»: T11: _ vbA.—,,<5—55> QXL; w LL 3 ”(2 »°”(1’G\1: +1141) )LB <1,,1—1> 21‘ A i @<5,,5—5> lg: +gj ”912. D< 1—11> E. < ~1,—7,3 > 3 3 .a __ __ 4 1o _ 2: I: .3: A" :2J 2k w "a “A 1, 1 1, 1 |-0+Z1+ ‘11 .2, 3 a @§1+J+§k ’3 M? a 3/ 0L 1 2 (p 1 2 1 \ +1 +1 D. —i+—j+—k 1 «a 1 ,5 "P 1: 3 3 3 3 v, 1;: __ ’ .1, ' .1, 1 1 1 MA 162 Exam 1 Spring 2008 7. Leta=< 4,2,3> andb=< —2,1,2>. Finda-b. u.» “A? A.11 0MB 3'" (“\(“A +(2’>(\) +(aMz) B. <2,3,5> :1 “mg +L +6; 0' 0 D. 2. o E 3 ' 2 8. Let a : i+ 2j + k and b 2 2i — 2j + k. Find 0080, Where 6 is the angle between a andb. a 4) —1 W ado L~L+ H A'ﬁ COS9WV ”a «a»? :1 n —7 M“?! ¢1+t++lm 33% C E : “fairwm : dam 'Wé AWN/x m“ g (341+2X “”Xg) ifs 13"? O «(Limix‘w B": _,_ W 5 Er x2+2Xd>§3 3 {9% a C' 3 ~ {Em-L; ‘60)02 : Q E g ’3 MA 162 Exam 1 Spring 2008 10. The area between the curves y2 = a: —— 1 and y = a: — 3 is [260% Q W ‘0 \wiamtiﬁw 4 WW “claims 3%,(3 ‘3’: “3 »x: VB’J’V 'i)(\7+3/ID- ((w—3)—\/CU_——.i) d3? 2‘1,w;0 ”(9 Z)(‘7i‘i 3:013 121((m_3)(x—1))dy /‘7 ’4’}, 799M ham-mi WW“ die:- W W {who may 11 What is the distance between the points( a}, x2 )and (:10, a: + 1) for a: > 2? §IW%~W ‘~+:UW::JKMJF @ 3132—33—1 B. m+1—m2 C. Cannot be determined. L WE 5.5%... Men‘s? Lﬁ<z ’9 7:)“ {S ﬁbN‘Lvl x—H Z 12. The region bounded by y— — 1 — m2 and y— — O is rotated about the :1:— axis. Find the «for X 7 L volume of the solid generated. 37 big Lg ’ 3 gmiaé “€115“ V:S (“bani“); ix : a: MA 162 Exam 1 Spring 2008 13. The region bounded by a: = 3/2 and a: = 2 is rotated about the line m = 3. Using the method of cylindrical shells, the volume of the solid generated is 271’ (QNX) ZR Cl); A. /02271'(3331/2_w3/2)dm 1/2_ 3/2 3/2.) &@/02 27r (65c 2:1: )dzr: C. / 27r(3—~x) dm 0 2 D. / 27r (Ga:- 2232) dcc 0 2 E. / 274395—902) dm 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 2.: 450 to the floor. How much work 18 dnoile by the person? ‘4 Ewmasw 1' tlog/“+501 -1/o,.1 Q) @200f’t—lb (1 r7: 7 S . 200 ft lbs M mg, C. 100 ft lbs WM; 2 F ~ "TD “f 073:3(293 t (%lt©l D. %ft—1bs — loo , 400 _. M M10 __ (7: «ﬂ» \ g E. ﬁft t—lbs 15. A water trough with triangular crosseseotion (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 c.mzm<%§fmm D. (62.5) (2—0) ft—lbs ( MA 162 Exam 1 Spring 2008 7T/6 16. / msina: d3: = 0 1 x/5 LLLAT‘TE”. (991‘ (A? >4 / Av: QM Ax @5‘5” “MAMA“ Vwcm B Ly; 1% “719 mg 2 2 g \Aéiﬂ‘k CLX 2:“ \$(WC0)7{)‘ '9” g ,(DﬁonX C. @_l o o o 2 12 T79 \/§ 7r ‘. N __ w. » (wXCosx +9mx>\0 D. 2 +12 1 \/§ =<~%(—E> axmw E— __ ME 4., ’ WW 4"” 12/ 2“ 7r/2 17./ 8111311300821} (153: 0 A 4 ' E :1 2 §>k\$ A/ 2 go 9% X0» X ' K a1—5 “7 C. :2— : ﬂ LUerLXX Coszﬂ NW AA 15 o —4 D. — : Sm)’ (082%, Loft/‘24) QNX 4% 115 D E. M UL; Cos>< , “a“ A“: “g'kx‘i’” M -éo\: QIMXM um'rwo 2| arm: COJTVL : 0 ...
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Sol-162E1-S2008 - MA 162 Exam 1 Spring 2008 1 What does the...

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