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midtermI_solution

midtermI_solution - Multiple choice questions[5 points each...

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Unformatted text preview: Multiple choice questions .[5_ points each]. A score of +1 will be given if no answer is marked. No calcuietors are allowed on this exam. Please show all work that you wish to he considered for partial credit and circle the letter correaondjng to your choice of answer. 1. The value of o: for which the vector v 2 —6i + ocj + 3k is parallel to the plane 2 = 2s — 53; + T is given by: (530 M wwmsfl I: he {235:4} (b) We — @3 .30 0:\/ Lo“. 2: —],Z -'§u{ "-3 Lil (d) 12 o" :53: :1“! 01:3 {e)15 2. Let v = (1,21 0} and u = (—2, 1,3}. The angle between 11 and v is: (5)3 (1345" J— ; : t- —2 + 2.3+ 9-3 :0 (eyes .5: (gm? Ms:0 [e)180° ‘3 . 92:30 3. The surfsee p = ees s5; sis2 s; can be described in cylindrical coor— dineteeas: {V g =Joflmsp " :j am"? {b}32+y2=3\/—($2+92)/32 f EfIP/e e {C)T=P/r' fee-4‘13: w'P/m:e> .2: = 1.2 . Ir fink; (e) none of the above 'I r. : ELF... .- ll“ ' x, (a) r = zeotfl Flt? 4. The road on which you are driving curves to the left. You gently 3.13131}r the brakes. If you use “12:00” for straight ahead, “3:00” for t‘lireetlllrr to your right and so forth, the direetion of your accelera— tion could beet be deeerib$ 113$: tr l 1“ 1‘” M” (a) 12:00 {b) 2:00 (o) 4:00 [2 points per figure] For each of the three pictures of real objects, choose the letter of the equation which best represents the object. Note that the equations are in various coordinate systems and may describe the object in an},r scale and orientation. Figure 1.- an apple core [top and bottom are rounded}= a fruit roll—up spirafling on a table, and a whisk [describe the wire part, not the handle} X. (a) p25' Wéwww Jami-41am: (b) s =r = 9,8 <_‘: 20 a 3193111.? cmw’afl u’fi mfiflh/éégm LIEU—{em X (c) 2: £- $2+y2 5 E octagon-mien; part oi L ufltmoiojr (d)r=9,0£s£1,0£9$38 #- rsfl‘i‘fi *r’ipefl Might 1, (6)981!”in 5 5 )2 s f a», a. {3166 f nine? :5 i a». a Livonia” Equation for core is which letter? 61. Equation for fruit roll—up is which letter? ei Equation for whisk is which letter? g 6. Let 11%) he a smooth curve {s(t),y(t),z(t}} for 1 g t g 3. Which of the following statements is true? (Only one is true.) {a} ff fit} dt ie the distance between to) and 113). (h) | ff 1" (t) dr| is the length of the curve traced by r[t) fromtz 1 tot=3. (c) L3 Jr’{t)| dt is the distance between r(1) and r(3). @ f13r’(t)dt is the vector between to} and 1-(3). B3 ‘6th ”FMfi-fimm‘gmfl marten J Lag/m dew” M” (Eocene/{L LEV-U3, {Re JiAPEMLMEm’? Vic/£701" rig} - r I n «Britt-152s to fr‘ melt '1’. Circle the letter [HQ—(E) corresponding to the vector whose cross product with the vector V has the greatest magnitude. All vectors are parallel to the plane of the paper. h M {3'4 height Silt-kw {en la wziflwtft‘ke RMw-flf 22", IE " fixer: Hider 92¢ mifigmafi bite/3.111% 4 r 3. [S paints] Compute a. unit tangent vector at (I, U, U) to the curve given parametl'ieafly by a: = eee[t3),y = ein(I‘§3)1 z =. t3. Mw‘iréee "hunt REM] :f(M{,er- flat} {,1 aLLMALLLr fMJme/i‘fl‘? {Jam :14 m 39..L.M.£ SFfiL-LE‘. Hurbifl_ LNJL 5.612. {kg/f 5‘1! :5 3. MIX} RAH l..— a. gimmoflkrog mwp-«hifw dun/M TUE}: 9"“ t r— 554.75, mfif} Ear-H —_'—_— 1 ’ ’ W :fi(r¢h 1‘, EMEJJ. EEK“; (L920! :Q‘rfllrflh‘r “#:5er F4 Answer (0; 3'? if ) dt-i' 9. [5 points] Compute the eeeuleting plane at the point (e1 1,1) to the enrve r{t)=(e*,t,1jt} . We knew {Lu/4 rr'Hi' [DEM inn-u. MLLLCA‘HMJ Payee (eCLEELF-lf?nu 1‘4 subway/3 {Ht flu!- MW'K‘Et-y my. J in a. WMELE winter:- {a “WK“ ‘3‘“ 5" LMJ’W M F"!!! 1 WWI: (flit—{jfietfl'fl‘g}; = (2 {'1 *Ede‘r—Nflei -a“ ). em Framer,” £91- we WMJ um :25 [£}~BEF-€)_ 3(3)th Feline El} 949% Am. JX—fiejnehotrq amfl Piagn‘wa {H 'ffqunLVJ {61m} Lu“! 3/4 -{E-3€-£+ 4:0 =10P:,2€_ Answer: EX-Sfig-EE +38 :{5’ «1r [8 points] The canopy covering the tables at Gutmannfest 200’? is fastened to the tops of two trees, one located 2'20 feet East of the podium at a height of 75 feet, and one located 320 feet North of the podium at a height of 50 feet. The third anchor point of the canopy is on a flagpole next to the podium and may be raised or lowered to any height. How high must the third ”int be in order that the wind which is blowing horizontally from the Northwest owl be blowing parallel to the plane of the canopy [thus minimizing $111, the chance of it being torn by the wind)? M w_\ {-111}. H.43l TEA}; F‘LAFK’EUM L”) 11¢ 4?an P’EflWEH'FCLFD-ufll l P51051059) Mr P141120, loaf/smile [3&an 3 N )_ :3 L10 Ill-I 9} ,lr ate} {a 49ml? {fur :n‘ll'UWJélW 9,4. M llrho - with “UL a 94th in: (H.011: am 2 {151:3} 1 capitalist“): -20; Jahangir; : ~25‘Tnarf- 100E _.§of Hiya-ma) 141. MILFMJ raven-r fud— L'l L1 timothy-Jewel? its morMigfy 3h {9 {l1 lull). M Sal-1M N 14 31cm 6}} “5+ L‘a*‘Q:0 3’11.“ P 1’1 “mph“! 0+320+91§0+1ftfl h J: "53502 The. Ew'l'erdec/flw corfi, 1mg Eflfifi a», more” cm»? 0+O+Har1".10=0 =1 eazs‘zozt— :30. Answer: [8 points] A ball is fired upward from the ground at an angle 3 from the horizontal and a speed of 28 meters per second. It travels until it hits a large vertical wall 20 meters ahead (er hits the ground first). What angle 3 maximises the height at which the ball hits the wall? Give your answer by stating the value of ten 9. 15—123 l' f f,iel=U‘eoaQ_mfjfslrfetu9 3 Kit): ”atoll! = Fmflrf=2cftm9 {Jaltltfiaffil‘t‘ngz-L :Zéa-Evjfi'hfi— ijl‘il mile. 1.112 jet/m em “9:10 Mo! was; a. [W W “new 3H” 59 20:26.me “if :3 JH‘FZ 2-3 It“. 9*... in“? 2) 4719 '83] L956: : ZO‘Eaugfilr ‘6 Te “filmy 3H} #3.? J’rtimfi sole: JIM—‘0' all“: 201m." 9 - E' ,2 as: 9 . {iii 9793M 9 (Quid: (3‘3" 9 Jr: jecgc’mufl) $9: 0: £04169 -S'*j€.c1t9fks9 =3 flue??- Answer: tan9= Z/ ...
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