113-rosay-06fa03-key

# 113-rosay-06fa03-key - NOTICE: This Material May Be...

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Unformatted text preview: NOTICE: This Material May Be Protected By Copyright Law (Title 17, US. Code) Math 113 EXAM III, Nov 30, 2006, '(50 minutes). NAME: SECTION: V 'Instructorzl TO RECEIVE CREDIT FOR AN ANSWER, YOU MUST SHOW WORK JUSTIFYING THAT ANSWER. paw (Wm uxac WW“ cm oi 4 (9‘ So w 'W%V@\av~g CM 0? 2 , Q35 Lroo‘ UAWqu dc“ {301me r CM 6803,)43 : “CO—2X 1 (mt, (Katha/V CC” CW0“: ‘" CC” Live; amok ‘\0°ziw°zlxoﬂ go (X: “+06 C“ & OO‘QMN‘JM (ngg/V‘ VtVi M6Wt\‘i II. ‘ (40 poin’gs) Find the weights W1 and W2 order that the ﬁgure shows an equilibrium. The right cable is pulling horizontally. Ar? tailoch 0, emu/a VJ“; QARVC it; a :35”; w\ _w7_ 1W3 90c : 0 wt moat)“ 45° I 0 - 5‘0 V 57 ‘7 (Jet?) w :wzm'bﬂ “.1 Ovc W35 WL : c4530” ' ) \ 3/...— WL> 5‘0 A; 5”]«7 C9030 go lax/MED A; 9—3” III. NO CALCULATOR. ( Iiet IZ=< 2,3 > and l7 =< —2,1 >. On the ﬁgure, show the vectors (7, 17, ﬁ +VV, and V — U. Evaluate the lengths, W} and IV! of the vectors (7 and 17, and evaluate the dot product (7- 17. Give the EXACT value of the cosine of the angle a between the vectors (7 and l7 (geometric angle in the range from 0° to 180°, with no orientation taken into account). Without calculator can you say Whether this is an acute or an obtuse angle? IV. (25' points) Let 2 and 2’ be the complex numbers 2 = 2 + 32' and z’ = ——2 + i. Evaluate z + z’ , zz’- and in Cartesian form (i.e. a + bi). If {7 = r(cos 0 + isin 9) is the writing of 22—, in polar (i.e. trigonometric) form, with r > 0 and -7r < 6 5 71', give the EXACT values for r, @030 and sin 0. No Calculator, you are not asked the exact value of 6. On the ﬁgure of Problem III, show the angle 6 with its orientation. Using your calculator, give an approximate value of 0 (in radians). ﬂit—Z]: Q-ljad>+ (:1ki\ : 12’ : £2.68 L~l+€\ :, nave-ti wan—m +2: Lia-Lean“ 2 an: 7 (2 +3L\ (.243 a ..i,,q,¢l~_es-2c {lag}; --—: .—————-—---~ : M .. V I 2" —2+L the) (and 5 -_ 3‘.» \2 gz‘ ,. Q>ﬂ f; g -:_ 31/ Z) ' (‘53 an?) ‘ Li 5 -1 8L\ ‘ z_ ‘1-g(,5;.(¢~—_§\ 27 " "‘L K? ‘2‘» - 5- tag > g , r L AV?" Sec Q bhgujm Chm e AQGDZ - ~ ~ - --ANSWERS_—--~---—~—-— z+z’= Lil: 22’: ~7-Ll“: A: :L _. ii 2’ 5— 3 r: ,cos0: ,sin6: 9 \lés’ Obvux'v‘eA \UA‘w‘t/A, Cod" ,«Ouk‘ 9:: -— ‘06qu I radians. fie... D908“ cg,ch gum, an I . O’M‘mwmxw NW (M 036%“ ‘96) 1”wa _ ‘ \ i. ‘ 01, (JJQOVQ. . (“awe Cm‘nnt Iain“ gym We oUNc/VM\ ‘ ...
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## This note was uploaded on 08/08/2008 for the course MATH 113 taught by Professor Rosay during the Spring '07 term at University of Wisconsin.

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113-rosay-06fa03-key - NOTICE: This Material May Be...

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