02faex3 - <.NAME Math 113 EXAM III December 4th 2002...

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Unformatted text preview: <.NAME; Math 113, EXAM III, December 4th, 2002. Omani“ SECTION: Instructor: To receive credit for an answer, you MUST show work justifying that answer. FULL CREDIT WILL BE GIVEN ONLY FOR CLEAR AND ACCURATE FIGURES. I. Find all solutions to the equation ' (20 points) cosm = cos(-8-:—1-7r), with eznggzflg £311 Tr: HOTI' + If . Sine Co’éx‘we IA 21‘: pew‘oala‘c. 8 8 C99 §%ln\=0n%- Sonic maul!)cher COBX: Anolm‘oue AcyQul/‘(SK Lo X: I; (gfikmlfi‘oaaaowfmmm‘m gaff) chowwoc d1» rule {fix/399w,th cmX: a I whmm we, ...)I§,.2.w,®, Ig+2tr) Egg—4W)”. II. A triangle has sides of lengths 3, 5 and 6 (units). evaluate the angles. (30 points) \l ems)? 0-6 glam“ M Mme, Lowro'ecom‘m,’ 6: 51+3"_2(3x5)co>o( WD‘:“:’S-~SO “£053.60 mil} mid -- — 3 6 LW 0%);th : So DQWPA—i‘g’SIS‘, ‘ $Cm¢¢ Pg-go' (alveaA»)oLv,go‘, bwwealoo QKVNANM («ms ‘DUGQ‘MAVQQ —- lb-k-OVPJB‘LVL M‘clk?) “0V [fix 3w" «we? [1». [pa 56.23] - Y”:\Xo°-(¢z+p\e PM" Nag; Fumltuz 5-th a" w: (Kw). h: we. Ch Qavflovt'QVVKQO became—e C(SMA‘QLKYAV\M ‘WCMSCC‘P Wolf 001%er ml‘c\ _ III. How much force is needed to prevent the 60 lbs bowl from running down the slope? (25 points) w W WM be. WW owl: view/{M (WEN) viva. alum». Ea. Qupw kafiwlvlb‘ 610w (CMULMJ) W 0— 2M gt ll; WOUWCA/‘mn O'Q‘MoVCM. —7 We, magma) ' I 5'50 IV. 1) (20 points) In the (m, y) plane, let l7 and W be the vectors given by their compo— nents: ' —o 17' =.<—6,4>, W =<3,4>. Show these vectors on the figure, evaluate their lengths and their dot product. , \2 W): \l 61+ Lrl=\lE-‘= ill—3 m : W .1 5 VYITHOUT CALCULATOR, can you say whether the angle between the vectors 17 and W is an acute or an obtuse angle? ‘ obtuse ‘OECQAAK Ell Aolpqeolwl/Co “68(1ch (CGEM‘MQ <o\ 2) (15‘points) In the three dimensional space, let (7 and T be the vectors given by their components: _‘ d U =<—6,4,4>, T =<3,4,4>. Evaluate the length of these vectors and their dot product. [u] = 35mm _— \168 - 1W7 ~3 lml: mucus :er .u fl" = G- 6135+um 1- [4“).- H. [ANSWERSu 1m: V. A river, 0.1 mile wide, is flowing south with a current at a speed of 0.7. mi/h. A swimmer swims across the river. The swimmer speed (relative to water) is 0.5 h. The swimmer starts from point A and point A’ is straight across the river on the other bank. If the swimmer is heading in the direction of 35" east of north how far from point A’ will the swimmer land (carried by the current), above or below A’? (30 points) $\'c2\ , Fmdfima Uta Oliver/hm. N 3 Vetoahlag pWMMV‘, R Cuvvmv , “\P/ “3 UQVOWM 3 .9 Lou/oi chweor\.\7\1: QS)L+L‘1)L“2(‘§*JC¢D5S§' V 4. so 4;“ fl AWC‘MMW‘ .\ Mata bdow A)“. 00:44.51; towel'xl. Not: (£34 QV‘C Owe/k Web&ods. You can try the following for 10 points (8+2) of extra credit (addednot to this midterm but to your total score of the semester). But you are STRONGLY advised NOT to try it unless you have done everything else on this midterm. Which should be the heading in order that the swimmer land as close as possible to point A’? (A good figure is the key). Which should be the heading in order that crossing takes the least time? (justify). Use back of the page. TRV AH"! ...
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02faex3 - <.NAME Math 113 EXAM III December 4th 2002...

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