04spex3 - Math 113 EXAM III(1 hour NAME SECTION Instructor...

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Unformatted text preview: Math 113 EXAM III, April 19, 2004, (1 hour). NAME: SECTION: Instructor: WHENEVER POSSIBLE, GIVE EXACT VALUES. TO RECEIVE CREDIT FOR AN ANSWER, YOU MUST SHOW WORK JUSTIFYING THAT ANSWER. I. ‘ (35 points) A boat is going straight north. An island is seen at an angle of 20" east of north. After a mile, the same island is seen at an angle of 25° east of north. How far is the boat from the island at the time of the first sighting and at the time of the second sighting? How close to the island will the boat go, if it continues in a straight line? Neal‘aht'QiV , 6W- QC 1 0) vsoi' kc heath i 1 a» \ II. Evaluate the length L. L a»! cl cm" was = If: 31+ 52- z (3 m coo 55" (10 points) Lzlf.‘ A III. 3 (6+29» points) 1) Find a solution to each of the following equations (keep EXACT values. You are NOT asked to find all solutions). (i)sin:v = 0083?”. C09 3T: 5&(I-3§"”).So 3C2W 3W::’Ell~‘ Lo aOale/lo“ z 3‘? t (ii)sin6 = —cos3?". a: '1": m a OM'W bu‘Mq 9Q y; bu‘v‘ 1%— O o 2) Find all solutions to the equation 1 sin26—cos202 5, in the interval [—27r , 0]. Z _ 9: do: waL9:l_Cop'-9)MA3¢K\ 2.01% M— IV. Determine the weight W and the angle a so that the figure shows an equilibrium position. (35 points) oqugmec. AM‘W E; 0% L h “ M‘W F3 ‘3- o bCMSSO p!” (-30m53, >/\ 0 E12<WAU3~°<)NC07°(> (may)? “1725 _7 __’ 0 55° 0 F3 2 4 o ) 3 > MA W: 3% A; LI _. —w \\ ~> ‘ FM" Fy‘TFLTr3ZO V. (25+10 points) 1) On a river flowing south with a current of 3 mi/ h, a boat cruises at a speed of 4 mi/ h. The river is .4 mi wide. On the 355mm bank of the river there is a point A. it is point A’ on the fitern bank. What should be the compass heading of the boat in order to reach point A’ starting from point A. How much time will it then take to cross the river? TR“ {cogent macaw/3 (in «Mm/3M at (397* V090qu VCJ‘M . bole-.223; opvs 9:: 43.50 (WVM’AQ/‘faoliwa “mild-6°: mt“) tune - 1.54 (MM) Directly across 395‘“ _ 2:. 45’ 9‘0qu p‘ue‘k 2' 61" g 0} inu‘vx tS 2) Now assume that a boat (on the same river) cruises at a speed of only 1 mi/ h. Starting from point A7 can that boat reach point A’? Justify your answer. Explain how the figurAeK below is the key for answering the following question: what should the heading of the boat be in order to land as close as possible to point A’? \l‘c’) CW 001% V0 Y‘caJlA A, \JJ't-CW dtxu: no t’U‘mAVKQA [MAJA do 1 3 (“pair/W MM Le (or: em 0&ov3‘g “BM-\A‘fi‘bvdA‘OAVl/‘WN‘.~\_ \ '\\ J31 \7 \ “(gublmaAA WvJouN‘,\/~Q \ Oak/tarrka Mi, mm! aveMoeflmMQObi ~\\ \ktwotdw “tow”?ka mevam ...
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04spex3 - Math 113 EXAM III(1 hour NAME SECTION Instructor...

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