Math141Sols4F11

Math141Sols4F11 - MIDTERM 4 SOLUTIONS (CHAPTERS 5 AND 6)...

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Unformatted text preview: MIDTERM 4 SOLUTIONS (CHAPTERS 5 AND 6) MATH 141 – FALL 2011 – KUNIYUKI 150 POINTS TOTAL: 44 FOR PART 1, AND 106 FOR PART 2 Show all work, simplify as appropriate, and use “good form and procedure” (as in class). Box in your final answers! No notes or books allowed. • Write units in your final answers where appropriate. • Try to avoid rounding intermediate results; if you do round off, do it to at least five significant digits. • We assume that all vectors on this test are in the usual xy-plane. PART 1: SCIENTIFIC CALCULATORS ALLOWED! (44 POINTS TOTAL) 1) Find the length of Side b for the triangle below using the Law of Sines. Round off your answer to the nearest tenth (i.e., to one decimal place) of an inch. (8 points) Find Angle C . C = 180 ¡ ¡ 72 ¡ ¡ 43 ¡ = 65 ¡ . Use the Law of Sines. We now know B , C , and c , and we want to find b . b sin B = c sin C b sin43 ¡ = 23 sin65 ¡ b = 23sin43 ¡ sin65 ¡ b ¡ 17.3 inches This makes sense, because b is shorter than c , and Angle B is smaller than Angle C . Remember that larger angles face or “eat” longer sides in a triangle. 2) Two boats leave the dock at Point B and travel along straight lines. The angle between their paths is 81 ¡ . At noon, one boat is 40 feet away from Point B , and the other boat is 30 feet away from Point B . What is the distance between the two boats at noon? Round off your answer to the nearest tenth of a foot. Hint: Find b , the length of line segment AC , for the triangle below using the Law of Cosines. Points A and C represent the positions of the boats at noon. (7 points) Use the Law of Cosines. b 2 = a 2 + c 2 ¡ 2 ac cos B b = a 2 + c 2 ¡ 2 ac cos B Take the "+" root. ( ) = 40 ( ) 2 + 30 ( ) 2 ¡ 2 40 ( ) 30 ( ) cos81 ¡ ¢ 2124.557284 ¢ 46.1 feet Note: A ¡ 59.0 ¡ , C ¡ 40.0 ¡ . 3) Find the x , y component form of the vector v that has magnitude 15 and direction angle 38 ¡ . Round off the x and y components to the nearest tenth. (7 points) v = x , y = v cos ¡ , v sin ¡ = 15cos38 ¡ , 15sin38 ¡ ¢ 11.8 m, 9.2 m 4) Let v be the vector 4 i + 5 j . (9 points total) a) Find the unit vector in the direction of v . Write it in x , y component form. Give an exact answer; do not approximate! Rationalize denominators in your answer. (5 points) Find the length (or magnitude) of v : v = 4 ( ) 2 + 5 ( ) 2 = 41 ....
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This note was uploaded on 02/07/2012 for the course MATH 2203 taught by Professor Ellermeyer during the Fall '10 term at FIU.

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Math141Sols4F11 - MIDTERM 4 SOLUTIONS (CHAPTERS 5 AND 6)...

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