MAC1114 Exam 4

# MAC1114 Exam 4 - MAC1114 004 TEST4 — A NAME: E )E )1 l I...

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Unformatted text preview: MAC1114 004 TEST4 — A NAME: E )E )1 l I :2 Only non-programmable calculators may be used. Time limit is 55 minutes. There are 18 six point questions - 13 multiple choice ones followed by 5 questions for which you must show your work (and can get partial credit) . Round yOur answers to two decimal places if necessary. 1) The polar coordinates of a point are given as (5, 70°). Find its rectangular coordinates: x=5~<~os15M74 B) (4.01, 1.59) \ a C) (470,171) 5:51 5mm: :17 4.?0 D) (1.59, 4.01) 2) The rectangular coordinates of a point are given as (0.7, -1.3) Find its polar coordinates with 9 in degrees. A) 1.48 32.58° : L0,?)z-rbl3)?’ CS 1.4% IN (30me ET. \ ‘3 a C (1.48, -32.58°) _ - .2..— g -— 6).?0 ‘ e is < -+> D) (1.48, 61.70°) ’ 0‘" O. f - a. (on, -13) 3) The rectangular coordinates of apoint are given as (~1, 2.9). Find its polar coordinates with B in radians __, L4 19).- A) 307,033 r: (431+ (1)"qu W "3.0? 1 ‘N QUADRANT 3L '. \ q C) (3.07, -0.33) -1 2. A, WW 7 Mum—w D) 8=£m TL +7C~l.cl (-307, 0.33) 4) Given the equation x2 + y2 = 4x in rectangular coordinates (x,y), express it in polar coordina es (r,9): 7.. A)rsinze=4cose IXZ+ 1:: Li'X % F :. LFX '3 r‘.r‘ : Ll—X waf— C) r: 4sin 6 r m D)rcosze=4sin6 ‘j P: ﬂ f”- C1058, \1.’,-:’.’,‘9 5) Match the given graph to one of the given polar equations: A)r=3+25ine B)r=3+2cos6 C)r=2+35in6 D)r=2+3cosB MAC1114 004 ' TEST 4 - A CONT. NAME: EDD LUTI (mg 6) Given z = 14(cos 45° + i sin 45°) and w = 2(cos 15° + i sin 15°) , find zw and :zv- in polar form : A) zw = 16(cos 60° + isin 30°) and z/w = 12 cos 30°, + isin 60° B) zw = 28 (cos 60° + isin 60°) z/w = 7(cos 30° + i sin 30°) C) zw =16(cos 30° + i sin 30°) and z/w = 12(cos 60° + i sin 60°) D) zw = 28(cos 30° + i sin 30°) and z/w = 7(cos 60° + i sin 60°) 7) Find all the complex cube roots of Z = 8(cos 60° + i sin 60°) . Give answers in polar form. A) 2(cosO°+isinO°) and 2° :{j—g' + i- anC°§:)) 2(cos 120° + isin 120°) and 2(cos 240° + i sin 240°) 20: 2-(mzowc—sznzo") W» 0°” B) 2(cos 20° + isin 20°) and ° 13 2(cos 140° + isin 140°) and \$39— =\’2..o . 2 cos 260° + i si 260°) C) 2(cos 60° + isin 60°) and 2(cos 180° + i sin 180°) and , 2(cos300°+isin300°) % _ 15(3351954 Linéo") D) 2(cos 90° + i sin 90°) and ' l ’ 2(cos 210° + i sin 210°). and 2(cos 330° + i sin 330°) 12.: 2 ‘(CosWOo—i- name) 8) Find the complex fourth roots of z = -16 with the argument in degrees: a [go 231%: \€°(c.osl80°+L-s\n155) ‘ 'N B) 16(cos 45° + isin 45°), and 16(cos 135° + i sin 135°), an 16(cos 225° + i sin 225°), and 16(cos 315° + i sin 315°) 2:0 - \1 4 C) 2(cos 90° + i sin 90°) and 2(cos 180° + i sin 180°) and < o 1 ~ ~9 ) ’ ' _ _ , 5m Lr) . 2(cos 270° + i sin 270°), 2and (cos 360° + i sin 360°) :10 " 2 asks 4 L 4 4 ° 5 D) »\/2(cos 45° + isin 45°), and «likes 135° + i sin 135°), and T), en, 0‘44 139. :Qo I {:5 32° 42% 4 4 Bx er: 42(cos 225° + i sin 225°), and 42(cos 315° + i sin 315°) 0 A) 2(cos 45° + i sin 45°), and 2(cos 135° + i sin 135°), and 2(cos 225° + isin 225°), and 16(cos 315° + i sin 315°) 9) Givenv = 7i - 51' and/u: 2i + 3) , find ||v — \l: MAC1114 004 'r' ' {r V, TEST 4 - A CONT. NAME: S O LU'TK ON 10) The vector v has initial point P = (3, 6) and terminal point Q = (—1, -2). Write v in the form ai + bj -i+4' OWL-13"“) 7— “Li I 2 _. f __.<5' C)v;4i+8; 5 =00» -(6) : -<g xv LH’ J D)v=-8i-4j 1 1) Find the unit vector 11 having the same direction as v = 4i + 3i ‘ B) =31?) u v Lei-+32 _ 4 - 3L . 3' 5 u M 5 "’ ’5?” 50‘ D) u = 20i+ 15j 12) Write the vector v in the form ai + bj, given its magnitude = 11 and the angle it makes with the positive x-axis.is: a = 45° A’“=‘“12—1" a: 44. mm”? 44. [2. .3 W2 , Z Z B)V= 1145i + 1145] r ._ 2 2 k g r #- ME C)V=-i2—2—i--’\é—§jl ‘0'; “- gm 44%? : M- wf, 2— D)v=12—11+11;/§j ‘1‘ 3) Given: V= i+4j and W=181i -j ,find the dotproductv - w A)0 B)? w=<%,-i> D)12 WW -.- it + 4-04) = 8—- u =4 14) Write the expression (1 + i)5 in the standard form a + bi . W H..an we is A“: , (“wavy c. sinOlS‘B) ‘ Q - "‘ — : '45 W» . azﬁoﬁmsR—S + L’ s‘nL‘S) I)" WW : ~L"_§|+L Z -—_ Z “L ’2 (1+i)5 = ' 2. 2. MAC1114 004 . TEST 4 - A CONT. NAME: ' S O LU T i ON S 15) Given V = 6i - 3i, and W = 9i + 9j , ﬁnd the angle in degrees between V and W — ——3 NH eat—35‘ \$136+” 2"“? ,_ — - '2: 1MB? a: \M\=W=W:m 9— («05‘ W W . :6_q+(_3}q: 5-4_2_‘:}=2.'+ . .. a VW \ angle= 16) Decompose V = i + 7j into two vectors V1 and V2, such that V1 is the projection of V along W = i + j and V2 is the part of v that is perpendicular to W = i + j. V; <1; V1 7» 1" : w: <1,1> V‘W31'l+7-4=l+?=8 “WIFE 1‘1» 4" = l 17) A tugboat is to pull a ferry directly across a river -perpendicular to the river's 5 mph current. To do so the tugboat captain maintains a heading that is 30 degrees upriver (to the right of directly accross) and then adjusts his speed so that the ferry moves directly accross the river. Determine the required speed of the tugboat. through the water. L: in 2) “\IH:\© 7. \ speed; \S) mph 18) A wagon is pulled horizontally by exerting a force of 30 pounds on the handle at an angle of 25° to the horizontal. How much work is done in moving the wagon 100 feet? : 30%st [00 + Q :3000. 1": 1.611 mzrk= ...
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## This note was uploaded on 09/04/2011 for the course MAC 1114 taught by Professor Emrekolotoglu during the Spring '10 term at FAU.

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MAC1114 Exam 4 - MAC1114 004 TEST4 — A NAME: E )E )1 l I...

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