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test-5

# test-5 - MATH 230-01 OPTIONAL TEST#5 PART A NAME KEY DATE...

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Unformatted text preview: MATH 230-01 OPTIONAL TEST #5 - PART A NAME: KEY DATE: Nov 29, 2007 TIME: 20 MIN mwmmammxﬁwmwmﬂ‘mmwwmﬁmﬁ owwm'ﬁwammaamﬁwmmmmmmwmmwm Instructions : a No calculator allowed in this part of the exam. g t .2 Give complete and detailed solutions to all problems. .2 Use correct math notation and symbolism. a Units must be given in final answers, where applicable. a All cell phOnes‘ must be turned off and stored out of sight. E E. E :2 g s; “7’ i G- [5] 1. Carefully sketch The Solid region represented by The iferafed integral Q. 63) 2 2— 2— _ _ _ _ Jojo y 0 x y dzdxdy and calcula’re I‘i's value. Whaf does This number represenf? '2 _ 555% Ire—ﬁlm. G:- {thrﬂ 053:1,osxsz-u,'o\$t\$2-¥~35 z z-g awn—i1 S g S 1 (1&0!!de 0 D o 2. 2-3 z-x—a r -. =8 8 Lil, 4U“: ' (9M 0 o X , ' = Slim D o (l-x-j)olxd~j 2. ‘2- 1-'31 = l - 1 :g [Own-2Q] 30"” +“4:1 1;“ “Wk” o =— q » 5°» 1. ; WM & : VQ-‘s lib-“Ht oi, - o Gwyn! My WWW“ °Ftl°\ --— III: L5]! 2.. Evaluate “)1le +322 dA 7for The region. R in The plane bounded above by liney = x . R _ I . and below by The circle x2 +y2 —2y = 0 (see diagram). mat—8 (Wm (-0 Po (0-: SS V‘WJA = S {Halal-F Patrol? .K 7 '1'! 2815.19) S “l' r— S g rsmle) alt ate .‘ﬁmk “W (9&1 an 21‘s» A ' 5 mm mu. ‘5» m‘ﬁuﬁrsx'fé‘I511ﬁVl‘lwam K D o mule) :. aoslel [1:30 “(9 M o = 51:. cylgswei] do _ _ : H591; sf"; (a) mute) de 563(- ° C “531603.15 : 1% z '+ S o MATH 230-01 OPTIONAL TEST #5 - PART B NAME: KEI DATE: Nov 29, 2007 TIME: 50 MIN InStrUctions: ' u A calculator is allowed in this part of the exam. Svm». Rmﬁmgcsxwwwmwwﬁwﬁa;rmmmﬁ-‘z‘am:mamamt-3mmawmmmewm‘ﬁmmwmwmmmmmmﬁmwwmﬁxwﬁuv :1 Give complete and detailed solutions to all problems. u Use correct math notationand-symbolism. u Units must be given in final answers, where applicable. a All cell phones mast be turned off and stored out of sight. ﬂ 1%: .. F" 9.. .. 'k L: r: . é .. ‘4' 4 .. 4‘ a; 2 1.‘ A lamina, corresoonding To The region R ={(x,y)|x2 +y2 34, 15x32} in The plane, has densiTy aT The poinT (x, y) proporTional To x. In The calculations below you musT show any i nTegral expressions you use To deTermine The desired quanTiTy. Give exacT answers. [3] 0) Find The mass of The lamina. £.[¥I3) .:. AM; ' 1 \(-¥" . m: kind”: :8 S ' 4" Add“ ' I — Huvlv :: 2K5 [3] b) Find The cenTre of mass of The lamina. 3‘3 ngmeévﬂ . “1:0 out so 75 z: 0 ‘f Hg; gxs n” 10ka 434,); = lit-“34817) ‘ -- H-yi E a: _= HT} : (tL-3-J3'l-W3) 5 urf; 1“if! LKJ— 3 I ’ 9"; (Loin, =(1Eq‘5-I-éi J 0). I . _' . [3] c) Find The momenTs of inerTia abouT The x and y axes. 8". gm”- wfé Ta: ‘d‘CKﬂ alng 5 ——-"' I - \l ‘t-XL S :1:El c. S g ram .L3 in a {£335 ' - JQ-x" . S [2] ad) Find The radius of gyraTion wiTh respecT To The x-axis and The y-axis. 'r will i ll " [3] e) Using polar coordinaTes, deTermine The area of The region R. Am. an; SS 1AA. T 1" * 'azg g r‘dr'JG o .L Gala) HWY—3J3 3 ll 2 :1) Use a‘ Triple. integral with order dzdxdy To‘find ’rhe‘ volume b paraboloids z=8—x2 —y2 and 2:3»:2 +y2. 'Iw-Luse-céw'. 9- 73—41": 3x‘ 4*." [3] ‘l'xL-I-Lq‘” :: 2 L L .— 1, ‘1‘! ’ gwfﬁt‘I—q - "l' V: g g S 1 IL}— 0b!- :11 I "2’ nﬁ—J: 3X44“. 'I- e'rween The 1: E 4 E - MATH 230 INFORMATION SHEET r . . . E j j 5(x,_ y) dA ﬂx5(x,y)dA j j y 5(x, y)dA g R R R E [sz 5(x,y)dA H322 6(x, y) dA mg? + y2)5(x, y) dA R R R . 11mm .uya<x,y)dA f. I _1i__— R - _ ﬂax, y) dA j j 6(x, y) dA J; R R :£ 4 {mam - («mm “am gamﬁcmmwm ﬁszg'b‘A ...
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