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Sol-162E1-F09

# Sol-162E1-F09 - 1 Find the radius 7 of the sphere m2 y2...

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Unformatted text preview: 1. Find the radius 7' of the sphere m2+y2+z2—2w+8y+9:0 Z Z (A) 4 /}éZ_~Z/>A 7L] 7L7 +gé/VL/43 7L g 5:“ (?7L/‘/’/é (B) 8 7‘ Z /_ ”Z; 2 2V? ZM~UZ+ (/4477 +23 ”‘ 5 (D) 9 (E) \/E W; "1/5? :- 21/2 2. Find projab Where a = (—1, —1,2) and b = (2,2, —1) @(171)_2> , ”j" : 22‘, p C; > <2,2,—4> @157 (if D 935/: (C) (~2,—2,1> 4’" ' / (D) 93:1) m "’4 (""6””0 Z) E 11 2 «a T <> <g,g,—§> 3. Find the area of the triangle with vertices at P(1,1,1) Q(2,—-1,1) R(1,3,—2). "M3 4/ (A) 4 / , ﬁzz WVQP‘F/Q (JED—2“E x, Z ,M; 57 Z ”3) (D) 3 175% w: 2 j _ (E) 3V5 “27¢ xW/Q : (4/32Z) 7% mm /~ W : .1. L 4. For What value of b are the vectors v =i+2j—k and W = —i + bj + bzk orthogonal? “A m.) (A)4 /7/", éé/VZO , (B)2 _./ +Zb~bzza (0)” ,, (D ——1 b Z, Z/j +/ 3 § @1 5. A force F : i+ 4j ~ 2k is applied to an object that moves from the point P(1, 2,0) to the point Q(0, 5, 4). Find the work done p25 1 (“/2 21%;??ng ‘: (C) 6 (D) 2 W: Pﬂsw/wzﬁrz‘ <E>12 6. Find the area between the curves 3/ r: —x2 + 333 and y : ac. 7. The base of a solid S is the region bounded by the curves y 2 ~30, y = 2:13, and ac : 1. Cross sections perpendicular to the x—aXis are squares. Find the volume of S. 8. A region R is bounded by the curves y = 1 — 9:2 and y = 0. If a solid S is obtained by rotating R about the line a: = —2, which integral represents the volume of S. l \__\\_W__M,/~// -1 éé 7P : Z // (/V 7L Z) (/H/Aé 22 5gfz’ (E) /7r(1 — IE2)2 d1? / —1 l: Z7T {/WLZ )//-sz(é% M/ 9. Suppose R is the region bounded by the curves :1: : 3y —y2 and 20 = 2. Which integral represents the volume of the solid obtained by rotating R about the y—axis? W2 MWWZJA/ Z 7‘“ g/ﬂﬂﬂa (E) ﬂigi-FZSG z. 'Z‘ 051—4) {174112257 (Kw/2:77 (gﬁﬂ 22/? «7772/ «(£1 /’ 3/ Z; Z, , Z % ) 7f: [ 27/631011ng a” 9’”)%O¢z / 10. A spring has a natural length of 12 inches. It takes 4 lb. to stretch the spring 6 inches. HOW much work is needed to stretch the spring from a length of 18 inches to a length of 24 inches? PM” :A/w (A) 8ft—1b. 1% : ﬂ (VZ) (B) 4ft—lb. :g (C) 6ft—lb. ﬁg ) : (cg/)5 (D) 3ft—lb. F 4b /’ (E) 2 ft—lb. w:- gwégé: :4—/:5 % ., 6 4572M of ﬁg” Xi / 12” / 11. omue 3711.2: :1: : 02/me 5., M_M/"/“»—vzﬂ,;%m C pt [ 1 d . Z 171.— / Z... ([1,. 4/.) \$1! jﬂé/M/VJ Jay (A) §+§ , B i 3 ﬁg: AWL/y (ﬂax/\$1411 H 2+2 62 1 6M“: AMAM ﬂ/‘z "/th @ ‘4’ +1 2 ’ A (D) §~1 r: ﬁf/z/cw a} 129% 2 2 Z’ 2‘ (E) Pi._l Z Z 2 4 :3 ,/>4 éﬂ/LM ”74%.; 4— C7 '2, ‘7’ 77% 7r/4 3 f 12, Compute / SGC4\$tan2\$dw 3: [2M4Aé 7;. {zed/(30 :«Z/‘LL ; g 0 ' ‘3 5" 3 5’” /5 . O I M«(‘/ 235 ”Z7144, (2)5 4444’ (A) § § 2 ‘3 .ddng/Z/yl {Km/c Z44 ,zﬂéd/ Z44 céo (B) 13 3 z / 2 1— (C) 1 ”i”: j(/7LZZ’LM 4&2ézﬂé/ Aﬂﬂﬂﬂb% 4 a: gmwe (D) ‘5 2/ Z aéa.:—/W%&é¢ 3 2: +54 “ a 5/; _ 3 p 15 5 U x” ”‘ éé 712.?” +6 2 .2 _..,. E 5‘“ ,7 {fawﬁ _/‘ @ﬁ/WU7L’C’ ...
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