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solution2A - [email protected] Be sure to bubble the answers to...

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Unformatted text preview: w @NOTE: Be sure to bubble the answers to questions 1 throuthO on ' your scantron. ' _ Part I: 2 points each In problems 1 through 5 indicate Whether each of the following statements 7 is true or false. 1. The equation :32 + 7 = 5:2} hasno real solution. X2“§?‘~ “a? “a {:3 rue dis cwméflgffll ;. (fly); .- (f- ‘ 7 ‘5: “" 3 6: - b False _ 2-. The inequality 3 W5 is equivalent. to the combined. inequality —'5 3 CB 3 5. ' 7 _ 7 _ . f _ l“) E “"3” Ha; mo «agflxcaiormlwm a. True ' _ fihfiFalse I . - (£15 ' Q/Wmffisa _ 3" Q) 3. (f3)2=(\/—+3)2 ffim __ Wrifi/ ‘3‘: True ZXE-fwox'f'7fig b. False _‘ I diam“:V‘akrtur‘eryrifi‘f” !. m" {ffla ‘71 r: m 5. The graph of the equation y = is symmetric with respect to the :c—axis. _ . , i j if? P a. True {‘fimaema an fro rams? a! ... ' wfifimgk l b. False r a. égb, 6. What is the solution set to the equation $2 — :0 —|— 1 2' 0 in the complex numbers? . _ l _ - hr 1 fi- _i .7 5 j: 77,} _ _ . . 8. Which of the following equations describes a circle-With center (1, ——2) and radius 3? ' ' a. (a:+1)2—:—(y-2)2=3 .b($*U”[email protected]+2F%3 9. Which of the points A =' (—4,6) or B m (—1,7) is closest to the I origin? - ' ' ' ' _ _ . - . ' * . . ' dew) W .5 a. A is closest and has distance 2x/1'3form the origin 3; mg; g b. Ais closest and has distance-10 from the origin 0! ii rm} ext-0% 7’2 @B is closest and has distance 5\/§ from the origin { ligciw ( five“? .-= - - e \, so d. B is closest and has distance 8 from the origin if gr 4? f _ = 57 - J? 3 10. The domain of MIL-«23; is a -— 3.x 2 a } w -aewwa v9xa°t who (—00, 2] a a”; E c. [—22] d. [2,00) Part III: 3 points each - 11. Which Of the following statements'is / are true? A.If-0<a<bthen%>%. 1-way ' ' _ B. The complex conjugate of m2 is 2. #fm- ‘ "'2" =3 '" 2“ _. C. If a) graph of an equation is symmetric with reapect to the origin and _ it contains the point (—3, 5) then it also contains the point (3, —5). 4min a a. A, s and c ' b. B only A and C 011in d. C only e. B and C only I 12; If M = (1, 3) is the midpoint of the line segment joining A and B and A=(.—1,w1),then g! X 7 _ (In?) 3(W#"+ '3‘ i ' l*-"~"‘t.2§- " .z'miqs»; dB=ma afiwwx tw~we " e.' B: 3 fl I s In? in. QR I 13. T he surface area S of a cylinder is given by S = 27773 + 277%, Where h ‘ is the height and r is the radius Of the cylinder. If the" surface area is 48% square inches-and the height is 2 inches, then What is the "radius r of the cylinder in inches? 64-8 ‘1? v: a?“ r2“ «#4 QWF’A / z; a???” as a rim-an as -' ' a. r 2: —6 ' b. r = 6 - - A. _ - {r wag-(“mtg C. T —4 ' we ‘3; if! I my. ex? swig! _- ' d' T : 4 - Mai» ; mafia: as t, 6% Va M5 F” “3'3 ' -516; e. This cannot be uniquely determined from the given information. 14. The inequality 2 +(551: + 3)‘1 2 has What solution set? ' a, (—00, mg] -2.- «r» file‘s—t3.- szfi 2; _§) ('33:. 43,)“; 4; o 16. What is true about the equation (m —i— 302/3 = 4? «a? W3 2‘: 5‘ r: i 2; an? . 3 ‘ '_ a. It has exactly one real solution and this solution is negative. _ b. It has exacty one real solution and this solution is positive. 9‘ a“? “3 V " It has exactly two real solutions and both are contained in the 7 interval [512,6]. ' ' d. It has exactly two real solutions and both are contained in the ~ . . ' . a . w' interval [-—6,12]. _ 65%;; {Mag} at w {may a (fig; a}; . V/ ' . I L 3;, a a: 6‘. s e. It has no real solution. “ (ft-3) 3 e 8" 4 £1 ‘ 5 17. The cost forl'producing 3: units of "a product is C' = 35 + 235'. The revenue from selling :0 units is given by the formula R = 1433 — $2. ' Then the company breaks even - 5 g3 ,1 g g My; «ex 2“ a. . .only if it sells exactly 5 units ‘of the product. K 2* w ’22“ "5'3"? fl " ’ ' ' {Kwéfl}{x~?) $53 ' - b. . . . only if it: sells exactly 7 units of the product. - M _ - - ' - ' x 2:: 5‘” are «it s/ c. . .l . only if it sells exactly 5 or exactly 7 units of the produCt. d. . . ;only if it sells exactly 6 units of the product.- e. . . . only if it sells more than 7 units of the product. 18. The graph of the equation 3; = 23:2 —_ 533 — 3 has gash; I . 1 l. '53 “‘2’ ":2- a- .y‘lnterceptSI —§, 3 m-1ntercept: ~3 _ _ ’ l I r K a» lelemmg its : b. —' t t : —l — ; . . V 3; 1n ercep s 2, 3 a: intercept _‘ 3 1 g gig; “blami- W3 c; -' te t: . :1:-'nte ce ts: ——~ ~3 ytin'rcepfl 3 V1 1‘. p 2: afiéxfyfxgfi) .- __ y—intercept: '—3 - x—intercepts: —%, 3 5 - ' . Kg: a; as?» 5% “:7 sin 'e. y~intercept2 —3 :c—intercepts: 2i @ in“ _ 19. In an isosceles triangle the vertices have the coordinates A 2 (1,1), B = (O, 6) and C: (—4, 2). What is the length of the height through _ the point A in that triangle? - ' . (Hint: The height is the vlength'of the segment AM where M is the midpoint of the segment BC.) - i: 18 - M flag»! 9. c; (k V” (fwr‘wa2fi" f5: {fa-96); C. r I “WWW I d. V I_ r 3' . ‘f‘ m ffi+fijl e. 26 _ I figs“? 20. (Bonus!) Given the equation 330‘2 w 73: +4 2 0. The following are the first two steps in solving the equation for :c by. completing the square: Step 1: $2~gw+§=fl . . 2 7 _ 4 Step 2. a: —— 5:13 * —§ Which of the following equations is a future step inthe process of completing the sQuare? ; 4 . _ . (“‘2 "’ , Mm a ,v i f - viii Isl ‘ -- g all}? 2 _ r Ann _:L e' a“ “7 337+ 6 — 34+ 6 . t a g i. e 2_Z I _E Z l b :13 3513+?) 3+3 2_Z Z _é Z c a: 3$+6 3+5 MAC 1140, Test 2 A, Part II Summer 2007 Section number: I Name: UF ID: ' _ ' Signature: _-W" 1. Find all real solutions to the equation I _\/5-—2I:1:—-\/2—3:'=1. (:5) if?” ’3' 2.v2_.*;? + 2 as: 1%) w} “:3 £3?» ‘2’}; ém) X 2. a; if £57} I K *3: '2.“ a?“ X 3%“ m“ .. Wflmw WWW fig?” w M"? Maggy" E flay-ma )7 w xii, w {we}? w V’s we viva t gym W frag“? “3 M E; W” E 9/ “a '“ ““~w-=..-. I. "ma; ‘wmflm M hm? hi fi '1? v Vg‘g 2’ Q \g’ (I ‘5 {1 w {a i“ V??? wt? ; f The solutlon set 18: .1. . . . . . n; , , , 2. Find all real solutions to the equation" .($+UU?—w+¢PM—6=o. (Hint: Use substitution!) r I. - :'\ I I I! if" . 2" I {Ks/f} 6'; ' f *f'”‘9 = C3 ma firm: at stmé. V‘s..." _ I ‘ 7...; rm; sfiaflsfiéufi (gm: Mgfi‘ffi‘) ' Egg, 7’: ‘ . - ‘ . I 5‘ fl 2 mum-m mm s l ‘1, x I VET}? m 5: H 33 ' ‘3? w» by “V The solution set is:' ._ 9;}. . . . . . . . . 3 3. Solve” the inequality and express your answer in interval notation: 2—%|5:};+31g—1 ' L2. w a: [5x -_ elf-(“£2 __; - {5"}: “:3: 5g; Sax "é a g: m g my 6 {— §x+3 Cm? affix gage}. me- E54333: @> K I; m- fix ~ - " é? I ,3;- '. Thesolution set 13%": 525?; 7.33.6? gag”) _ 10 4. Peter rides his bike from his apartment to school at an average speed __ of 12 miles per hour. His roommate J ack leaves 20 minutes after Peter and he drives his carto school at an average rate of 36 miles per hour. J ack and Peter'arrive at school at the same time. How long does it take Peter to drive to school? ' HOW far is the commute from the apartment to school? m r . . v 4 {a e - ‘7? m 2:: 9%,, ' massages P gsyfigmre p drier,er WE _ ; § . f w . ggwfi 2:: gss ~ g g I - s. ““ ll g; ,x I - “2;: “*" 5 2m {"2 “"— X i .7 Cd; {- '2 8a " "“ 3”" [H v:- EQ WW “an? a A f” lime/If”- gha >2 a? . J. u m , I Peter’s tlme IS: . .37.. . 2"“. WW. . .. The distance 1s: . . t‘ffifizg . . . . . . . . . . 11 5. A fruit punch contains 15 percent apple juice. Apple juice concentrate contains 95 percent apple juice. How much of the puHCh and how much of the concentrate needs. to be mixed to get 40 gallons of a new drink'that Contains 20" percent apple juice? ' total amount amount of apple in gallons juice in gallons % of juice punch concentrate new drink. Concentrate needed: . @éfQEitél . 12 ...
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