mth127 exam1 - cami'liifid MTH 127 Exam 1 Spring 2008...

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Unformatted text preview: cami'liifid MTH 127 Exam 1 Spring 2008 Name: (Please Print) Signature: E9 3 Please work neatly and clearly indicate your answers. You must Show your work to receive full credit. If you use special features of your calculator, show your calculator steps and entries. Points may be deducted for faulty reasoning and improper notation even if your numerical answer is correct. Remember to use units Wherever appropriate. Vocabulary (2 pts each) 1. The 810 P9. of a line describes the rate of change. See p. I f and the notes paeketfitom thefirst day ofclass. 2. If cost and revenue are equal, the company will bmoxlé - (1U en See p. 43 and the notes packetfitom thefirst day of class. 3. A(n) $1 n (jug! our“ matrix does not have an inverse. See p, 138 4. A system of equations with no solution is called a(n) In c 9:} atgien'l, system. See p. 74 True or False (2 pts each) Circle your choice. 5. True 5. [A][B] * [BRA] Seep. 125, Homework Question #1 Sec 2.5. Quiz #4, and Matrix Multiplication Handout 3 6. False 6. The lines y m EX — 9 and 4x + 3y = —8 are perpendicular. 3‘3: '8'“ » 14H ) kat‘ #29429» '5: ,973’413): LCCP. , 0771614107" MCQ 1077 ALL . , VL’ZZ 1 2 0 0 7. ® False 7. The matrix{: 1 l6] isin row-reduced form. Seep. 84, example 3. Multiple choice. Circle your choice. (3 pts) 8. Consider the line y = 2x + 20. If the x coordinate decreases by 30 units, l; . then i) the y~coordinate a. increases .decreases i ii) by ”units a. 5 b. 6 @25 d. 30 e. 50 See p.11, Homework Question #1 Sec 1.2, and the notes handoutfitomfinst class, 30 (is?) z 2 5w (2 pts) 9. Which of the following matrices has no solution? 1007 b,08 109 diooo 1036 a)0102 )012 @4“.. )0100 6)0350 0010 000 000 0010 0000 See p, 98, Homework Questions 1, 2 Sec 23, Quiz 3 (2 pts) 10. A typical linear demand equation will have a w slope. A 5 Pr 1: e f, \ a) positive .negative 0) zero d) undefined Du mand +3?“““3 A Seep. 33, Homework Question #12, Sec 13, and Quiz 1 (6 pts) 11. Which 119 of the following are NOT valid row operations? a) Interchange two rows. (RiHRj) @ Add a constant to a row. (Ri + c) c Multiply a row by a non—zero constant. (CRO @ Multiply a row by zero. (ORi) e Divide a row by a non~zero constant. (Ri/c) t) Replace a row by the sum of that row and a constant multiple of any other row (Ri + CR,- 0 ¢ 0) See pp, 85 —86, row operations handout, and all notation used/or row operations in Sec 2.2 ’5 homework, (8 pts) 12. The size of [A] 2 4X5. The size of [B] is 1X5. Give the size of the following matrices. If the matrix does not exist, explain why. at 3[B]: "IX 5 (wupn'piémég eaoln 1335333 3 clogs noé aha (BMW .4, See p, 113, Homework Questions #3, Sec 2 4 31 1C 04: 4% & mahi b. [A]": does no’c exist. A l5 no): 3 uare. Seep. [37, Homework Questions #1, #2, #7 Sec 2. 6 c. [B]T : S X l Cm-lerchcm grows and mlumn$\ Seep. 113, Homework Question #8 Sec, 2. , Quiz 4 d. 14 : L7' X V (32 Um-C 3 SUBSrJ‘Q", moltccti‘e} 7 wws\ See pp. 125—126 1 9 5 a a f (2 pts) 14. Let [A]: ~3 0 2 and [B]: —c 2d 22 . Let [D]=[A}[B]. 0 -1 4 g ~9h 5 f oe-wadww vvw Hi inks ('09) 3 9m Me I?! malmx W\% (‘Olvmh Q 0; 44m QMImalY-x See p, 124, Homework Sec 2.4, Quiz 4 (2 pts) 15. Give the equation of the vertical line that passes through the point (—7, 5). “"3 See p, 18, Notes handoutfromfirsl day of Class, Homework #4 Sec. 1.2, (2 pts) 16. Suppose C(x) = vx + f and R(x) = sx are the cost and revenue functions of a certain firm. Write the firm’s profit function. PDQ: 961% ((7% = 8x ~[vx+$\ = Sx —\/;< ~4‘ 115-le ~¥i (18 pts) 18. The demand for watermelons is known to follow the linear formula p = -0.75x + 9, where price is in dollars and quantity is in thousands. See p. 43, Homework Queslz’on #3 Sec. 1.4 a. Interpret the slope of the demand equation. H: Pr: c9. decreases $7 3, , Wm zuqnlwl’wl de m ended lncreases [9.3 V00 0 w ale I (“elm ’3 nee a, '75: .. . 7S— 5 ._._.....E__._. I ‘1 zuonlil‘tk or) I: 91'ch decreases 39.75‘ , 441cm qun’h‘ +3 on area 3e 3 b3 looo cue-lat me lcmS Seep. 17, handoul’fi‘om Ihefirst day ofclass, Homework #11 Sec. 1.2, Quiz #2 b. Interpret the p—intercept of the demand equation. ( e 3 Cl 3 lg: PULL Is 99 lie/v a wolumelon, no one go.“ lousl‘phem. (O demand} See handout/ram thefirsl day ofclass, Homework #9, #11 Sec. 1.3, Quiz #2 c. Find the X—intereept of the demand equation. :v'.’lx '73X 3“: 9 See p. 19, handoul‘fl’om thefirst day of'class, Homework #9, 12, d. Interpret the x-intercept of the demand equation. (13,0) 1-? woA-Q{m2,\0h5 GYQ he (PYNe flo\' onloEIQOOO x P w.” \oe demanded. See handoutflom thefirst day Qf'class, Homework #9, #1] Sect 1.3, #3 Sec 14, Quiz #2 e. The supply of watermelons also follows a linear trend. Based on the table below, find the equation of the least-squares line. (If you can’t do this, see your instructor.) x(1000’s) 1 2 3 4 La 3M) CQ\Q)L,,L3,LmR63 196) 2 3 3.5 3.7 La See Sec 15, all homeworkproblems/Mm Sec 1.5, Quiz #2 f. Using your answer to part c and the demand equation given above, find the equilibrium price and the equilibrium quantity. .‘73x 1»? : [.G§+.§LX P:/.GS4-§G [5:01) 735': l-le '9 : «+79 5,01 96 X Equilibrium price: fl (f 7 9 Equilibrium quantity: '5' 6/0 wmiermeim See p. 46, Homework #7, #8 Sec 1.4, Quiz #2 m $.Cs 3 Wm; Banal Wfii‘evmong (ll pts) 17. A new machine is bought for $75,000 and is depreciated linearly for 8 years with a scrap value of $4,000. Lett = the number of years after purchase. a. Find an equation expressing the machine’s value, V, in terms of time, t. (o) 7€0C>o\ qooo ~7s-ooo _ m: - ~887S (g)qooo3 ‘24.) \j : “9875 'L + 75‘000 (olvs‘fi/‘é—m’rercae’r =75 =7s‘ooo See p, 31, Homework #2, #4 t ec 1,2, Quiz #2 b. What is the domain of the function? \ sL O .3 £5 8‘ “l—unckoa :5 oval: Vodxc) 9“ W1” €3f$ Seep. 30, note listing of domain in problem descriplions such as #4 Sec, 1,2 machme. \oses vodue a} 0 ”(lg oi: c. What is the rate of depreciation? 3 M g? 7 5 e( 42:; r ( W slave See p. 32, Homework #2, #4 Sec 12, Quiz #2 d. What is the value of the machine when t = 2? Vs 4375(avwsooo = ‘51 57.95721 See pp, 16-17, Homework #1 A 6 Sec 13, Quiz #2 (4 pts) 21. Set up, but do not solve, a matrix equation of the form AX = B that could be used to solve the following system of equations. 2x ~ 3y = 9 X ‘3 E Conslq“t 3y+224 _ x -— z = 7 8) 3 0 q 0 3 1 Li l O l 7 See pl 143, Homework #3 ~ 6 Sec 2 6 (6 pts) 19. Pivot the matrix about the boxed element. Show your row operations. Use correct notation. [4 g] 75:13: a l q Ra'7Ri a l 9 3 -7 q 43 0 4°; See p. 86, Homework #2 Sec 2.2 (10 pts) 20. A chef is creating a party mix containing pretzels, bagel chips and Chex® cereal. For this particular party, 90 cups of mix are needed and the chef would like to use twice as many bagel chips as pretzels. a. Set-up an augmented matrix representing this situation. (If you can’t do this, see your instructor.) P b C Consioni: P+b+c : 90 l l l 90 99:“) :7 3?-b=o a —1 o 0 See p. 83, Homework #7 w 9 Sec 2. 2, Quiz #3 b. Solve the matrix (by hand or with a calculator). 1 1 \ ‘io Raw???“ t \ l 90 115/55 1 ‘ -—-# -—~—? g ,1 o o O '3 '9 ’9” O l Rt'R'J l c; '/3, 50 av rreHEA’D 7 O 1 2/3 (‘0 : l o ’/3 3° 0 I 2/3 éo a7 Solution: 30‘1/36 3‘60“ /5(L ) C. (P)b)C> \ 90 3/3 $0 Ptck a value. ¥cxc_ I chose (1: 30 c. Give a specific recipe. The chef can use 3 O C ”P s pretzels, V O C ugs bagel chips and 50 Q03 8 Chex® cereal. See pp 87w 90, Homework #7 ~ 9 Sec 2. 2, Quiz #3 See pp 100—101, #6 Sec 2.3, Quiz #3 (l0 pts) 22. A company produces plastic products and electronic products. The input- P E output matrix for this company is [A] = Plas .10 .40 Elec .20 .20 a. What’s the meaning of the .40 entry in the matrix? Te} manui-ac-lure. $1 mo-~(‘\’\\ of: declmmxcs, 5905'“) wm‘t‘n a? okrSHcS ore mzmred. See p, [53, Homework #1 Sec 2. 7 Suppose the company would like to sell $25000 worth of plastics and $32000 worth of electronics. b. What production level is needed? K 2 (I _ A)" D x - (9. “cl «3.x :1] " t::‘:::] 51257: P sag/2,5 E X“: The company needs to produce 3 5/ 9 $0 worth of plastics and 5 5' 9 8 / 57 l 5 worth of electronics. c. What is the value of the plastics that were consumed internally? g X—AX=D .. O : 202513 5:252: aioo :] so “WAX u) Want/LA SUN “”5"” See pp. 155—156, Homework handout sec 2. 7 ...
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  • Spring '08
  • KimberlyShryock-Boyke
  • Math

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