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Midterm1%20with%20solutions - 22M 10 MIDTERM 1 NAME...

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Unformatted text preview: 22M: 10 MIDTERM 1 September 26, 1997 NAME. SIGNATURE. PART I. Do all 3 problems: A, B and C. 20 points each. Show all of your work in order to receive full credit. Every answer must be properly written with logically and grammat- ically correct sentences and mathematical expressions. Show all of your work or indicate its location in the space provided after each problem. PART II. Do all 8 problems. 5 points each. Circle your answers below: 8. a. G.) c. d. e. DO NOT WRITE BELOW: PART I. PART I. PROBLEM A. For each of the following systems of linear equations, i. write the augmented matrix, ii solve by using the method of row operations, iii. state whether the system is consistent or inconsistent, iv. indicate the number of solutions and v. give all of the solutions. a: + y + 22 = 6 a. a: + 2 Z 2 y + z = 6 Q) \ x "2. C: I O l '2. O i i (a ‘1 ‘0‘?- :—( [\‘+4§,3_:§__;0\\L{— Q» 0001‘ (iii) 44% syslccm is intensisttnt on No gown‘ons, a: + y + 22 = 6 :1: + z 2 2 rci :3 U) [i 'l 7—\(¢‘X 3&3le ML‘O ‘\Q‘& R1=rz'q>Eo\\\:/-X V:w%:hion e01) ‘0 i ‘L. 1‘16 4WM. Q“ ) $ \jgiom i5 (mt 54m”: Kiu j Sfl‘Rfmi‘kagj U‘XCVV‘j éoMoMI-Q’LO W3 1444 7t+%:')_ y+e=4 E anj Coax 2 PROBLEM B. A coin collection consists of 37 coins ~nickels, dimes and quarters. If the collection has a face value of $3.25 and there are 5 more dimes than there are nickels, l how many of each coin are in the collection? I NJ: D+ (Q =37 GUSNJru‘JODJrflSQ: 325' m» SNMODHSWMS" D:N+5 mbeN=5w~N+D ES 3 33L L N\ T? C? 5? earl—9r. ‘ ‘ ‘ 3"“ 5.; 7495 “‘0 S gar—Barn 0110;; Mr (8% o 1% a3] 0 2A 149/ ge \ 1 1‘3? :L—Z— _ a r.‘L 7% Babb) 19:2 it _ W .."[Q:"\L\' flat-‘2 D+4C17 1’1?’"9D:1O .‘zcyHSJrlégfg 33;)5 ALT. DzN—tb" 2N ‘ N+CN+53+Q=3?5 @239— g at? 1 2 leg; 5N+toCN+9)+:15(32~—2N) 3 5 395% l5N+ 50 “£00 "SON : 325 -3544 = 325 42:50"; 3 525 N z; 2.5:.” log ‘5' D120} Q6 32’30:-2 x. ""-_'_..—— 35‘ 4 j PROBLEM C. 2 0 3 1 LetP=[3 2 4],Q= U 3 2 ,andC= 2 1 l 0 3 A factory is asked to produce 3 types of products P1, P2 and P3. A purchase order is received: P1: 3, P2 = 2 and P3 = 4, which is denoted by the order matrix P. To produce each product the factory needs three kinds of raw material M1, M2 and M3. The matrix Q represents the units of the raw material needed for each product, where rows are for P’s and the columns are for M’s. The cost of M1, M2 and M3 are $1, $2 and $3 per unit respectively, as represented in the unit cost matrix C. Compute each of the following and interpret each {H75 i. PQ M, M1 M F M 2 03 PI [CGHD (6+4) (fit—qfl— Do to \3]* or #mderalES ,1 4:] . (f: 3 1 Ml ML M5 F, Pl P3 2 0 Pa ) (raw ML WC/(Dfifl CM-piam mliCa—DC— (4’ (“marks 5} mat atQYiQfl 3V6 1i. QC F 5* '\l . Pl 1 9 S '2 :3: ._.. [it—Q 2 [12] ”P; Lt’ P55 pa 0 3 2D' 3 ml '- 14—9. 5 P3 113 1 I 3 ES M1 M1 [19 Cflfi‘i‘ a? . film P03 ”’1 Cat/man Dad—or 1:5 @051": airmxt mafia/tale ”1216;45ij "50 G7FOC£LLO€ A Md: QC @— iii, Which matrix represents the total cost of this order? What IS the total cost of this order? 721325 QC : teal Cost 0.}, each proclmp “W cost P- (QC) [3 1 LU [1‘2 =[33+2q+19;) = 33439 1&6? BFJCs. PART II. 1. What are the slope and y-intercept of the line 23; + 4:1: 2 12? )1 = _ 1% + Co .Slope = —2, y—intercept = 6. b. Slope = 4, y-intercept = 12. c. Slope = 4, y—intercept = 6. d. Slope = —2, y~intercept = 12. 6. None of the above. 2. Let L: y = 2:1: — 3, M: y+ 23: = 3 and N: 23:; +2: "—- 3 describe 3 lines in the icy-plane. Which of the following is true? A. L is parallel to M. .Ja. M is perpendicular to N. g L is perpendicular to N. d. M is perpendicular to L. e. None of the above is true. 3. Each Sunday, a newspaper agency sells copies of a certain newspaper for $0.90 per copy. The cost to the agency for each newspaper is $0.60. The agency pays a fixed cost for storage, delivery and so on of $300 per Sunday. How many newspapers need to be sold for the agency to break even? a. 500 C, =5 R b. 1000 vGX+ 500: RX C. 750 20C : \BX d. 250 ‘ow : e 100 7‘ 4 Whichofthefollow' itrueforthi 5 st oflineare nations 2x + y = 5 9 . rngs syem q 4x+2y:8' a. It is consistent and has a unique solution. b. It is consistent and has infinitely many solutions. c. It is inconsistent and has infinitely many solutions. d. It is inconsistent and has a unique solution. .It is inconsistent. 5. For which x is the following true? surnames H5 6. Which of the following is a least squares line of best fit to the set of points _.__ ‘ -3 {(—1,—3),<0,0),<1,4)}? A” [m 2 g A“ [a] .aryz3x' c bfy=4x. .y=77“’+% ll 6. None of the above. 10 m 1m 2 1 1 [" ‘ O a] ‘23 ‘1 [33.0 333:5]:334 7.WhatisA‘1ifA= 3 4 2 J? - \ll ll —2 —1 1 J a' [ — — — - -10! '3 q’ 3 4 2 Ni 3]: “MM 2 3 ‘t 7 b. 1 4: awn-ta M51 —1 2 llul C-[ill] 342 d. A“1 exists, but it is none of a, b or c. @A‘1 does not exist. 8. Eric has some oranges and Pat has some apples. They trade some apples for oranges. Eric keeps 70% of his oranges, gives the rest to Pat and in return Eric gets 60% of Pat’s apples. Assuming that this trading is fair, they want to know the comparison of the values of their fruit, after the trade. Which of the following is true? a. Pat’s fruit is worth twice of Eric’s fruit. Eric’s fruit is worth twice of Pat’s fruit. c. Pat’s fruit is worth the same as Eric’s fruit. (:1. Pat’s fruit is worth % of Eric’s fruit. e. Eric’s fruit is worth g of Pat’s fruit. ‘2? ...
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