This preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
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 éoMoMIQ’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
CMpiam 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 yintercept of the line 23; + 4:1: 2 12? )1 = _ 1% + Co
.Slope = —2, y—intercept = 6. b. Slope = 4, yintercept = 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 icyplane.
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: awnta 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? ...
View
Full Document
 Spring '08
 Kirk

Click to edit the document details