Problem Solving Coaching Notes(April 2012)

8/2/2019 Problem Solving Coaching Notes(April 2012)

1/42

Math 110. Express Z14in the form a+bi, if z _; _ iz=eill/4z14=ei141l/4The period of quality of eZ is eill/2z14=eill/2 = _.28. A six sided dice is known to be counterfeit, the probabilityof rollingany even number istwice the probability of any odd nu mber. If the dice is thrown twice, what is the probability thatthe first roll would be 5 and the second roll would be 672IB:U(!l2 solution included)

46. The eigenvalues ofthe matrix A=[~-4+(b-1)=2+( -1)b=6

b ] are -4 and b-1. Find b-1

64. What is the domain of the function f(x) =4 - .J3x3 - 773x3-7 ~ 0x 3 ~ t- 3x3 ~ 1.33 (note: wri tten in coaching , maybe cor rect i f no 2 .33 avai lab le in cho ices)X3 ~ 2.33 (correct answer in calculator)


2/42

M A T H1) ~;ncf +he : ! : t o r X4 + x2/ - x / ~ 18 .d )(SO Lu1 l01J :+ x 3( 1 ) ( + x ' J . 2yd.1 + / " ' } x c A ' j . -x 3-/d'l-/dx;; 0(4 x3 '/'2y, -l)d.i. i- ( x '1 Q 1 - ~)


3/42

Moth 1t J f i0d th e 6Ul11 o f1 2 . 3- + - +-t ..2~ 3~ 4 .

1& = 1- (nt~)~\\lhen !\:0:, , B

29 .) T r e h, c ta 9 ( . t 10 i\lc CUf'Je ' i : ; ' X e ) l . a t the,p . ; i . " ' t ( \ I I) posses tY' l rough the p " 1('l, ~v) .Nflot- is y o .

[ Y o " e t i l'2 t ~J \ 1 ' 0 t \S

1 Gth e e \g en" clue?

CD( 0 . 5 ) A ere I~ G\Jf' foce aced ro s the 6OfflC f \u\ '0enco\

Value as \'\s ";Oun"e. \ ' \ j ot is tne cPgfuot t cr dhl ?


4/42

\ A a - ~ . u ) .1 8 \ r i A d x iA ~ h i 1 V t t(x)' x- a r c f V 1 h f. i . t . f 'e x ) ' - 1

reX) -e 1 - I ~ y 1- ~ iI Ij-;1,~-]x~~ 4, 1 < ~


5/42

M I\Q~~~~ 1e~lM )


6/42

M-~ r n m ;n~mlX\t ret) =: f i ; 1 T V ~ - 1 7 . ~t, i in I ~ VT \ ' \ 1 ."\lh~ h -f'Lv L t W 'V ' \ J < . . MHx tvrnm o f iV\vuffll'\.tJll-tm *'It. Bn{ mm'~1?- l R t: 1 t 1 T V { , - - M' t J o f ( - O &t )

An '02t~';-ott~ .@ - t : : 3

d J \ V i - O .~(3 ') - :J-"l 0~ - o U l ) -t - - I L -!t",~~ m m + l ' )A t i :H v w j t Y \ J I J ' \ j --fl~ olM ,~ :::x~ t-x'~ - t X -1mt~ H ' l v X -Q\i \ l~?

VL~ L -1 ) 3 V z z : --I, - 4 . O J V . 3 _ ; : . r ,O I fw - t v v r . \ ~ e t t (y\ f ~

~\i- f ~ { , ~ "-t g~2 z: b~ I c , i N : - I { ; X 2 t _ ! 1 2 : : . O J )h I h O l . J t I~ th~ ~-~ rvJ-c; t th t , ~ '~ u fIf) rs(;t:hm ~

4 ( q - fl t g ! j ') _= , 4 -\ ~ z : iIt


7/42

~ - M - ( ? J ~ ~ o. ~'h~ W l u r t s i . . s o - h . b e r ' , t ) ~Of l7hht ; t - ~Y\.~Ie I J \ l 0 W l ; \ 1 1 1 v 1 T h e o r < . " , , _ \ - v _hf- l l

@ N o o t f o ~ l l e . \ ed~~ o f o - 9bJ.(J(( f f W t n i dr 2 - \ ~ ~)J


8/42

, ~ ' C 4 t h t , t f l a t i ( J ~ ) .~)

1 1 )

P'r"IQti.~ ,I a t u qt'' ' '1 ot e rot,.~ o o t t ~ , (lho~1 an~}).\I~'t i s th t Pllf\.lbtion ~~ \ ~ ~ ~ClrJ? p Q~ \; b ; s 1 e o k .J d P ~ S [ 0 Oil H) .lr

p : : ~ . a ~ ~ 2 } rl t t, A ~ t~ 0 , 1 f - , '20'

1()O:: e A ~ ~ : ; " JP ~ Q 0 4 ( ~ ) '1 t r (~ t q ( ) ~

P : 131,44 tho\llQn~ .4X 1 6_ 1/ rX~hS: ( O , 1 ) V ( 3 ) o D ) y1)(1, gj~; ~ 4

x 2 t ~1. ; ~S \J}j st; ~k "


9/42

Math (Pat and Glenn)1. Keyword: al = aAns. Idempotent2. Find point of inflection of equation y "" lru:x

l-ltlXy",,---X2rr -3+21nxy = x30=-3 21nx

3-=lnx2x =4.4817SU b in given: y = 0.3347(4.4817,0.3347)

Sol'n

3. Given matrixabcFind c

Solutiona+2b+3c"04a +Sb +6c= 17a +8b +9c=0

then find c*Note: not real values given inside second matrix; Just to il lustrate concept


10/42

P ( l n G l t : a 1 v a i u e ~ i LI

J e f f09 1 : \ < ~~. e ~ If) (it 1) d t . F ."lti ~ ~t-

o~. o t y - : : e 1 " : \ \ Y 1 ( ) < 2 t 1) 2y :o H

$2' W n o . i r s # \ e ~IVld .ev - ~ ' a ' ~ 7 ~ lOV\$ ' l~

Q \ . h _ ~ 2. 'I. ~-I = ' 2. 'l~ _ ~ r:;d~ ~I' a /1 - &~~~ ; ~ = % ( 1 ' / " - ) = ~

~ ~ o l ' Z \ r Io x - #{ ~ ~ - ? r r' / . - : : : 1 -1 . . 1 1


11/42

f \ f i A \ T H 1\ J . . ' ) 0 \ ~ e ( \ : dl~r4 1 I t ? I D i r m ~ t v t " e r t i d l ;r l V 1 d d i ( ) ~ D Y l a \ S

~n~: ~L~ :: \ V7 . "

}O-) ~1." ~4 L I-J")f \N~ t 9 o w \ ) f f

i\~) b i v t l t l ~ ~ ~ \ 0ts> , D~-1;o 1 1

~ : : - ( ' l - y J(X ~ ' ) L Y 1 ) : : :(10)00 ) O ~ )x y t - : - ~tl


12/42

i J f i n d it., d u 1 V O n ' 4 t 1 o f J' ~ 1 - - J" " " f \ A ~ ~ t o ~ .

. t o ) 1" ono\.~t\t funcno",~ I i f ~ (J) it O n t N l t l r e . t u t ' l d i o n ftd' ls r o u n d e d I~ o f (J) t l l J t - \ ' b e , G l t p n . t t f )M t t u n c l i o V i . T h U : it ~ri~ 0 1 : _ _" " L io u \ l i I I e . " T h e o r e M

~g). A m a t r i x I . t t o i d t v bt _ N~ it i s 0t 1 U f ' f U m ~ l e . " a f r i J ' . ,~ ltfO r o W s tlttt a ~ p e o r . . c o t ~ ~Ih ~ W I t- r r o t r i 1 . I o n a i ' t e -f i t ' $ t V i W I ~ O e r I t r _ y a t o~ ro ~ ~weo r . > h > ~t- ri.9~ o f ~f, ~ r . s : tt 1 J i n lu o ~ " ' o ~ h i.9 ~ ~ ~ .(VI e c N r l o V l

& c , ) ~ : , (3) u ' (~,-9) " rjn d \ ? I V - U I, , - , = Ils,~{i)-(~,-'l)\

. \O,${ji21~ 1. 2 q

7) ~ ~ e h > \ O r(ih1~otof r o ~ 0 ~e~~cient~ r-r~nn()r\CL o f (g . l\e. flQnr u t . t i c t , W I t r d r i g c r o t o r It $)'~. N n - A . i s : ~ l o w c . s : t -km?Uoture #titC O n b e o b t o in e a iM r i d c , ~ r t f u ~ o t o f ?N1 t . p . _!L1 i \ - T~

( , = it . N V 'l o t t \ ( ~e, r h c r x l r l ' l l . l t l lflu.,LlfOL s t r e s s i f it c o r r i c ' ~ (jI ~di~ m o r n e . n . t o f ( p , 1 W N -m ?' "V ) f ,~

b d ' 2~ ~ (C c l X X J )Coo~ rt1>(O.'lfn')2: l~M P a h

812) A ~lil1dc.r wi~ 0 diameter o~ , em ot 30'(, it h > b e - slit ~ c ; I c _ c :\~ o k o f ! 0 ~tu.l ? L o t . ( _ w i ~ o d i( ; \ V Y 1 e -w t ) ( . \C lq 1 e m a t ~OG . T o l \I~{.ftt t .vY1~Otuft n u c t . ~c, & t c . c l . p t o t c . . be , ~eotcd? o(rtw. If. JO~(}file


14/42

b~ n ~ ~ ~ \ 2 I ~c\lJ " : " \ t" '0 t ..,.U< \~ -bQJ\)(dx~1.. b 1,s:N~t t ' lJm~er:

'"'~ I~o~n: tJ ~ {\r-c


15/42

frM iI-\ ( \.10 \ ~ t > " \. ., ., " 'P , ,i) ~'f) - 1 : eve ~ o . V \ !-

\\'1- -, ~2 .,. _ _ ,

. ,0 v \ "" '.~t ') ~t '\ C\f (,XU'V' 9;-

3 ; ' ) . ~'V1 l..\{~~'.,v\ 't\' " ' 11 0. r 1 v ' \O j ' \ Z . s, ~ _ "\ 01~01C M ~ : 1 '/J t~ \~ ~ '\ 't \l\ \'

( ) G . ~"{'V1 V I " : . \ - ;A , . 0."D &t' rJ tVl V ) : . '~5if\d t 'V}t\) : N A. . 0 \ ' 1 \ ~ , 11 t . .; t ' 3_-~:;. V 1 . . r . ' f l f ~ T 4 v y ; i ~ t c\. 0 \ tiL"\P - : '1 D . ~v (fi\di ((t C-\< ' F ' . . I . y = \~ A It

~ -:. ~,,:>':) " ' ; t ' J T) -; G _ i l t 1 \ ; ; V.'\ \. .35 - ~ - '~ ~ 1 1f -- I


16/42

iM. t-\~~ \A II'~ \ ~ ('l.l.~ ({')&i ltv M~ ; ; > t >W N-~D ~ ( P c ' W 'Id~ ~ Oc \IV)

< J D \ ~ f = (plv ' \ M" t ' \-UJM t"\ b..(.\)c{t.~b t 1 < - tl'" c{{ft'\rli~ V l 2 t > O V ) : : n r v 1 P (>, 1..__.~--c o D~)lo:~)'

80\ V 1 ' .~ ; . \ ' < i ? O " ' ~

V v 1 t - c . 1 '1 r C\ Y \ t j ( : . . Q L 1 - \C\ 11 0 -'9 " C'\ V\~ ' i t ' C 1 ~ ~V\c.\tfev\(t' V : : : . 1 0 -l)~

... "l\~O) tC.v1 t t l O - " l t : ) : -Me' y . ( , , , \A ' l . { ) ' . .


17/42

f ' v I A : i:l'\!) 5 ~ 1 - 1 \ x _ _ ~ ~11 U h K )z) t-(je[",\J7t(tE' ..:f('jet1~Je.(_'h:l\,f 0 0 F -V l C l - i U ; X [ I ( ~ , J~/f.'; j~i'1. " 'O I ( U ' f ( A _ \ J c. : Z . . J " ) _ _ , .

f - . ~ c V " L1 \/< (':,kV e f ~ s : C 2 .\ \) ): : : ' l ~eq \j~,(a~ -r 3 -.: C t \ I )1. ,'\ (C { < ;( 'Z \ t ( () o-~ (11 (:lCft!-. I ~~",--:"\??/ {J' I. 0 - VJ()


18/42

'2~.~ A , , , e { ( " ' c - < f ~ ~ l hOt$ . .~'t- 0\. $ . ' : :N \J.-s, f. f CJ~t ~"h < 7 r e " , .c(~~M t )c . "l~ .hOG ? ' r~ -~~ l ,I! vi c. )

~ o.q~v -

2.-_ . ~ :2 s f :~-: : z l '1 '6 $

(,f{(\iwl-Q 7Ylflti,\t)h.h.~ 'H u'h ..H v n c . . . . _ I t . < ? ~!)~4{t'


19/42

GEAS 1

10. What power would a spindle 55mm in diameter transmits 480rpm? Stress allowed for shortstaff is 59N/mm2

16Tl:=rrd3 59 = 16T T=1927391.637N (The measurements used Is in mm. conver t to m. by dividing 1000)rr553 T=1927.391637 N

28. What is the percent composition of oxygen in oxide when magnesium ribbon weighing0.32g is burned in oxygen which results to an oxide weighing 0.53g?(Note: this is the same statement in coaching but does not make sense how a 0.32g would end up 0.53g when burned inoxygen, nonetheless, solution as follows)

0.53-0.32 X 100% = 40%0.53

46. A household heat pump is used to maintain an inside temperature of 20e on a day whenthe outside temperature is -10e. If the heat pump delivers heat to the house at a rate of 15kW.How much power is supplied to run the heat pump?TH= 20+273 = 293K Tc=-10+273 = 263K

293K 9.766293K-263KPower = rate Of heat = 15kW

cop 9.766


20/42

~tM l\)4 ) i 1 J G \ . r ~ ~ t b~lhu, h" s .~~& v \ . m . 2) M . I 1 t 1 i s ~ t f o S ;~ ( { I1 10 V ' f I C\~C,~~u t t \ iW I 'I lJi~h f r t S l " r e f II~k ftl . IJIlU tiV l''\\\! iMuut r r r t ! IJ

W ~ i > l If - l i l t IM(rl\~\ em ~ ~ ~ ~ \m f I~~ o I l o \ ~1) ' \ .n1' l~IIS\j. 1 1 1 ! ~ ill~rt~t \ \ t H \ A r t \ \f ) - - t l t \ b Q \ l l u n 1 ~\I1'\\'\U If) ~ ~H\I'.r. W ~ U t t 11. {V I ~ !. - \ I I ! I I I V \ 1 ' 1 11 ' " \ r t e t , , 4 ~ ! rM I.

2 j) t ~N~)NV \~ - t \ I I S j , l o ~ Y " ' ) ( 8 I ' i l V l r ~ e l.R)~I A : ~ . 3 ~ ' J . . 10~ J // ( P o o l S . ) Q J ~ !\~~)~

/ 2 ~ eR ~ Q . \ \ ~ ~ j \ \ ) ' i ) ~ / o- = - \\.t;~ 1 1 / 0 /j (l \ s . )

4 t ) - r h t ; t ' l 1 U f u t t ' l C f f C i \ ~ h r ( \ IJJ~er~tD1 ~ I? r~ i r t .5ml l ' l'Wl~ s\\t. n ,~ f f f V 1 \r~{rr n x i " , , , , J f \ 10 \ "b le S lt t r#lm un~1 ~ b tr'ft~ b e c O t v 1 s t j~ ( ) c c ~ r J

1 M ~t f \ ) r i 1 i . ~ 1 ~ . e f i r s t b r t 1 e rI l \ ' f i im . ! . f ',l'inJi! .rht r ~ t l l r t 1Wh~.~ II ~L S t r " r ~ - h u ( ) b t i W l C V >~( JiiH ~f A : ; ~ ~ z : ~ ( 0 ~ W H 1 ' )"- \.5mMl' (AM)

1 1 ) W ~ v r t is ~e ~ ~ i m c ' h \ ) V \ -\i"'~~rr U G \ \ t \ - \ ' l y) u f ~ 0 \ ( \ c 'v l u ~ l l e . r co f ef r ( } .~~I>\ \.. \ I , ) W~\jtl[~.jj.,

\ " J . . \ ~ rf' .

EtNt~!Q"~~Ht 'fI\N'{tS~~\)


21/42

G E A S t11.)A ..stet! .5 ( i ) 1 Y " , ~c'"9h ( ' \9 \C 'l9 . . .crhcoll~ suPI)(ds

Q lead of zooo N lJcgltCllf\9 me \ \J~9ht of f e\'VlCe.,c:ldCX'l"f 'i'(lc the dlCh"l"eter If ttIe srrcss IS I '\C\to exceed 140 MPa ond t he - e c 1 '9 < . 1 ti o l \ I S ( '\ 0- 1 r oe)(cad 4 r(1tn. t: 2.00, (]X) I / l P o .

cons' ,dc(1 l '9 1hC s'n:$.~:r ~A1'10X 106 0: '2000s . d'l4

d o < 4 . '2 1 9 1'('1'(' Jconside t i rg iY lC dC rgO \\C ( '\ :

s : ; ~ PLAfo 00 4 ~ (2000) ( (; )~ d2 (~CC,CCO~IOG)

29.)A elding r(lcc~ine costs ~ -+ S.C CO N IIh O f'l ~tin"C\tc~ II~oi ~ ~oorG The.rol\lQge value. ,-6 ~ ') . SQ(). Dcte rt.'\.nCthe a:.prcclGt100. mtC u&ij),g o&i'C''Cllg\'\t \ i , " l ( ; . IYIdt\Od.

d e Co - eN 4S,COO''2.S00 : B. 9VOn !5

dep ro re ~ j _ _ x l O o o /~ - 8,~O x 100 . o J .C : ; , 4 5 , COOI - ~ - ra-re-' 1 < 0 . b < 3 " i " J

ti) A heal p0N'\~ iG \0 1\"('Ii(',roi\ 01". u,\


22/42

1 1 ' )

T c : e , q 1 0 C t 11 1: ~ 7 1 0 kT t t ~ ~ g q ' C r 1 1 $ : Q ~ 1 k '~ ~ 1 _ ~ ; _ _ 10 :.r H I q t 1

S i n j \ , { . r o l1 lf O \l~ 4 - 1 = ado r ; I ~2l: 4 - 1Ol t )~; I}

~ t O b 4 H ) ~ 0 \ , 3 1~ -, G r ~

~ , ,~ i - r t f 1 < d i M ' \ (00. h '" ' 4 t~t \ , . / c r l < J\Jt\~ vith ~m~ , ' I , f . ! L A ' " m ~ ~ I 4 . < )h:- \ 3 ~

W hoJ \ s ~ ( t " ' , l~"'~~~ ?t ; : A

~nt ~ m ) l ; l~ -,


23/42

~ p t . t h { ) i \ ~ V I r 1 \ , \ hY\~ - j? r ~ t~, (At'J'- ~ t'J, ~- b e r t f 'Y ' -hKI P i l l \ c k f~. F . t r m tL~Y\ r rf\-tlftrv ~ , (, I (\h~V\'\'\(, (,I'Y' \>Y\--i '~l I ~ I s~}1 ttA~\tlh.A,r--u. . , ' t , , ( " 1 ""-v 'M i l 1 4 'w ~ i\ Iv I 'Y ) ~ , IVh -u - i s

U ( l i ' _ K " f i t ~ ) 1~vtvhil') ' r 'H\v f C ~ o~nt ~p . . : U t A (14 - T s 4 )

z : ( t ; . G 1 ; < 1 - ~ ) ( t ~ ) ( ( . ~ ) ( '3 1- f f . - 1 9 { 1 ~ )f~ 1 ~ g - , i ' \r\(. , o i l C t 1 A 1. i\'C,lt4{ fq,. r.-tJ I ( tV 1 . t1 1 1~"1' i Ir~u 'iV)l,('(I' ~ < . . d ~ 1~0,v n 1h(t i~ if , C - ~ \ ) 1 1 1 { _ , P ( \ l ~ V \ ~ f ' 1r

~-t~'ll t V V 1 ' r ' t t , i(\0{~r~i-f : _ '(,+~)'\

F _ p s - o ( (n!): : : . ..,_, -_--F ~((."ffiWh ( , l I t ' ; > 'HIt; ('(V..ll"Y\l,~~ ~lv o f rthckt,-v i ' fPii"~ c \ . , \ " VYl{/t("r l~ jl),\fYl 0\(\'( ~;:: ~ 1m --

J 'J,. ( i : : . , ,?~ j_ - = - f I 2 2 _ I IY\fY\ )I'Y\ > . l : > - r n;Y"


24/42

& E A S 1I) A student rJ+h Cl 2.0 KB bloc!< o - P ice@ oc, piaces it o n q IC lrg e rookCtlcariY1g Ql'1ol wGl tohes it me-l t . "'nettis the ohqhSc of cniroPi o~ the i c e - ?SOLUTlOV:Q . ' " ml,f l 1 = - - ' 2 , 5 1 < 9L; 3.34)( 105J/K90. " ' (2.5K3) ( .3.3 '1)< 40.5 J /K~)Q" 835x105JS > < _ g _ : 8.3$Xl05J =[3059 o J / K ]i 2 '73 K .....:-----~

19 ) V l /h C l l - ; . 5 tre bCB t r c s o l v i V l 9 p o w e r at'Q lens when the spqce betvvCO' l tV)clens - (Jr')o\ tne object I'~ a liqvl'cj V ' J /OVl IV lo\CX o - J : Y ' c - P ractio1) of 1.55. Usc()1 1 1 ' 9 1 ' \ t wClv'c-lef"'l.jth 0 + ')(10-rm.SOLUTION:

t - J A ~ y) Glnplet ~ = - TO ' .far m a x i mvm NA~ A : : : 15,B l.5 in ('1-0 ')] ~ 1 ' 1 - 'RP" (j.Gi'A

I \ , J ARP C (o .GO(GJ(lQ -'f) :::[2.51)( 10-'1 m \

, t ( ; ; '

. 3 1 ' ) A t p e n d t u l v l Y l consists 0 + q . 3 - P twire ~, xed crt o~ enq and CQrn e sCI tlb obJect at- the othCf'. It sVlii 1 ' 1 9 5b o O ! < qncl -tortn a t - q vert i eql plat') anq\ 'V as -P o un d to have a vvtoCiry 0 + IOm/swhen tht': aVl,gle 0+ ' dc+lectio l1 is 45'.A + thqt i ( )s tC{nl( whqt is the tension of+hc strj n5~~OLuTIO fJ .T '" r n v 7 + n ' 19 C.OSvRlet- ~ :: 'tS'm '" 41 b r 3:- Slu93~ ~ + - / s 32V '" ';0 #/5R = 3 + +T = l f 2 S I \ ) 9 ) ( 1 0 - p + / s ) 2 t ( 4 I b ) c o S ( + S ,

gf+


25/42

G E A 5--p ., > ; 1 I 1 P ~ ' s ~ \ ? p a r t e J b c Q n 1 .1 0 II') l o t 1 J . c . (m i e J 'J- U ~ ; r Q I W 1 , J 1 s f n b > 1 - i d l o o t ! o ~ 2 0 v , t J i f Y ' l P d e r m iN + h t'J?Iv~ d ~ 1 1 1 , f } 1 l ' ' I l1Vh"l J~l'vr ',"1 t h e . beom c M a . ib / 1 0 , 1 > l d o d .

5 1 ) w 1 ' 1 0 t - !t: F ' I . e \ - t R 1 z 2 0D k iJ'2 . 1 2 \ - : 2 0 0 k t - JI i : : : I O O k 0 l - - ? (11)1'

0 - O~ qr''/ A 'f. _! etf t"" e . 7< ' O C l > ~ L1 e{y-"fA 0.2 '~l.Il~ (3

r . < : l . l A .I.L . [ " " 12 0 d U - 1 J' __L '. i.. t ;.J. - h" l 2 T L~~ y r , v f " f I 7 J - . , (J\ . / I " ' -V ' J \ ' I l < - ~ e f r"'JIG t-- I> dd .HWl ' r r " " ' "a ~ v t ~ r !e~roJ1uV\ 0 + - I h oJ j< I l l 41 l - d d's ~"1 H o e p ) x ; I - t " , , /l e V I t~l . I . f1 J (..~ S 5 6 111)1.

r-: ( : : 1 e . D c t - e r m i l ' { - i t < -diCit",d~ o~ f 6 "~ f'1lf;) i> 301",'1

( 1- \ I 1.>lf~ )e -: l~tJ ;"') \ I L W l2 S (N\')


26/42

G a s tIll~1 B f l d l~~V~lA.fVl N U , t )e r i M . ( ~eY{ule W i H 1 r e h a t t i V { f ~ 1 C ( e ;J / , 3 1

N , A . ' ; n S I ( t ~t U S t ~ " lV ~ ~ I V t h \ X l t l l l t W ! N / ~ .

f J . l \ . " L! r S i n ~O

p . h A l l TL ~ c h u J \ v w l d w c .tf h t l t l 1 + ( ' % ' 1 1 - . )W l\~ f, , { l

A ~ Sl{r~e a~l S I = C h C H ' l 0 e i ( 1 ! u v t f L r & t k it


27/42

& ~S~ 7If (} .p e v r o t t l feCtl v e s (,;.? m e A do~~ of aII'm pavhctf" ,hew mUGt1 e.xposute does -H1e p YSO n VlQ v(" f~ I evmSc r f t tmrem e t ' C t o t (Q F)

f u r Gt{pnQ I &v.oh t y ~trr z : 20t'tVlt - = O'? ('20) z : L t U 1/

1~ tVl i t1~ s t u d _ Y t ; f - s tnnc fluloi I t t 1 - e force e xe rfe cl by\ A . K l - t e _ r d V I o v em e a I f6 f " e l ~ t o n e - e n fit; t e a O ~ 0 p o , V lr ~ ' " (lr ceV1lf" o f ptt s - ! \ t tC . If tk~ c p If' l c l rOAlaro . ~ c t ftle wa te r S UvfQ cf L - f ~i ~tlf t o ttze r o C fo f -H\e r - JC , ot vtktlt ti.lS t a n c t f v t > v n fft~ ~ ! e rc ur face (t tile CeM. fer o f f J V < ! & S ' u ~ .rrcl~CP = - 4 - f - !=-~ + . 0 > 4 '" s : . dfI( ~ 1~ '2(1) 8


28/42

6. t~i~)J ) ! / J I / Q . l e n s ftul\H ( > / c u r v a i 4 1 t l t h C A Y )

(cmal'( 1 ( I f I ~ I1Id'I\)} r i clArllUJe ']Ir e t r o < i l - J Q . . i n < k . X = - I 51

f i Y ' d f o a t l l e r l 4 t hA I 'K : I )1~~l) ( - 11f l 1 2 1 ~ ~

J ; 0 (1-1 ) ( ~ ~ _ ~ )f; - 1 ' 1 C W \

7 : - ) N \ O i l ' Y l U W I d i ~ < e , I ~ 1~ ~1j ~< 1 ~ \t ~ \ e ~ f J P o ' t C \ ) '\ d W C \ ~ r@ ~ \ o t~ 1 tC J 'J i ( ~ - _ < t - ~ ~- c ! ; 1 4 4 f

l~ \)If))~ - (2.q~)'l-:: ?'~

4~}>i~~.f;raS~ e d 1 l . o d tj~ T e r n p t o . f v l r e~,n.1 1 1H .A tA ~ I\d ' Z O . c ~f f < D d

-1t...b --- t :


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GEAS(Pat and Glenn)

1. ind moment at A given the figure below 100N10m l . ,

Consider half of the beam100N

R,Andget V~lby summing moments at center ofthe half beam

Sm

2. ind the power gilt n amount of heat and two temperatures in "C.SoI'n:First find the coefficient of performance ofthe system:

l'cCOp= Th-Tc

Wtll~reboth temperatures must be in Kelvin.To find the power, use

QcoP='WINhere Q = heat in joules and W = power in watts

3. ind rate of di ffusion given molecular weight of an element.

Sol'n:Rate of diffusion:: ~vJlfIVINhere MIN ismolecular weight


30/42

I n R ~ d T r a ~ I lI 1 i { { , I 1 Y I R ( X . - f t - o J - ( ) 1 1 k : w , i~ F 1 I G t i j I I - d . . L l l 1 " 'q Y ,d~f V . d i c t ~ a + : n 1'1l~ll\l i(\ iM R c t - l t ~h - \ t t l ? ft

h ' l~ r l l ( h i l t ' C j h ~o J t1 J I I n ~ 0 ~ I e d l t j )fJ c 9 0 ' r ( ) d I C l ~ CUI~ I e

~ q o o _ J r Cf w m f l l j l i e v J ~ J e e, t ( j ! O ~ I " J { p . n (~!')

- ~ ~1_ I 0 1 ~~1

- r ~ ~ l~-4 { f{~~4 !K h' d:~'-I1'te ~ ~ttt;IW ( ) . f \ t i T I 1 k 1 ( 1 1 1 ; # 4 ' ~ ! I t ~ 1 I : l1 ) ( ' " ~ ~ [ { q ! !~U~~q { K U l l1 ) ( , ~ l U ( e l i M ~ t


31/42

C D - t t L d ' B f l ' ) > ; 3 V 1 ( f \ ~J .. .,.(me.,f , 1 1 9 c 1 6 r i t L )1( ) i~e YnWJv .Kme ;J o ~ ll i ~ ~ O d 8 . r r . D . P . v e f .~i~;1q\ I c ' { t i " ' { d B I ' ) 0 .

~o~\.H'll,J

@ ! ) ; 1 & m I / t - f k M D c A l 1 c d ! 2 e i W l . t l ' , e l 1 'l ( .k ( l , V : - i - h sur faUl , refrod."'i;-f,( o~ 4 ~ C til'1LI o J r I 1 V > ~ Lh e , i ~ ~ ( , ~ 101:) rdt ob,,-.(o!. 5 1? /). le ve l10..u\lllN iY\ ' ': , , \ . > + 't o 5 h

= 4 - r o -I - 4 . Cl}h'\~ 4 - 5 G\.~ -f F lU I,NOll\":

h i~rill h v r c i a J ) 0 + ~(t~j

P ( f e M l ' ( tk > L t ' H c : r - C f. V I l J e . . o \ - 1 ' c . v d i f l 1 t d k ~ o v J . / \ ~ ~ o . t 1 ~ u l W ' d;~+t>nlt. of fk OYlt~G' o r CAuwtOl1.! t ror .s fh~c S 7 J e m w'+l ' . w < i - + c r - 0 ' 0 i 1 ~ 1 e . toyYIpo~rJj a , . ij 0 3 r a J

-& -0 ' : d-o t (3 0- : 0 .1 + O .~U o : : ()4 r ~ -1' p.).l~


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tz,T\t ) t t V ' q c r o ( 5 ' ~ h ' - I n C \ B f

(g , v e V ) 10 d bA r K I d ~ x : ; q o -1D :; J O d J ; f

, - o o o 4 r ;o D D O ~ r - I) hdD u

h D S . 4~N " ~ A R f f t t ~ ~ It

4 q b l v e V l C ~ ~ D J A fR ~ J K

~~ . .f l h n ~ a C 1 n 0 t . z, _ I_

f 4 f \ C


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-

: & s: . ! Z ! . - \ \ )q iJ-J t . i " i j o 2 S: t ; : ; = I \ . 2 1 Jl ~ ( f \ N S )

Q r } . 1 V \ M i c r ' v v U \ v t ~um",""\(!I\.n~t'lS I\ V \ f . A \ \ J . t \ , t ( ,w r h ~ n t ~ f l o s s w~n\\~~i\ilj ~ J l e - l i l ' f q q . q C f J j ' I .

S~\o.l \1II1/I~~ , " \ l l f ~ - l u 'jl- ~ )

:. -10 \~ u - U . q ~ ~ q ~ S ):: $~. \ Ij ( I \ t . J S . )

~rJ~~S~ r 1 t ' \

~~t',jI\Nif~I f \ \ )


34/42

tS, {1.l' ~ . p~k

P b ; (1 I < b P s~ . I),~ ~ ~b .Ig \ J

1 1 - - -J~ ~ c..- .-_ \t --o

~ I' ) M~ I + i p a t ~ t H tL J :


35/42

E S T 1i. A e(r .Je\O\Je/ c\f'"\o~ 'n \ 0{ a tD& \C rt\cpnorlveno (le \ \\\ \coted n(l\ a \ C I e o \ 1 z CO~IC~ e x p e r i e n c e d~ f'< '\{ '\\r< '\J< "< ' ~'\J.tc cle\o~ ot 4uO UG . De.\-c(\ 'Y'I\ne \"\'\et \ lO)(\ \ ' { 'v \"X\ ao-c\ute C\0:j thd\ ~ f r cq~enc~ 1roff\ eoo

0 1 QGOO H l. (O" 'gc c o . eX ?e r\ce.Mo)(.. E D ; : ; 4Co uS T ~13)uSI t J I 0 = '2 , 15 us J

29) In hber opncs,onc 01 tnc ioctor! ~(J\ offed~ fueoss , cc (SQ0 \\ co s 'IS tnc "..\1ca\ gop \ 0 G &thor CQuses frcs \ tess, clue 10 cno'(\gc \'" n:froc~,'()de~ 'TrOif\ \he COre en,) 10 c oir ( 9)' on blJC\" toW"\t cere l fq) . If n,~ LQ and 9 :: L 3 , fh'\O the-fres ()e \ k . . . < ;

frc -n e\ \ c , - ~ 10'\08 ( ( ' ) 9 + 0 I ~ = - ' 0 \ ~ ( - t 2 0 t'2\Ln - i J 1 . 0 -11. )I - - - - - - - - - - - - - - - - - - ~ ~= 9. ltd J

41.) In trdn


36/42

EST110. A 1004Hz test tone istransmitted over atelephone circuit at OdBmand received at -16dBm.Determine the 1004Hz circuit gain.

OdBm+(-16dBm) = 16dB or lossof 16db

28. A European ITU-TTDMsystem is using added channel framing to achieve framesynchronization. If the number of bits per frame is 512 and the number of bits per frame code is8,what is the number of bits needed to acquire frame synchronization?

N b f bi f f hroni N2 5122um er 0 Its or rame sync roruzatron =--L- =--8- =S12(2-1) 2(2-1)

46. In room acoustics, if the absorption coefficient is to be measured at 500Hz, what volume ofthe chamber is required?f=1253~

~Vm3


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. y h C \ t i > H v l"< -Illt.; ~ iCH:;[(l"f ~ l - e " ( 1 ) < . i c l j1t-C11IS,,,,,,, m L~n


38/42

EST(Pat and Glenn)1. Find clBrn level of the signal given signal level of 42dBm, 16dBrnC noise measurement and-4OdBmTLP.

Sol'n:dBm = signal level- (-9OdBmJdBm=-4Z+90Ans.48d8m

2. How long should aw ire _A be to be considered a transmission l ine?

Sol'n:0.1A

3. In microwave communications, what is the amount of loss with reliability of 99.995%

Soln:loss = -101og(l-R)


39/42

E) Deterl'Y);ne thl: Y 'Y l lV l l y Y 1 U m cmo i V ' I ' v 1 t h(JCCC5sary to pass 20 Kbps blnClrysi 9 f ' 1 Q I u S , ~ 3 ASK .SOLun 0 1 1 1 :6~:: .pb

NFor A S I Vl ~ 1BW;: 20 :< bf~ ~ 1 2 o J < l - t t I

1

; < f ) )t' l ClCOlJstj C/ - P O I " C l temp ChQfl9C O t 50 'c\ ' I I ('Ie! j- IS 1 i - - e speed o~ SDUf'd I ) dry C I ir~SOLUT IO I \ J :

V ~ 33 ,. 4S J Tk\ 2+3v ~ 331. + 5

31) Wflat- ,' s tire ~csidvaJ BI't C 'fro f' Rcrjoof Q Y1 l9 " " c P " ' a < : ; j e rea.l c;"CtJl t ~'il If. C !kl"Stv! d~ 5000 Km ~sO LuT lO tJ .RcBR = l x .5) ( i0- q

.! 5 000l '" s 000


40/42

E S T( ~ A W optlCC l I H ber- n o 5 (;I bJrd w t c l l t 1 r l ! t 1 l ' 1 9 0+X-oolv tH !--l:m { . v~cd L S Htf r o r c tW t c t~ 0 1 - (A~ se~e vl_ " Wb\e

f J ' N : : S DO N 'L 1 c - 1 < m ~ 8wGltto (i i < v r 1?ooof t : : 0& 1 KW l

o / t jh C O M A , W ~~ tc n ,e 1!e .~l red m.ob~eplWnC t v C A V l S w l l t t c r ~ , . . If fttI f c l ~ V J Q I m m ~M ea~ u rW af ~ k x 1 ~ e l~r r z: -1w - to 1~P , t: _ ;q . ('t\S a . ~ r 1 lr : z : \ . o q f \ Wt

_ 2 3 1 5 J . 1 \V (clem)1m ' "


41/42

n"e . \ ' 055 c l J c: , - ~ -li-(. C~'j' ~ iV'~ t j . n {'r~(.I( " ' t o \ '1'{ ,-,O ft. \ \( (1, -e - I ~ I l~" \. :$

\

" OJ ~l'}O ~ .. ? oj) -1 ,? ,

-;:1.:'}" Iu d t?G.: \ 1\ ' iJ A~-r-n" ~I ~"t f>\ .fleo:: lorobps.

" "' fl) r ' U t 'c ~ l1 I\.~ I < > . - t . u 0;: .L, z ~f lo [ f > t>&' i :> ( ) - .

tk\..~ \'o(t"'l~ 0-0\ "'~Cl :-..!-?,.~


42/42

(~T2) Wrot i~ ~ p c v ~ f rc~

rror ~uenCj 0 $1 k .H ! I 0b l rok O &\:~?I\J1 1f. I In - ~ I

2 rC - ~ 3 1 l,

2

w . a h o o o f 0 blror~ s : t C ' 0 t ' 1 O L wi~s{Dc.t frr~ t -C ~ ~ H l 0 d i~put

20') W h 1 t I~ t r c ~ { . l o o d r o 0 (NLR) 0 ~ lJ~rol.l" 0 N o r ~ A l 'f 'W c o nA 1 s 1 toM W s c , o o ollow ~ ~ tm '1'VI NL R : -I~ h> log til

: -I" I 10L~ 3(,00t - J L R ' \ q k (. I

N o n ; N'~ ~IU ~ o f'IJm~p

~ ~ ) J Y l h u P O ~ ~ l t t 1 ( . scotlc r ~ ro~ oV 'I ~t (ur o ce rc fro cl1 vi~ o ft ro~ , i~ _ g e e o n I . e 2 0 4 u V ' O ~t S \ J r f o C l rdro(hv,~ 0 r C G C J l J ' t \ jJ t C n o V l I~ ~ 0 2 \\ jh?t i!; t o c i v a l ~ r f o c t r t~ochv ,~?r- N~: N t{ t N r s

27 ~ 0 4 I 2 Q !

2N{ ! l O ! b I

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Problem Solving Coaching Notes(April 2012)