wo(..lr.i L"'J b]. tr+ +&..) i'> 't\uow).,...,. (o.. J \,} --ti \(' m'\...\,,.q.)).

Size: px
Start display at page:

Download "wo(..lr.i L"'J b]. tr+ +&..) i'> 't\uow).,...,. (o.. J \,} --ti \(' m'\...\,,.q.))."

Transcription

1 Applying Theorems in Calculus 11ter111ediate Value Theorem, Ettreme Value Theorem, Rolle 's Theorem, and l\ea11 Value Theorem Before we begin. let's remember what each of these theorems says about a function. ntermediate Value Theorem ) i ec,..._ "'v..bc.a. O'o'\. [o..l b1 o-j.. ; ') <.f('o) er (b) < '), \c; o± lust-- (a.., 'o; s (c.):. v.j11 q Extreme Value Theorem.f(.,..)\} W"\Vc,..v,:)._ (o._l b] ) MVS1" b,_ o.- o\v\.--e. >'Y\JW\ aw.cl <>.\, a\l..)t r,1 wo(..lr.i L"'J b]. oh) -c<i., <JJ,;,&..., " a.. ) x :. \,, &-r CJJ-\-\, u..1.. v t; A.,\:>]. Rolle's Theorem.f<.,. ') is c.c,-.,.+;"'u " C:: ct., 'o] q:-t.r <tl? c ( o..., lo +(cu:: ), l '-\tq / o c.. CV\ (o..., 'o) '?1Jc1_... '(c.') -= 0. Mean Value Theorem tr+ +&..) i'> 't\uow).,...,. (o.. J \,} --ti \(' m'\...\,,.q.))... '> o.j-e.,j... "t?>.,u.st \JJ_, 1,L <!. :o.) 'o) '$1.lek... -t'(c.') = +co..)-+c'oj_. o..-'t>,\

2 The rate at which waterloows oui)ofa pipe. in allons per hourl is given by a differentiable function R of timer. The table below shows the rate as measured every 3 hours for a 2-1-hour period <hours) R(t) (gallons per l l hour) a. Estimate the value of R'(S). indicating correct units of measure. Explain what this value means about R(t} S?: 0.\";3 Q pvhr..j 'R.'(s') {<.(' )- ( ) 3-'- -3 c.l 'R'(s') :::i, o l '("Q.t Q..+ v..>h.t wo4.u- is ft.-wi P 't) f> L \ * LV\c.. "u J.. t.:.s. b. Using correct units of measure. find the average rate of change of R(t} from 1 = 3 tor = 18. Co;) -'Rl.\V _ - \O."t - \0,1 -S c. s there some time,. 0 < t < 24. such that R'(t)= O? Justify your answer. Slf'\ca. (2.(.lrj i':. f e--bjo\e. 9"Y\ ro, 2 4:\'] o,.,.,.d C.t>') -:: R(24J = C\. L. 1 -tt...c. ceol.4's '-- : f) t " O<'...t<- '-1' ck 'R.(-t"') c.

3 .,Jc: The total order and transportation cost C(x). m ofbottles of Pepsi c>t- Cola is approximated,,\ C(x) = 10.oonf'.!+ "f: 1opoo -t,-. 'l.. l '\x x+3,k G.-t\)J where xis the order size in number of bottles of Pepsi Cola in hundreds. Answer the following questions. by the function a s chere guaranteed a value of r on the interval O S r S 3 such that the average rate of chan ii of cost is equal to C'(r)? Give a reason for your answer. Slv\c.A..tt:,.'), u o.:k- :.O, C.. ) 't\ 't O'V\. [0 3], e/ N\,\) :r d,l)._\.i>'\uhv.) 8" ea. o... v O r c C: re::. Sv -tt..jt C.. 1 (r') -: C (o) -CC: ). 0-3 b. s chcre a value of r on the inter v al 3 Sr S 6 such that C'(r) = 0. Give a reason for your answer and if such a value of r exists. then find t value of r. J St C. )\ W'U t<.:,.): [x '1. :x.+3 3)1.. [3,ol cl.,;. ' c ):. 10)000 [ (x "" 1'1')(1,,_;.'l)- (2.)(. j)("'\>o.-\-351 b'y\ (3 1 b) f>-a C.u)-=. ( ) : ; 3 3 c. (i.) = to 3. 3!».3 -t 3 ) j C.C.lo)-: <g J \e. e.-,... eu ;""voj '- b'\ '('" o. V\ (., '=>J sl.lek C.. ( r) :0. +'c C.. 1 ()0.') fw,. (:;,b)) Q.. 1 (r) =a,=- 4.0C\.

4 A c a r company introduces a new car for which th where tis the time in months. umber of cars so. S. is modeled b S(1) =30rfs '!00 ( 6't-t\O-j \T eo\',._ the function a Find the value of S'(2.5). Using correct units. explain what this value represents in the context of this problem. S'c.s):: \33.'333 wrs -solcl fu- Met\ StV\.C.L s 1 c2.. c;) '> o 1 o..,:. s N"O"'- 't\ljm\.o.,w- <;o \ t \. b. Find the average rate of change of cars sold over the first 12 months. indicate correct units of measure and explain what this value represents in the context of this problem. S(o')- (\'2) -,;o - \'301. \"t3 - a, ll'o. _u 0-\ - _,, F.r \ ""' ", WQX"e.. o\.[_ e.r- V"t"O"' ' -.,.,,..,.. -, ;o f\""o\, e.yo 'ifo o-\"2-100 = 9,'+'-g (_+..Jc ').'j- \ C\t..1.r'- (-l-ti) ::. 700 j 't.. -t-\' 2. :.! 5. l"i2. t.= - 1. s.,..c;2.. -?

5 X /(x) f'(x) g(x) g'(x) - 6 -t JO Z' \?0 The functio r all real numbers. andlg is strictlv increasmjb The table above file i omj iii{1mffllrt'ir.ust derivatives at selected values ofx. The function, is given by a Find the equation of the tangent line drawn to the graph of { ' when x = 3. \ V\ (-,.') ':. ( (: )) 0,.) : ( ;-Co h'( l (5C.\)). f(1) 1-\ l ) (3<: J-(. : : 1,- " :. :2. -r = -, < :- -_ -::, ) - c;.. b. io (,) t o Z ) : r or the interval Z,) - h(;') _ ::f( )- :C\-C. = \-3 c. Explain why there must be a value of r for < r < 3 such that h(r) h():: h(;) = \_ -,?,. 1'.Uo...- Stw:.a. nuv ' o,.j.jjt:.. --, '+'l _,._ L'Jol t-'is. o c:..-...\,;.\'\u. SiV\ \..J (.:"\ - 3 ' \) :-7 h(r J = -;l J -' h11- :[:'.'J.,. o-. ' Vo-..',,. -u r 6-n lr):. - d. Explai; why ere is a value of c for < c < 3 such that h'(c) = J... tl.r 3Sc.JC" ""(?J2.. v-.(>c.') \... J, lc J,+-i -+ir.v t{\. \. T. 9i'-1e-.Y"tL1 1 o... vo.l ca. C.. '- C. '- 3 sucj.-. 't--. '(c.,") = -? s, t -ft...t. t, <..3.

f ', the first derivative of a differentiable function, f. Use the

f ', the first derivative of a differentiable function, f. Use the f, f ', and The graph given to the right is the graph of graph to answer the questions below. f '' Relationships and The Extreme Value Theorem 1. On the interval [0, 8], are there any values where f(x)

More information

APPH 4200 Physics of Fluids

APPH 4200 Physics of Fluids APPH 42 Physics of Fluids Problem Solving and Vorticity (Ch. 5) 1.!! Quick Review 2.! Vorticity 3.! Kelvin s Theorem 4.! Examples 1 How to solve fluid problems? (Like those in textbook) Ç"Tt=l I $T1P#(

More information

P a g e 5 1 of R e p o r t P B 4 / 0 9

P a g e 5 1 of R e p o r t P B 4 / 0 9 P a g e 5 1 of R e p o r t P B 4 / 0 9 J A R T a l s o c o n c l u d e d t h a t a l t h o u g h t h e i n t e n t o f N e l s o n s r e h a b i l i t a t i o n p l a n i s t o e n h a n c e c o n n e

More information

A L A BA M A L A W R E V IE W

A L A BA M A L A W R E V IE W A L A BA M A L A W R E V IE W Volume 52 Fall 2000 Number 1 B E F O R E D I S A B I L I T Y C I V I L R I G HT S : C I V I L W A R P E N S I O N S A N D TH E P O L I T I C S O F D I S A B I L I T Y I N

More information

OH BOY! Story. N a r r a t iv e a n d o bj e c t s th ea t e r Fo r a l l a g e s, fr o m th e a ge of 9

OH BOY! Story. N a r r a t iv e a n d o bj e c t s th ea t e r Fo r a l l a g e s, fr o m th e a ge of 9 OH BOY! O h Boy!, was or igin a lly cr eat ed in F r en ch an d was a m a jor s u cc ess on t h e Fr en ch st a ge f or young au di enc es. It h a s b een s een by ap pr ox i ma t ely 175,000 sp ect at

More information

Executive Committee and Officers ( )

Executive Committee and Officers ( ) Gifted and Talented International V o l u m e 2 4, N u m b e r 2, D e c e m b e r, 2 0 0 9. G i f t e d a n d T a l e n t e d I n t e r n a t i o n a2 l 4 ( 2), D e c e m b e r, 2 0 0 9. 1 T h e W o r

More information

z E z *" I»! HI UJ LU Q t i G < Q UJ > UJ >- C/J o> o C/) X X UJ 5 UJ 0) te : < C/) < 2 H CD O O) </> UJ Ü QC < 4* P? K ll I I <% "fei 'Q f

z E z * I»! HI UJ LU Q t i G < Q UJ > UJ >- C/J o> o C/) X X UJ 5 UJ 0) te : < C/) < 2 H CD O O) </> UJ Ü QC < 4* P? K ll I I <% fei 'Q f I % 4*? ll I - ü z /) I J (5 /) 2 - / J z Q. J X X J 5 G Q J s J J /J z *" J - LL L Q t-i ' '," ; i-'i S": t : i ) Q "fi 'Q f I»! t i TIS NT IS BST QALITY AVAILABL. T Y FRNIS T TI NTAIN A SIGNIFIANT NBR

More information

WALL D*TA PRINT-OUT. 3 nmth ZONE

WALL D*TA PRINT-OUT. 3 nmth ZONE T A B L E A 4. 3 G L A S S D A T A P R I N T - O U T H T C L».>qth» H e ig h t n u «b»r C L A S S D A T A P R I N T O U T it************************************ 1*q o v»rh # n g recm oi*ion*l orient n

More information

MAC 1147 Final Exam Review

MAC 1147 Final Exam Review MAC 1147 Final Exam Review nstructions: The final exam will consist of 15 questions plu::; a bonus problem. Some questions will have multiple parts and others will not. Some questions will be multiple

More information

INTERMEDIATE VALUE THEOREM

INTERMEDIATE VALUE THEOREM THE BIG 7 S INTERMEDIATE VALUE If f is a continuous function on a closed interval [a, b], and if k is any number between f(a) and f(b), where f(a) f(b), then there exists a number c in (a, b) such that

More information

T h e C S E T I P r o j e c t

T h e C S E T I P r o j e c t T h e P r o j e c t T H E P R O J E C T T A B L E O F C O N T E N T S A r t i c l e P a g e C o m p r e h e n s i v e A s s es s m e n t o f t h e U F O / E T I P h e n o m e n o n M a y 1 9 9 1 1 E T

More information

::::l<r/ L- 1-1>(=-ft\ii--r(~1J~:::: Fo. l. AG -=(0,.2,L}> M - &-c ==- < ) I) ~..-.::.1 ( \ I 0. /:rf!:,-t- f1c =- <I _,, -2...

::::l<r/ L- 1-1>(=-ft\ii--r(~1J~:::: Fo. l. AG -=(0,.2,L}> M - &-c ==- < ) I) ~..-.::.1 ( \ I 0. /:rf!:,-t- f1c =- <I _,, -2... Math 3298 Exam 1 NAME: SCORE: l. Given three points A(I, l, 1), B(l,;2, 3), C(2, - l, 2). (a) Find vectors AD, AC, nc. (b) Find AB+ DC, AB - AC, and 2AD. -->,,. /:rf!:,-t- f1c =-

More information

SOUTHWESTERN ELECTRIC POWER COMPANY SCHEDULE H-6.1b NUCLEAR UNIT OUTAGE DATA. For the Test Year Ended March 31, 2009

SOUTHWESTERN ELECTRIC POWER COMPANY SCHEDULE H-6.1b NUCLEAR UNIT OUTAGE DATA. For the Test Year Ended March 31, 2009 Schedule H-6.lb SOUTHWSTRN LCTRIC POWR COMPANY SCHDUL H-6.1b NUCLAR UNIT OUTAG DATA For the Test Year nded March 31, 29 This schedule is not applicable to SVvPCO. 5 Schedule H-6.1 c SOUTHWSTRN LCTRIC POWR

More information

r(j) -::::.- --X U.;,..;...-h_D_Vl_5_ :;;2.. Name: ~s'~o--=-i Class; Date: ID: A

r(j) -::::.- --X U.;,..;...-h_D_Vl_5_ :;;2.. Name: ~s'~o--=-i Class; Date: ID: A Name: ~s'~o--=-i Class; Date: U.;,..;...-h_D_Vl_5 _ MAC 2233 Chapter 4 Review for the test Multiple Choice Identify the choice that best completes the statement or answers the question. 1. Find the derivative

More information

0 k?j'..e L-+, v\.l.s t) So ~ a,pp ij ct-vh CJYIJ?t-J --1 h8-' ~ ~ erv-i

0 k?j'..e L-+, v\.l.s t) So ~ a,pp ij ct-vh CJYIJ?t-J --1 h8-' ~ ~ erv-i fv1 ~/1ti 1 D 7, f; V,~vi t=l fi &'-Y) 0 k?j'..e L-+, v\.l.s t) So ~ a,pp ij ct-vh CJYJ?t-J --1 h8-' ~ ~ erv-i o chred Math 70 7.8 Variation Objectives: 1) Direct variation 2) nverse variation 3) Joint

More information

Integrated II: Unit 2 Study Guide 2. Find the value of s. (s - 2) 2 = 200. ~ :-!:[Uost. ~-~::~~n. '!JJori. s: ~ &:Ll()J~

Integrated II: Unit 2 Study Guide 2. Find the value of s. (s - 2) 2 = 200. ~ :-!:[Uost. ~-~::~~n. '!JJori. s: ~ &:Ll()J~ Name: 1. Find the value of r., (r + 4) 2 = 48 4_ {1 1:. r l f 11i),_ == :r (t~ : t %J3 (t:; KL\J5 ~ ~ v~~f3] ntegrated : Unit 2 Study Guide 2. Find the value of s. (s 2) 2 = 200 ~ :!:[Uost ~~::~~n '!JJori

More information

176 5 t h Fl oo r. 337 P o ly me r Ma te ri al s

176 5 t h Fl oo r. 337 P o ly me r Ma te ri al s A g la di ou s F. L. 462 E l ec tr on ic D ev el op me nt A i ng er A.W.S. 371 C. A. M. A l ex an de r 236 A d mi ni st ra ti on R. H. (M rs ) A n dr ew s P. V. 326 O p ti ca l Tr an sm is si on A p ps

More information

Student Study Session. Theorems

Student Study Session. Theorems Students should be able to apply and have a geometric understanding of the following: Intermediate Value Theorem Mean Value Theorem for derivatives Extreme Value Theorem Name Formal Statement Restatement

More information

Using the Rational Root Theorem to Find Real and Imaginary Roots Real roots can be one of two types: ra...-\; 0 or - l (- - ONLl --

Using the Rational Root Theorem to Find Real and Imaginary Roots Real roots can be one of two types: ra...-\; 0 or - l (- - ONLl -- Using the Rational Root Theorem to Find Real and Imaginary Roots Real roots can be one of two types: ra...-\; 0 or - l (- - ONLl -- Consider the function h(x) =IJ\ 4-8x 3-12x 2 + 24x {?\whose graph is

More information

I M P O R T A N T S A F E T Y I N S T R U C T I O N S W h e n u s i n g t h i s e l e c t r o n i c d e v i c e, b a s i c p r e c a u t i o n s s h o

I M P O R T A N T S A F E T Y I N S T R U C T I O N S W h e n u s i n g t h i s e l e c t r o n i c d e v i c e, b a s i c p r e c a u t i o n s s h o I M P O R T A N T S A F E T Y I N S T R U C T I O N S W h e n u s i n g t h i s e l e c t r o n i c d e v i c e, b a s i c p r e c a u t i o n s s h o u l d a l w a y s b e t a k e n, i n c l u d f o l

More information

l [ L&U DOK. SENTER Denne rapport tilhører Returneres etter bruk Dokument: Arkiv: Arkivstykke/Ref: ARKAS OO.S Merknad: CP0205V Plassering:

l [ L&U DOK. SENTER Denne rapport tilhører Returneres etter bruk Dokument: Arkiv: Arkivstykke/Ref: ARKAS OO.S Merknad: CP0205V Plassering: I Denne rapport thører L&U DOK. SENTER Returneres etter bruk UTLÅN FRA FJERNARKIVET. UTLÅN ID: 02-0752 MASKINVN 4, FORUS - ADRESSE ST-MA LANETAKER ER ANSVARLIG FOR RETUR AV DETTE DOKUMENTET. VENNLIGST

More information

L=/o U701 T. jcx3. 1L2,Z fr7. )vo. A (a) [20%) Find the steady-state temperature u(x). M,(Y 7( it) X(o) U ç (ock. Partial Differential Equations 3150

L=/o U701 T. jcx3. 1L2,Z fr7. )vo. A (a) [20%) Find the steady-state temperature u(x). M,(Y 7( it) X(o) U ç (ock. Partial Differential Equations 3150 it) O 2h1 i / k ov A u(1,t) L=/o [1. (H3. Heat onduction in a Bar) 1 )vo nstructions: This exam is timed for 12 minutes. You will be given extra time to complete Exam Date: Thursday, May 2, 213 textbook.

More information

EXAM 3, MATH 233 FALL, 2003

EXAM 3, MATH 233 FALL, 2003 EXAM 3, MATH 233 FALL, 2003 This examination has 20 multiple choice questions, and two essay questions. Please check it over and if you find it to be incomplete, notify the proctor. Do all your supporting

More information

Le Chatelier's Principle. 2. How changes in each factor affect equilibrium (Le Chatelier's Principle)

Le Chatelier's Principle. 2. How changes in each factor affect equilibrium (Le Chatelier's Principle) Chern 12 Notes 11.4 - Le Chatelier's Principle Goals are to learn: 1. The factors that can cause changes in a system at equilibrium 2. How changes in each factor affect equilibrium (Le Chatelier's Principle)

More information

Properties of Graphs of Polynomial Functions Terminology Associated with Graphs of Polynomial Functions

Properties of Graphs of Polynomial Functions Terminology Associated with Graphs of Polynomial Functions Properties of Graphs of Polynomial Functions Terminology Associated with Graphs of Polynomial Functions Detennine what types of polynomial functions/, g, and hare graphed below Give a reason for your conclusions

More information

AP Calculus AB. Sample Student Responses and Scoring Commentary. Inside: Free Response Question 1. Scoring Guideline.

AP Calculus AB. Sample Student Responses and Scoring Commentary. Inside: Free Response Question 1. Scoring Guideline. 218 AP Calculus AB Sample Student Responses and Scoring Commentary Inside: Free Response Question 1 RR Scoring Guideline RR Student Samples RR Scoring Commentary 218 The College Board. College Board, Advanced

More information

Interpretations and Applications of the Derivative and the Definite Integral. d dx [R(i)] = R '(t)

Interpretations and Applications of the Derivative and the Definite Integral. d dx [R(i)] = R '(t) Interpretations and Applications of the Derivative and the Definite Integral [A.MOUNT]= The rate at which that amount is changing dx For example. if water is being drained from a swimming pool and R(t)

More information

SOLUTION SET. Chapter 8 LASER OSCILLATION ABOVE THRESHOLD "LASER FUNDAMENTALS" Second Edition

SOLUTION SET. Chapter 8 LASER OSCILLATION ABOVE THRESHOLD LASER FUNDAMENTALS Second Edition SOLUTION SET Chapter 8 LASER OSCILLATION ABOVE THRESHOLD "LASER FUNDAMENTALS" Second Edition By William T. Silfvast - 1. An argon ion laser (as shown in Figure 10-S(b)) operating at 488.0 nm with a gainregion

More information

Score: Fall 2009 Name Row 80. C(t) = 30te- O. 04t

Score: Fall 2009 Name Row 80. C(t) = 30te- O. 04t Math 1410 - Test #3A Score: Fall 2009 Name Row 80 Q1: This is a calculator problem. If t, in minutes, is the time since a drug was administered, the concentration, C(t) in ng/ml, of a drug in a patient's

More information

'5E _ -- -=:... --!... L og...

'5E _ -- -=:... --!... L og... F U T U R E O F E M B E D D I N G A N D F A N - O U T T E C H N O L O G I E S R a o T u m m a l a, P h. D ; V e n k y S u n d a r a m, P h. D ; P u l u g u r t h a M. R a j, P h. D ; V a n e s s a S m

More information

or - CHAPTER 7 Applications of Integration Section 7.1 Area of a Region Between Two Curves 1. A= ~2[0- (x :2-6x)] dr=-~2(x 2-6x) dr

or - CHAPTER 7 Applications of Integration Section 7.1 Area of a Region Between Two Curves 1. A= ~2[0- (x :2-6x)] dr=-~2(x 2-6x) dr CHAPTER 7 Applications of Integration Section 7.1 Area of a Region Between Two Curves 1. A= ~[0- (x : 6x)] dr=-~(x 6x) dr 6~ 1356 or - 6. A: ~[(x- 1) 3 -(x-1)]dx 11. [~/3 ( - see x) dx 5- - 3 - I 1 3 5

More information

APPENDIX F WATER USE SUMMARY

APPENDIX F WATER USE SUMMARY APPENDX F WATER USE SUMMARY From Past Projects Town of Norman Wells Water Storage Facltes Exstng Storage Requrements and Tank Volume Requred Fre Flow 492.5 m 3 See Feb 27/9 letter MACA to Norman Wells

More information

APPH 4200 Physics of Fluids

APPH 4200 Physics of Fluids APPH 4200 Physics of Fluids Rotating Fluid Flow October 6, 2011 1.!! Hydrostatics of a Rotating Water Bucket (again) 2.! Bath Tub Vortex 3.! Ch. 5: Problem Solving 1 Key Definitions & Concepts Ω U Cylindrical

More information

Robado del Archivo del Dr. Antonio Rafael de la Cova

Robado del Archivo del Dr. Antonio Rafael de la Cova Robado del Archvo del Dr. Antono Raael de la Cova http:www.latnamercanstudes.org/ Muster Roll: 655-858. Under ea.ch COlnl?ny are recorded the nams o the man wth nom.:lton show ng ran.'l< when hare and

More information

Vera Babe!,ku Math Lecture 1. Introduction 0 9.1, 9.2, 9.3. o Syllabus

Vera Babe!,ku Math Lecture 1. Introduction 0 9.1, 9.2, 9.3. o Syllabus ntroduction o Syllabus 9.1, 9.2, 9.3. Vera Babe!,ku Math 11-2. Lecture 1 9.1 Limits. Application Preview Although everyone recognizes the value of eliminating any and all particulate pollution from smokestack

More information

Ğ ğ ğ Ğ ğ Öğ ç ğ ö öğ ğ ŞÇ ğ ğ

Ğ ğ ğ Ğ ğ Öğ ç ğ ö öğ ğ ŞÇ ğ ğ Ğ Ü Ü Ü ğ ğ ğ Öğ ş öğ ş ğ öğ ö ö ş ğ ğ ö ğ Ğ ğ ğ Ğ ğ Öğ ç ğ ö öğ ğ ŞÇ ğ ğ l _.j l L., c :, c Ll Ll, c :r. l., }, l : ö,, Lc L.. c l Ll Lr. 0 c (} >,! l LA l l r r l rl c c.r; (Y ; c cy c r! r! \. L : Ll.,

More information

PINE STREET. DURBAN. Issued by It Action Committe of African National Congress & Nattl Indian Congress

PINE STREET. DURBAN. Issued by It Action Committe of African National Congress & Nattl Indian Congress M A Y IB U Y E - A F R IK A! UFIKE EMHLANGANWENI OMKHULU! RED SQUARE PINE STREET. DURBAN. NGO SONTO 31st AUGUST NGO 2. 30 Ntabama Issued by It Action Committe of African National Congress & Nattl Indian

More information

~,. :'lr. H ~ j. l' ", ...,~l. 0 '" ~ bl '!; 1'1. :<! f'~.., I,," r: t,... r':l G. t r,. 1'1 [<, ."" f'" 1n. t.1 ~- n I'>' 1:1 , I. <1 ~'..

~,. :'lr. H ~ j. l' , ...,~l. 0 ' ~ bl '!; 1'1. :<! f'~.., I,, r: t,... r':l G. t r,. 1'1 [<, . f' 1n. t.1 ~- n I'>' 1:1 , I. <1 ~'.. ,, 'l t (.) :;,/.I I n ri' ' r l ' rt ( n :' (I : d! n t, :?rj I),.. fl.),. f!..,,., til, ID f-i... j I. 't' r' t II!:t () (l r El,, (fl lj J4 ([) f., () :. -,,.,.I :i l:'!, :I J.A.. t,.. p, - ' I I I

More information

35H MPa Hydraulic Cylinder 3.5 MPa Hydraulic Cylinder 35H-3

35H MPa Hydraulic Cylinder 3.5 MPa Hydraulic Cylinder 35H-3 - - - - ff ff - - - - - - B B BB f f f f f f f 6 96 f f f f f f f 6 f LF LZ f 6 MM f 9 P D RR DD M6 M6 M6 M. M. M. M. M. SL. E 6 6 9 ZB Z EE RC/ RC/ RC/ RC/ RC/ ZM 6 F FP 6 K KK M. M. M. M. M M M M f f

More information

o V fc rt* rh '.L i.p -Z :. -* & , -. \, _ * / r s* / / ' J / X - -

o V fc rt* rh '.L i.p -Z :. -* & , -. \, _ * / r s* / / ' J / X - - -. ' ' " / ' * * ' w, ~ n I: ».r< A < ' : l? S p f - f ( r ^ < - i r r. : '. M.s H m **.' * U -i\ i 3 -. y$. S 3. -r^ o V fc rt* rh '.L i.p -Z :. -* & --------- c it a- ; '.(Jy 1/ } / ^ I f! _ * ----*>C\

More information

I n t e r n a t i o n a l E l e c t r o n i c J o u r n a l o f E l e m e n t a r y E.7 d u, c ai ts is ou n e, 1 V3 1o-2 l6, I n t h i s a r t

I n t e r n a t i o n a l E l e c t r o n i c J o u r n a l o f E l e m e n t a r y E.7 d u, c ai ts is ou n e, 1 V3 1o-2 l6, I n t h i s a r t I n t e r n a t i o n a l E l e c t r o n i c J o ue rlne am l e not fa r y E d u c a t i o n, 2 0 1 4, 1 37-2 ( 16 ). H o w R e a d i n g V o l u m e A f f e c t s b o t h R e a d i n g F l u e n c y

More information

bounty Herald Times THURSDAY,- SEPTEMBER!7, 1925

bounty Herald Times THURSDAY,- SEPTEMBER!7, 1925 420 J 925 UU L 875 L 0 U «OJJ U U J OUU U ««J =» V ULU»» L U 4; J O O ] ; F < L < L V VV J 29 840 3 9 2 5 85 5 V U U»2 U U L L O OU F O OV O; X F O U «] ; U (JOVV q O ; < (» 4 V 50 26 U 7 925 UU OQ ; F

More information

~i~, ~';J M.1 "A.X;t7~~

~i~, ~';J M.1 A.X;t7~~ Ci1 ;w -,IL I MX-- AA.R- v-r ';t ""lz"""" f 7ll\1. 13/cd Vt.dJt-l (l{ t f1.)-: ) -;::- r,.o.

More information

Sub: Submission of the copy of Investor presentation under regulation 30 of SEBI (Listing Obligations & Disclosure Reguirements) Regulations

Sub: Submission of the copy of Investor presentation under regulation 30 of SEBI (Listing Obligations & Disclosure Reguirements) Regulations matrimny.cm vember 1, 218 tinal Stck xchange f India Ltd xchan laza, 5th Flr Plt : C/1, Sand Krla Cmplex, Sa Mmbai - 4 51 Crpte Relatinship Department SS Ltd., Phirze Jeejheebhy Twers Dalal Street, Mmbai

More information

Ranking accounting, banking and finance journals: A note

Ranking accounting, banking and finance journals: A note MPRA Munich Personal RePEc Archive Ranking accounting, banking and finance ournals: A note George Halkos and Nickolaos Tzeremes University of Thessaly, Department of Economics January 2012 Online at https://mpra.ub.uni-muenchen.de/36166/

More information

,\ I. . <- c}. " C:-)' ) I- p od--- -;::: 'J.--- d, cl cr -- I. ( I) Cl c,\. c. 1\'0\ ~ '~O'-_. e ~.\~\S

,\ I. . <- c}.  C:-)' ) I- p od--- -;::: 'J.--- d, cl cr -- I. ( I) Cl c,\. c. 1\'0\ ~ '~O'-_. e ~.\~\S Math 3306 - Test 1 Name: An d {"0v\ ( _ roj ~ ed Date: l'( ~0 { 1\ Fall 2011 1. (to Pts) Let S == {I, 2, 3,4, 5,6,7,8,9, 10}. of each of the following types of mappings, provide justification for why the

More information

PHYS 232 QUIZ minutes.

PHYS 232 QUIZ minutes. / PHYS 232 QUIZ 1 02-18-2005 50 minutes. This quiz has 3 questions. Please show all your work. If your final answer is not correct, you will get partial credit based on your work shown. You are allowed

More information

Pledged_----=-+ ---'l\...--m~\r----

Pledged_----=-+ ---'l\...--m~\r---- , ~.rjf) )('\.. 1,,0-- Math III Pledged_----=-+ ---'l\...--m~\r---- 1. A square piece ofcardboard with each side 24 inches long has a square cut out at each corner. The sides are then turned up to form

More information

A0A TEXAS UNIV AT AUSTIN DEPT OF CHEMISTRY F/G 7/5 PHOTOASSISTED WATER-GAS SHIFT REACTION ON PLATINIZED T7TANIAI T--ETCIUI

A0A TEXAS UNIV AT AUSTIN DEPT OF CHEMISTRY F/G 7/5 PHOTOASSISTED WATER-GAS SHIFT REACTION ON PLATINIZED T7TANIAI T--ETCIUI AA113 878 TEXAS UNIV AT AUSTIN DEPT OF CHEMISTRY F/G 7/5 PHOTOASSISTED WATER-GAS SHIFT REACTION ON PLATINIZED T7TANIAI T--ETCIUI APR 82 S FANG. 8 CHEN..J M WHITE N14-75-C-922 UNCLASSIFIED NL OFFICE OF

More information

Beechwood Music Department Staff

Beechwood Music Department Staff Beechwood Music Department Staff MRS SARAH KERSHAW - HEAD OF MUSIC S a ra h K e rs h a w t r a i n e d a t t h e R oy a l We ls h C o l le g e of M u s i c a n d D ra m a w h e re s h e ob t a i n e d

More information

,,- : (~e:se (A<e \')O-T. po Vl\(} \ '(\ \s X \JQ\\JeS. LOX''(e-L-~) Linear Function Review. a. I(x)./ c. 1M ,/ 5000 I - ~.

,,- : (~e:se (A<e \')O-T. po Vl\(} \ '(\ \s X \JQ\\JeS. LOX''(e-L-~) Linear Function Review. a. I(x)./ c. 1M ,/ 5000 I - ~. ,. Name: Class: Date: _ D: A Linear Function Review 1. Jennifer is a car saleswoman. She is paid a salar of $0 per month plus $00 for each car that she sells. Her salar can be modeled b the equation ()

More information

STANDARDIZATION OF BLENDED NECTAR USING BANANA PSEUDOSTEM SAP AND MANGO PULP SANTOSH VIJAYBHAI PATEL

STANDARDIZATION OF BLENDED NECTAR USING BANANA PSEUDOSTEM SAP AND MANGO PULP SANTOSH VIJAYBHAI PATEL STANDARDIZATION OF BLENDED NECTAR USING BANANA PSEUDOSTEM SAP AND MANGO PULP BY SANTOSH VIJAYBHAI PATEL B.Sc. (Hons.) Horticulture DEPARTMENT OF POST HARVEST TECHNOLOGY ASPEE COLLEGE OF HORTICULTURE AND

More information

^l,2-, 3. f 2_ ' >v., 4. b/-e. of- fee. -^3-5- I70(fa = )&*>$)

^l,2-, 3. f 2_ ' >v., 4. b/-e. of- fee. -^3-5- I70(fa = )&*>$) & ^l,2-, 3 f 2_ ' s\ >v., 4 b/-e of- fee O = )&*>$) -^3-5- I70(fa \J QQQ ~E - V-?' = f rff ^ if -j- 41 -Ofc -Ofc v OH OH ST/VT H SoJU^, 55-3 2. ^ T_ 2, _ ^ * ^3W^(M7 2. X 2.! Z. d-f- S-5- /V Z 33?> 5YJ

More information

Parts Manual. EPIC II Critical Care Bed REF 2031

Parts Manual. EPIC II Critical Care Bed REF 2031 EPIC II Critical Care Bed REF 2031 Parts Manual For parts or technical assistance call: USA: 1-800-327-0770 2013/05 B.0 2031-109-006 REV B www.stryker.com Table of Contents English Product Labels... 4

More information

^ 4 ^1)<$^ :^t -*^> us: i. ^ v. é-^ f.. ^=2. \ t- "tì. _c^_. !r*^ o r , -UT -B6 T2T. - =s.- ; O- ci. \j-

^ 4 ^1)<$^ :^t -*^> us: i. ^ v. é-^ f.. ^=2. \ t- tì. _c^_. !r*^ o r , -UT -B6 T2T. - =s.- ; O- ci. \j- Q «L j T2T "S = $ W wwwplemlzz cm Lez Pe 4692! "ì c O c 9T UT =2 4 u & S4 4 é B6 j H Fcebk Pl Emlzz egme Yuubegplemlzz Skpe plemlzz 7 424 O S& wwwplemlzz cm Lez Pe 4692 M O ~ x g È «p 2 c & b U L " & K

More information

Jsee x dx = In Isec x + tanxl + C Jcsc x dx = - In I cscx + cotxl + C

Jsee x dx = In Isec x + tanxl + C Jcsc x dx = - In I cscx + cotxl + C MAC 2312 Final Exam Review Instructions: The Final Exam will consist of 15 questions plus a bonus problem. All questions will be multiple choice, which will be graded partly on whether or not you circle

More information

DIAMOND DRILL RECORD

DIAMOND DRILL RECORD iitft'ww!-;" '**!' ^?^S;Ji!JgHj DIAMOND DRILL RECORD Molftflp.'/^ f* -. j * Dtp * ^* * Property '^^^J^ - I/^X/'CA*- Etev, Collar Locatioa..-A^*.-//-^.^ /Z O f* j\. Is!/'. ~O stt^+'r&il, Di turn.....,,,...,.,......

More information

Trade Patterns, Production networks, and Trade and employment in the Asia-US region

Trade Patterns, Production networks, and Trade and employment in the Asia-US region Trade Patterns, Production networks, and Trade and employment in the Asia-U region atoshi Inomata Institute of Developing Economies ETRO Development of cross-national production linkages, 1985-2005 1985

More information

Drury&Wliitson. Economical. Planning of Buildings. .(Chilecture B. S. DNJVERSITT' OF. 11,1. 1 ibkahy

Drury&Wliitson. Economical. Planning of Buildings. .(Chilecture B. S. DNJVERSITT' OF. 11,1. 1 ibkahy Drury&Wliitson Economical Planning of Buildings.(Chilecture B. S. 902 DJVERSTT' OF,. ibkahy 4 f ^ ^ J' if 4 ^ A 4. T? 4'tariung iint) 4':>bor. f LBRARY or TMl University of llinois. CLASS. BOOK. VO.UMK.

More information

Beginning and Ending Cash and Investment Balances for the month of January 2016

Beginning and Ending Cash and Investment Balances for the month of January 2016 ADIISTRATIVE STAFF REPRT T yr nd Tn uncil rch 15 216 SBJET Jnury 216 nth End Tresurer s Reprt BAKGRD The lifrni Gvernment de nd the Tn f Dnville s Investment Plicy require tht reprt specifying the investment

More information

p r * < & *'& ' 6 y S & S f \ ) <» d «~ * c t U * p c ^ 6 *

p r * < & *'& ' 6 y S & S f \ ) <» d «~ * c t U * p c ^ 6 * B. - - F -.. * i r > --------------------------------------------------------------------------- ^ l y ^ & * s ^ C i$ j4 A m A ^ v < ^ 4 ^ - 'C < ^y^-~ r% ^, n y ^, / f/rf O iy r0 ^ C ) - j V L^-**s *-y

More information

[ ]:543.4(075.8) 35.20: ,..,..,.., : /... ;. 2-. ISBN , - [ ]:543.4(075.8) 35.20:34.

[ ]:543.4(075.8) 35.20: ,..,..,.., : /... ;. 2-. ISBN , - [ ]:543.4(075.8) 35.20:34. .. - 2-2009 [661.87.+661.88]:543.4(075.8) 35.20:34.2373-60..,..,..,..,.. -60 : /... ;. 2-. : -, 2008. 134. ISBN 5-98298-299-7 -., -,,. - «,, -, -», - 550800,, 240600 «-», -. [661.87.+661.88]:543.4(075.8)

More information

- 0 -:2" n n n :2 0-

- 0 -:2 n n n :2 0- 'U'O:u t1cd O''C Qt1 :2" :2 8 e 2 8 ' o o () A :22 S' o So M o': :2' :2 :: ;j :2" Qq R Ro o' :J :2"!" :2 " t1 :2 = = 5" f o' Co : Do M ) _!,,, ' Do 6! Do M :2 C ' M C 1 "!j ' 'OR' R] :8 _ fa M M B, M R!

More information

Ninth Marine Air Wing To Be Decommissioned. ment of the Transport Air Broup.

Ninth Marine Air Wing To Be Decommissioned. ment of the Transport Air Broup. N M W T B D $ R V /RNE M N 2 C O R R & F O T T O O N T TTON-CHERRY ONT NC B D OM O z C M H N M W O z M 944 T W ; N W j j C T q T N W T W z ; q q z - M 30 946 F T G O R [MR 252952 C q -C - T G VMR 252 V

More information

P a g e 3 6 of R e p o r t P B 4 / 0 9

P a g e 3 6 of R e p o r t P B 4 / 0 9 P a g e 3 6 of R e p o r t P B 4 / 0 9 p r o t e c t h um a n h e a l t h a n d p r o p e r t y fr om t h e d a n g e rs i n h e r e n t i n m i n i n g o p e r a t i o n s s u c h a s a q u a r r y. J

More information

/ =0. (c) Section P.3 Functions and Their Graphs. (c) g(-2) = 5-(-2) 2 = 5-4 = 1. (e) g(x) = 0 for x = -I, 1 and 2. 2.

/ =0. (c) Section P.3 Functions and Their Graphs. (c) g(-2) = 5-(-2) 2 = 5-4 = 1. (e) g(x) = 0 for x = -I, 1 and 2. 2. Section P,3 Functions and Their Graphs 3 Section P.3 Functions and Their Graphs. (a) Domain off." -4 < x < 4 ~ [-4, 4] Range off:-3 < y < 5 ~ [-3, 5] Domain of g: -3 < x < 3 ~ [-3, 3] Range of g: -4

More information

poe;,"llcm =-~ o 7 '3 (p :. -'6 g ~!L.. I (q~3 -ICf 22. \'1 ~ meot \o-..n ::-\~ ~ Z _ i 1 -8 ~l{ (V\-t-I) =~ C'1J-:: ~..

poe;,llcm =-~ o 7 '3 (p :. -'6 g ~!L.. I (q~3 -ICf 22. \'1 ~ meot \o-..n ::-\~ ~ Z _ i 1 -8 ~l{ (V\-t-I) =~ C'1J-:: ~.. Statistics 1, Section 6 Exam 1 Name ~ _ October~ Calculators and one 8.5" by 11 " sheet ofhandwritten notes allowed Show all work and answers clearly in the space provided Questions 16 are worth 15points

More information

----- ~... No. 40 in G minor, K /~ ~--.-,;;;' LW LllJ LllJ LllJ LllJ WJ LilJ L.LL.J LLLJ. Movement'

----- ~... No. 40 in G minor, K /~ ~--.-,;;;' LW LllJ LllJ LllJ LllJ WJ LilJ L.LL.J LLLJ. Movement' Area o Stdy 1 Western c'assica' msic 16001899 Wolgang Symhony Movement' ocd1 track 2 Amades Mozart No 40 in G minor K550 Flte Oboes 12 Clarinets 12 in B lat Bassoons 12 Molto Allegro Horn 1 in B lat alto';

More information

INFORMACIÓN SOBRE LAS MEDIDAS QUE AFECTAN AL COMERCIO. Presentada por: NIGERIA

INFORMACIÓN SOBRE LAS MEDIDAS QUE AFECTAN AL COMERCIO. Presentada por: NIGERIA RETRICTED ACUERDO GENERAL OBRE T/TÍTttíl de 98 ARANCELE ADUANERO Y COMERCIO Dtrbucón epecl Comté del Comerco Aropecuro Ornl: nlé INFORMACIÓN OBRE LA MEDIDA QUE AFECTAN AL COMERCIO Preentd por: NIGERIA

More information

[Name: [ Final Exam ECE301 Signals and Systems Wednesday, May 6, Cover Sheet

[Name: [ Final Exam ECE301 Signals and Systems Wednesday, May 6, Cover Sheet SoLUT10N [Name: [ Final Exam ECE301 Signals and Systems Wednesday, May 6, 2015 Cover Sheet Write your name on this page and every page to be safe. Test Duration: 120 minutes. Coverage: Comprehensive Open

More information

YORK UNIVERSITY. Faculty of Science and Engineering Faculty of Liberal Arts and Professional Studies MATH A Test #2.

YORK UNIVERSITY. Faculty of Science and Engineering Faculty of Liberal Arts and Professional Studies MATH A Test #2. YORK UNIVERSITY Faculty of Science and Engineering Faculty of Liberal Arts and Professional Studies MATH 317 6. A Test #2 June 27, 212 Surname (print): Given Name: Student No: Signature: INSTRUCTIONS:

More information

YORK UNIVERSITY. Faculty of Science and Engineering Faculty of Liberal Arts and Professional Studies. MATH B Test #1. September 28, 2012

YORK UNIVERSITY. Faculty of Science and Engineering Faculty of Liberal Arts and Professional Studies. MATH B Test #1. September 28, 2012 YORK UNIVERSITY Faculty of Science and Engineering Faculty of Liberal Arts and Professional Studies MATH 1013 3.00 B Test #1 September 28, 2012 Surname (print):------------ Given Name: Student No: --------------

More information

e) r a9".^) -FaBn^- &* B(*pl *hr_*lma:n* u

e) r a9.^) -FaBn^- &* B(*pl *hr_*lma:n* u SL SIc1- tal 1. (a) State the conditions under which the Poisson distribution may be used as an approximation to the binomial distribution. (1) A farmer supplies a bakery with eggs. The manager of the

More information

Mathematics Extension 1

Mathematics Extension 1 BAULKHAM HILLS HIGH SCHOOL TRIAL 04 YEAR TASK 4 Mathematics Etension General Instructions Reading time 5 minutes Working time 0 minutes Write using black or blue pen Board-approved calculators may be used

More information

to", \~~!' LSI'r-=- 5 b H 2-l

to, \~~!' LSI'r-=- 5 b H 2-l Math 10 Name_\< Ei_' _ WORKSHEET 2.2 - Surface Area Part 1 - Find SA of different objects Usepage 3 of your data booklet to find the formulae for SAof objects! 1. Find the SA of the square pyramid below.

More information

F l a s h-b a s e d S S D s i n E n t e r p r i s e F l a s h-b a s e d S S D s ( S o-s ltiad t e D r i v e s ) a r e b e c o m i n g a n a t t r a c

F l a s h-b a s e d S S D s i n E n t e r p r i s e F l a s h-b a s e d S S D s ( S o-s ltiad t e D r i v e s ) a r e b e c o m i n g a n a t t r a c L i f e t i m e M a n a g e m e n t o f F l a-b s ah s e d S S D s U s i n g R e c o v e r-a y w a r e D y n a m i c T h r o t t l i n g S u n g j i n L e, e T a e j i n K i m, K y u n g h o, Kainmd J

More information

Transactions on Engineering Sciences vol 5, 1994 WIT Press, ISSN

Transactions on Engineering Sciences vol 5, 1994 WIT Press,   ISSN Numerical solution to two-phase Stefan problems by the heat balance integral method J. Caldwell & C.K. Chiu Department of Mathematics, City Polytechnic of Hong Kong, 83 Tat Chee Avenue, Kowloon, Hong Kong

More information

THE WORLD BANK GROUP ARCHIVES PUBLIC DISCLOSURE AUTHORIZED

THE WORLD BANK GROUP ARCHIVES PUBLIC DISCLOSURE AUTHORIZED THE WORLD BANK GROUP ARCHIVES PUBLIC DISCLOSURE AUTHORIZED Folder Title: Finland-LN-61 - Photographs - Volume 1 Folder ID: 1721443 Fonds: Records of Office of External Affairs (WB IBRD/IDA EXT) Digitized:

More information

~---~ ~----~ ~~

~---~ ~----~ ~~ t =n :! ::::t C) 7(...; f J t h r==n : t::r,,.! 7 m 7 m {J) :AT rn rn L. "; j i =t :;;;: t.. :, h ). ")?J.. r;..., X h U,< r Q.!. i: :J; :!"")EYJ },_. c ". " :( (;. ). " t? / t e t!r J t j "! t)! (j) N

More information

Advanced Placement. Chemistry. Integrated Rates

Advanced Placement. Chemistry. Integrated Rates Advanced Placement Chemistry Integrated Rates 204 47.90 9.22 78.49 (26) 50.94 92.9 80.95 (262) 52.00 93.94 83.85 (263) 54.938 (98) 86.2 (262) 55.85 0. 90.2 (265) 58.93 02.9 92.2 (266) H Li Na K Rb Cs Fr

More information

o ri fr \ jr~ ^: *^ vlj o^ f?: ** s;: 2 * i i H-: 2 ~ " ^ o ^ * n 9 C"r * ^, ' 1 ^5' , > ^ t g- S T ^ r. L o n * * S* * w 3 ** ~ 4O O.

o ri fr \ jr~ ^: *^ vlj o^ f?: ** s;: 2 * i i H-: 2 ~  ^ o ^ * n 9 Cr * ^, ' 1 ^5' , > ^ t g- S T ^ r. L o n * * S* * w 3 ** ~ 4O O. THE PENALTY FR MAKING A FALSE STATEMENT IN THIS REPRT AND/R CERTIFICATE IS S5. R SIX MNTHS IMPRISNMENT R BTH "D "? y. " cr TJ Xl^ " Q. rt 5' "g s r ^.. C i :? S :.. y ' : s s ^ST (X. I ^^ ^ ^ S : t ^ :

More information

ECE 417 Lecture 6: knn and Linear Classifiers. Amit Das 09/14/2017

ECE 417 Lecture 6: knn and Linear Classifiers. Amit Das 09/14/2017 ECE 417 Lecture 6: knn and Linear Classifiers Amit Das 09/14/2017 Acknowledgments http://research.cs.tamu.edu/prism/lectures/pr/pr_l8.pdf http://classes.engr.oregonstate.edu/eecs/spring2012/cs534/notes/kn

More information

I-1. rei. o & A ;l{ o v(l) o t. e 6rf, \o. afl. 6rt {'il l'i. S o S S. l"l. \o a S lrh S \ S s l'l {a ra \o r' tn $ ra S \ S SG{ $ao. \ S l"l. \ (?

I-1. rei. o & A ;l{ o v(l) o t. e 6rf, \o. afl. 6rt {'il l'i. S o S S. ll. \o a S lrh S \ S s l'l {a ra \o r' tn $ ra S \ S SG{ $ao. \ S ll. \ (? >. 1! = * l >'r : ^, : - fr). ;1,!/!i ;(?= f: r*. fl J :!= J; J- >. Vf i - ) CJ ) ṯ,- ( r k : ( l i ( l 9 ) ( ;l fr i) rf,? l i =r, [l CB i.l.!.) -i l.l l.!. * (.1 (..i -.1.! r ).!,l l.r l ( i b i i '9,

More information

Limits and Continuity. 2 lim. x x x 3. lim x. lim. sinq. 5. Find the horizontal asymptote (s) of. Summer Packet AP Calculus BC Page 4

Limits and Continuity. 2 lim. x x x 3. lim x. lim. sinq. 5. Find the horizontal asymptote (s) of. Summer Packet AP Calculus BC Page 4 Limits and Continuity t+ 1. lim t - t + 4. lim x x x x + - 9-18 x-. lim x 0 4-x- x 4. sinq lim - q q 5. Find the horizontal asymptote (s) of 7x-18 f ( x) = x+ 8 Summer Packet AP Calculus BC Page 4 6. x

More information

Kr7. wd /J-t- To pick up your graded exam from a box outside 5100A Pacific Hall sign here:

Kr7. wd /J-t- To pick up your graded exam from a box outside 5100A Pacific Hall sign here: wd /J-t- To pick up your graded exam from a box outside 5100A Pacific Hall sign here: Kr7 chemtsrry 140A FTNAL EXAM 1v & s 6" Eo1 DEC 8,2011 NAME (please print) SIGNATURE FIBST LAST ID NUMBER LAST NAME

More information

i;\-'i frz q > R>? >tr E*+ [S I z> N g> F 'x sa :r> >,9 T F >= = = I Y E H H>tr iir- g-i I * s I!,i --' - = a trx - H tnz rqx o >.F g< s Ire tr () -s

i;\-'i frz q > R>? >tr E*+ [S I z> N g> F 'x sa :r> >,9 T F >= = = I Y E H H>tr iir- g-i I * s I!,i --' - = a trx - H tnz rqx o >.F g< s Ire tr () -s 5 C /? >9 T > ; '. ; J ' ' J. \ ;\' \.> ). L; c\ u ( (J ) \ 1 ) : C ) (... >\ > 9 e!) T C). '1!\ /_ \ '\ ' > 9 C > 9.' \( T Z > 9 > 5 P + 9 9 ) :> : + (. \ z : ) z cf C : u 9 ( :!z! Z c (! $ f 1 :.1 f.

More information

fur \ \,,^N/ D7,,)d.s) 7. The champion and Runner up of the previous year shall be allowed to play directly in final Zone.

fur \ \,,^N/ D7,,)d.s) 7. The champion and Runner up of the previous year shall be allowed to play directly in final Zone. OUL O GR SODRY DUTO, ODS,RT,SMTUR,USWR.l ntuctin f cnuct f Kbi ( y/gil)tunent f 2L-Lg t. 2.. 4.. 6. Mtche hll be lye e K ule f ene f tie t tie Dutin f ech tch hll be - +0 (Rece)+ = M The ticint f ech Te

More information

MPM 2D Final Exam Prep 2, June b) Y = 2(x + 1)2-18. ~..: 2. (xl- 1:'}")( t J') -' ( B. vi::: 2 ~ 1-'+ 4 1<. -t-:2 -( 6! '.

MPM 2D Final Exam Prep 2, June b) Y = 2(x + 1)2-18. ~..: 2. (xl- 1:'})( t J') -' ( B. vi::: 2 ~ 1-'+ 4 1<. -t-:2 -( 6! '. MPM 2D Final Exam Prep 2 June 2017 1. Express each equation in standard form and factored form: ~ ~ +et's 'leu t W (.. ".>tak( a) y = (x + 5)2 + 1 on ::t~'t.{1'" ~heeh v 1' K 1 C'. T.) '. (J. lr lov J

More information

THIS PAGE DECLASSIFIED IAW E

THIS PAGE DECLASSIFIED IAW E THS PAGE DECLASSFED AW E0 2958 BL K THS PAGE DECLASSFED AW E0 2958 THS PAGE DECLASSFED AW E0 2958 B L K THS PAGE DECLASSFED AW E0 2958 THS PAGE DECLASSFED AW EO 2958 THS PAGE DECLASSFED AW EO 2958 THS

More information

QJ) Zz LI Zz. Dd Jj. Jj Ww J' J Ww. Jj Ww. Jj I\~~ SOUN,DS AND LETTERS

QJ) Zz LI Zz. Dd Jj. Jj Ww J' J Ww. Jj Ww. Jj I\~~ SOUN,DS AND LETTERS SOUN,DS AND LETTERS.--< Say the name of each picture.llsten to the first sound. Then circle the letters with that"sound..-.. Dd QJ) Jj Ww J' J Ww Zz LI Zz Dd Jj Ww Dd Jj Zz Jj LI Ww Jj LI Ww Jj Ww Zz Dd

More information

c. What is the average rate of change of f on the interval [, ]? Answer: d. What is a local minimum value of f? Answer: 5 e. On what interval(s) is f

c. What is the average rate of change of f on the interval [, ]? Answer: d. What is a local minimum value of f? Answer: 5 e. On what interval(s) is f Essential Skills Chapter f ( x + h) f ( x ). Simplifying the difference quotient Section. h f ( x + h) f ( x ) Example: For f ( x) = 4x 4 x, find and simplify completely. h Answer: 4 8x 4 h. Finding the

More information

(ril"s::lli '*Y, ,dr4{n. w.j. ",;:ii:{..._, I i,ai I. AOEP'IIICKOTO MyHI4TIUIIA.JTbHO O PAI,rOrrA nepmckoto KpA.fl TIOCTAHOBJTEHPIE

(rils::lli '*Y, ,dr4{n. w.j. ,;:ii:{..._, I i,ai I. AOEP'IIICKOTO MyHI4TIUIIA.JTbHO O PAI,rOrrA nepmckoto KpA.fl TIOCTAHOBJTEHPIE '*Y w.j TOCTOBJTEPE.MCTPU{ OEP'CKOTO MyTU.JTbO O PrOrr EPMCKOTO Kp.fl 26.02.20t3 e387 -l fo uecet Meellf [epe.rer 3eMeJrbbr ycrkb rrperr3ebr r pecrbjreg MferbM cembfl Mr ytbeprme r ctbjrerrem MrcTpr r

More information

5 s. 00 S aaaog. 3s a o. gg pq ficfi^pq. So c o. H «o3 g gpq ^fi^ s 03 co -*«10 eo 5^ - 3 d s3.s. as fe«jo. Table of General Ordinances.

5 s. 00 S aaaog. 3s a o. gg pq ficfi^pq. So c o. H «o3 g gpq ^fi^ s 03 co -*«10 eo 5^ - 3 d s3.s. as fe«jo. Table of General Ordinances. 5 s Tble f Generl rinnes. q=! j-j 3 -ri j -s 3s m s3 0,0 0) fife s fert " 7- CN i-l r-l - p D fife s- 3 Ph' h ^q 3 3 (j; fe QtL. S &&X* «««i s PI 0) g #r

More information

Name: Math 29 Probability

Name: Math 29 Probability Name: Math 29 Probability Practice Final Exam Instructions: 1. Show all work. You may receive partial credit for partially completed problems. 2. You may use calculators and a two-sided sheet of reference

More information

III Illl i 111 III illlllill 111 Illlll

III Illl i 111 III illlllill 111 Illlll t - - - - - QUQMOLY"lJl) 7 M ft Fi t FQRMRT* ;ty- - / OC../^. l_.^... FIGURE: 4 III Illl i 111 III 111 111 illlllill 111 Illlll Areal \\Jct (p~~7 v~v t 42C81NW0009 eel COWIE 200 " - t ipa- - cs-a x s\-8.xjw

More information

We enclose herewith a copy of your notice of October 20, 1990 for your reference purposes.

We enclose herewith a copy of your notice of October 20, 1990 for your reference purposes. W-E AND ISuC ATTORNEYS AT lhw 10 QUEEN STIlEET P. 0. BOX NO. 201 NEWTOWN. CONNEWICUT 06470 OEOROE N. WNCELEE HENRY J. ISAAC BUWrpOff 203 9992218 FAX NO. 903-4P6-3011 October 30, 1990.. The Master Collectors

More information

Universal LaW of J^latGre: TboagbL tbe Solvent of fier Problems. CHICAGO, A U G U S T what thoy shall or shall not bollevo.

Universal LaW of J^latGre: TboagbL tbe Solvent of fier Problems. CHICAGO, A U G U S T what thoy shall or shall not bollevo. VO J^G: GO G 13 1892 O 142 " V z K x x' - * G -^ G x ( '! 1 < G O O G j 2 O 180 3 O O z OO V - O -OOK O O - O O - q G O - q x x K " 8 2 q 1 F O?" O O j j O 3 O - O O - G O ; 10000000 ; O G x G O O q! O

More information

f~ 72- C- V z ::::/2- ( g.'67>«0 -(" f )((67- V Y

f~ 72- C- V z ::::/2- ( g.'67>«0 -( f )((67- V Y s Physics 1B(b) Final Exam Winter 2010 Version A Problem 1: A parallel plate capacitor (dimensions 1 cm x 1 m) is designed to store energy. Putting a dielectric into the capacitor makes a huge difference

More information

CHEM 10113, Quiz 5 October 26, 2011

CHEM 10113, Quiz 5 October 26, 2011 CHEM 10113, Quiz 5 October 26, 2011 Name (please print) All equations must be balanced and show phases for full credit. Significant figures count, show charges as appropriate, and please box your answers!

More information