TABLE OF CONTENTS cont. TABLE OF CONTENTS. Picture & Matching Cards cont. Biomes Flow Charts. freshwater marine wetland desert forest grassland

Size: px
Start display at page:

Download "TABLE OF CONTENTS cont. TABLE OF CONTENTS. Picture & Matching Cards cont. Biomes Flow Charts. freshwater marine wetland desert forest grassland"

Transcription

1 TABLE OF CONTENT Bios Fow Chrts frshwtr rin wtnd dsrt forst grssnd tundr Pictur & Mtching Crds trrstri qutic frshwtr rin (ocn) wtnd dsrt forst grssnd tundr rivrs & strs ks & onds cost/stury/intr-tid ocn cor rf TABLE OF CONTENT cont. 3 Pictur & Mtching Crds cont bog rsh sw rid dsrt si-rid dsrt cost dsrt cod dsrt conifrous/tig/bor forst dciduous/trt forst troic rinforst riri st s svnn Arctic tundr in (ountin) tundr 11 11, 26 11, 26 12, 27 12, 27 13, 28 13, 28 14, 29 14, 29 15, 30 15, 30 16, 31 16, 31 17, 32 17, 32 fi 18, 33 18, 33 19, 34 19, 34 20, 35 20, 35 21, 36 21, 36 22, 37 22, 37 23, 38 23, 38 24, 39 24, 39 25, 40 25, 40 Hndwriting Prctic Pgs 41, 44, 47 (nuscrit, D'Nin, cursiv) Bios Chrt Pg 2 of Bios of th Word

2 Bios (th nvironnt found in rgion) r dividd into two in grous: qutic (wtr) nd trrstri (nd). Ths two grous r thn furthr dividd into svn in grous. Ech of th svn grous r dividd into sub-grous. BIOME OF THE WORLD qutic fi trrstri frshwtr rin (ocn) wtnd dsrt forst grssnd tundr Using th ictur crds, cn you sort th qutic fro th trrstri bios? Pg 3 of 52 Bios of th Word

3 Frshwtr is wtr with no st contnt. Th frshwtr bio is dividd into two in grous: FREHWATER Rivrs & trs Bodis of fowing wtr tht ovs in on dirction. Rivrs nd strs strt s hdwtrs (which y b srings, snowt, or ks) thn trv th wy to thir ouths, usuy nothr wtr chnn or th ocn. Th wtr is coost nd crst t th sourc, nd hs or oxygn. Th rivr or str is widst towrd th idd. Towrd th outh, th wtr is urky nd hs ss oxygn. fi Lks & Ponds Lks nd onds rng in siz fro fw squr trs to thousnds of squr kiotrs. Pg 4 of 52 Bios of th Word

4 Mrin bios hv stwtr. Th rin bio is dividd into thr in grous: MARINE fi Cost/Estury/Intrtid Ocns Cor Rf Whr ocns nd ss t nd Ocns r th rgst bio nd Cor rfs r found in wr nd/or frshwtr bios. ho to th sst nkton nd wtrs nd r or vrid on th rgst crtur on rth - th bu st cost of continnts. wh. Pg 5 of 52 Bios of th Word

5 Wtnds r rs of stnding wtr with qutic nts (ond iis, cttis, tc.). Not wtnds r frshwtr bcus so wtnds hv st wtr fro incoing swtr. Th wtnds bio is dividd into thr in grous: WETLAND fi Bogs Mrshs ws A s, vry cidic body of wtr A body of oving wtr, frsh or A wtnd siir to rsh but tht hs no ntur ints nd is sty, with rds growing in it. A usuy rgr in r. It suorts surroundd by rings of vgttion. rsh is usuy nr rivr or s widr vrity of nt if, incuding A t of grsss y grow on to. cost. trs nd shrubs. As th grsss di nd buid u, th bog wtr is rcd by songy ss of t. Using th ictur crds, cn you tch th qutic bios? Pg 6 of 52 Bios of th Word

6 Dsrts r rid (dry) rgions tht rciv ss thn 50 c of rinf yr. Th dsrt bio is first dividd into two in grous - hot nd cod - thn dividd into four sub-grous: DEERT t Dsrt hot dsrts fi cod dsrts Arid i-arid Cost Cod Arid dsrts r vry hot i-rid dsrts r hot Cost dsrts r found A dsrt is ny r tht nd dry nd r usuy nd dry nd usuy in th rs of Cntr rcivs ss thn 50 c found nr th qutor. furthr north of th nd outh Aric. of rinf yr, which qutor thn rid dsrts. ks ost of Antrctic nd Grnnd dsrts. Pg 7 of 52 Bios of th Word

Pupil / Class Record We can assume a word has been learned when it has been either tested or used correctly at least three times.

Pupil / Class Record We can assume a word has been learned when it has been either tested or used correctly at least three times. 2 Pupi / Css Rr W ssum wr hs b r wh i hs b ihr s r us rry s hr ims. Nm: D Bu: fr i bus brhr u firs hf hp hm s uh i iv iv my my mr muh m w ih w Tik r pp push pu sh shu sisr s sm h h hir hr hs im k w vry

More information

Finite Element Method FEM FOR FRAMES

Finite Element Method FEM FOR FRAMES Finit Ent Mthod FEM FOR FRAMES CONENS INROUCION FEM EQUAIONS FOR PLANAR FRAMES Equtions in oc coordint sst Equtions in gob coordint sst FEM EQUAIONS FOR SPAIAL FRAMES Equtions in oc coordint sst Equtions

More information

Preview. Graph. Graph. Graph. Graph Representation. Graph Representation 12/3/2018. Graph Graph Representation Graph Search Algorithms

Preview. Graph. Graph. Graph. Graph Representation. Graph Representation 12/3/2018. Graph Graph Representation Graph Search Algorithms /3/0 Prvw Grph Grph Rprsntton Grph Srch Algorthms Brdth Frst Srch Corrctnss of BFS Dpth Frst Srch Mnmum Spnnng Tr Kruskl s lgorthm Grph Drctd grph (or dgrph) G = (V, E) V: St of vrt (nod) E: St of dgs

More information

a b c cat CAT A B C Aa Bb Cc cat cat Lesson 1 (Part 1) Verbal lesson: Capital Letters Make The Same Sound Lesson 1 (Part 1) continued...

a b c cat CAT A B C Aa Bb Cc cat cat Lesson 1 (Part 1) Verbal lesson: Capital Letters Make The Same Sound Lesson 1 (Part 1) continued... Progrssiv Printing T.M. CPITLS g 4½+ Th sy, fun (n FR!) wy to tch cpitl lttrs. ook : C o - For Kinrgrtn or First Gr (not for pr-school). - Tchs tht cpitl lttrs mk th sm souns s th littl lttrs. - Tchs th

More information

12/3/12. Outline. Part 10. Graphs. Circuits. Euler paths/circuits. Euler s bridge problem (Bridges of Konigsberg Problem)

12/3/12. Outline. Part 10. Graphs. Circuits. Euler paths/circuits. Euler s bridge problem (Bridges of Konigsberg Problem) 12/3/12 Outlin Prt 10. Grphs CS 200 Algorithms n Dt Struturs Introution Trminology Implmnting Grphs Grph Trvrsls Topologil Sorting Shortst Pths Spnning Trs Minimum Spnning Trs Ciruits 1 Ciruits Cyl 2 Eulr

More information

5/9/13. Part 10. Graphs. Outline. Circuits. Introduction Terminology Implementing Graphs

5/9/13. Part 10. Graphs. Outline. Circuits. Introduction Terminology Implementing Graphs Prt 10. Grphs CS 200 Algorithms n Dt Struturs 1 Introution Trminology Implmnting Grphs Outlin Grph Trvrsls Topologil Sorting Shortst Pths Spnning Trs Minimum Spnning Trs Ciruits 2 Ciruits Cyl A spil yl

More information

CSE 373: More on graphs; DFS and BFS. Michael Lee Wednesday, Feb 14, 2018

CSE 373: More on graphs; DFS and BFS. Michael Lee Wednesday, Feb 14, 2018 CSE 373: Mor on grphs; DFS n BFS Mihl L Wnsy, F 14, 2018 1 Wrmup Wrmup: Disuss with your nighor: Rmin your nighor: wht is simpl grph? Suppos w hv simpl, irt grph with x nos. Wht is th mximum numr of gs

More information

Minimum Spanning Trees

Minimum Spanning Trees Minimum Spnning Trs Minimum Spnning Trs Problm A town hs st of houss nd st of rods A rod conncts nd only houss A rod conncting houss u nd v hs rpir cost w(u, v) Gol: Rpir nough (nd no mor) rods such tht:

More information

Limits Indeterminate Forms and L Hospital s Rule

Limits Indeterminate Forms and L Hospital s Rule Limits Indtrmint Forms nd L Hospitl s Rul I Indtrmint Form o th Tp W hv prviousl studid its with th indtrmint orm s shown in th ollowin mpls: Empl : Empl : tn [Not: W us th ivn it ] Empl : 8 h 8 [Not:

More information

A prefix word in each of these sentences is incorrect. Rewrite the prefix words correctly.

A prefix word in each of these sentences is incorrect. Rewrite the prefix words correctly. Spring Trm 2 Cirl th possssiv pronoun: Th hilrn wr thrill tht th i tht h n hosn or th inl prout ws thirs. Rwrit this sntn with th vril phrs t th ginning. Don t orgt omm! Thr wsn t on pi o pizz lt tr th

More information

ECE COMBINATIONAL BUILDING BLOCKS - INVEST 13 DECODERS AND ENCODERS

ECE COMBINATIONAL BUILDING BLOCKS - INVEST 13 DECODERS AND ENCODERS C 24 - COMBINATIONAL BUILDING BLOCKS - INVST 3 DCODS AND NCODS FALL 23 AP FLZ To o "wll" on this invstition you must not only t th riht nswrs ut must lso o nt, omplt n onis writups tht mk ovious wht h

More information

Section 3: Antiderivatives of Formulas

Section 3: Antiderivatives of Formulas Chptr Th Intgrl Appli Clculus 96 Sction : Antirivtivs of Formuls Now w cn put th is of rs n ntirivtivs togthr to gt wy of vluting finit intgrls tht is ct n oftn sy. To vlut finit intgrl f(t) t, w cn fin

More information

TOPIC 5: INTEGRATION

TOPIC 5: INTEGRATION TOPIC 5: INTEGRATION. Th indfinit intgrl In mny rspcts, th oprtion of intgrtion tht w r studying hr is th invrs oprtion of drivtion. Dfinition.. Th function F is n ntidrivtiv (or primitiv) of th function

More information

Outline. Circuits. Euler paths/circuits 4/25/12. Part 10. Graphs. Euler s bridge problem (Bridges of Konigsberg Problem)

Outline. Circuits. Euler paths/circuits 4/25/12. Part 10. Graphs. Euler s bridge problem (Bridges of Konigsberg Problem) 4/25/12 Outlin Prt 10. Grphs CS 200 Algorithms n Dt Struturs Introution Trminology Implmnting Grphs Grph Trvrsls Topologil Sorting Shortst Pths Spnning Trs Minimum Spnning Trs Ciruits 1 2 Eulr s rig prolm

More information

Ch 1.2: Solutions of Some Differential Equations

Ch 1.2: Solutions of Some Differential Equations Ch 1.2: Solutions of Som Diffrntil Equtions Rcll th fr fll nd owl/mic diffrntil qutions: v 9.8.2v, p.5 p 45 Ths qutions hv th gnrl form y' = y - b W cn us mthods of clculus to solv diffrntil qutions of

More information

PH427/PH527: Periodic systems Spring Overview of the PH427 website (syllabus, assignments etc.) 2. Coupled oscillations.

PH427/PH527: Periodic systems Spring Overview of the PH427 website (syllabus, assignments etc.) 2. Coupled oscillations. Dy : Mondy 5 inuts. Ovrviw of th PH47 wsit (syllus, ssignnts tc.). Coupld oscilltions W gin with sss coupld y Hook's Lw springs nd find th possil longitudinl) otion of such syst. W ll xtnd this to finit

More information

CREATED USING THE RSC COMMUNICATION TEMPLATE (VER. 2.1) - SEE FOR DETAILS

CREATED USING THE RSC COMMUNICATION TEMPLATE (VER. 2.1) - SEE   FOR DETAILS uortig Iormtio: Pti moiitio oirmtio vi 1 MR: j 5 FEFEFKFK 8.6.. 8.6 1 13 1 11 1 9 8 7 6 5 3 1 FEFEFKFK moii 1 13 1 11 1 9 8 7 6 5 3 1 m - - 3 3 g i o i o g m l g m l - - h k 3 h k 3 Figur 1: 1 -MR or th

More information

Minimum Spanning Trees

Minimum Spanning Trees Mnmum Spnnng Trs Spnnng Tr A tr (.., connctd, cyclc grph) whch contns ll th vrtcs of th grph Mnmum Spnnng Tr Spnnng tr wth th mnmum sum of wghts 1 1 Spnnng forst If grph s not connctd, thn thr s spnnng

More information

Language of position. 1 Follow the instructions to show position. 2 Follow these instructions to draw: Circle the child in the middle.

Language of position. 1 Follow the instructions to show position. 2 Follow these instructions to draw: Circle the child in the middle. Lnguge of position 1 Follow the instructions to show position. Circle the child in the middle. Put cross under the child on the left. Circle the ug on the fr right. Put cross ove the ug tht is etween the

More information

Curry Farms Park. Pheasant Hill. Park. Greenwood Shores Park. An n. Lake Ann Park. Chanhassen Recreation Center. Sunset Ridge. Park.

Curry Farms Park. Pheasant Hill. Park. Greenwood Shores Park. An n. Lake Ann Park. Chanhassen Recreation Center. Sunset Ridge. Park. nwsht i n nw sh t R gi on l r innton iddl nhstr rsdriv hsnt Hill Sgrbsh Grnwood Shors Rod Crr Frms Crvr Bh lgrond owrs Bolvrd l snt ViwRod dow Grn Crvr Bh Krbr ond o t s North ots Univrsit of innsot ndsp

More information

1 Introduction to Modulo 7 Arithmetic

1 Introduction to Modulo 7 Arithmetic 1 Introution to Moulo 7 Arithmti Bor w try our hn t solvin som hr Moulr KnKns, lt s tk los look t on moulr rithmti, mo 7 rithmti. You ll s in this sminr tht rithmti moulo prim is quit irnt rom th ons w

More information

Page 1. Question 19.1b Electric Charge II Question 19.2a Conductors I. ConcepTest Clicker Questions Chapter 19. Physics, 4 th Edition James S.

Page 1. Question 19.1b Electric Charge II Question 19.2a Conductors I. ConcepTest Clicker Questions Chapter 19. Physics, 4 th Edition James S. ConTst Clikr ustions Chtr 19 Physis, 4 th Eition Jms S. Wlkr ustion 19.1 Two hrg blls r rlling h othr s thy hng from th iling. Wht n you sy bout thir hrgs? Eltri Chrg I on is ositiv, th othr is ngtiv both

More information

CSE 373: AVL trees. Warmup: Warmup. Interlude: Exploring the balance invariant. AVL Trees: Invariants. AVL tree invariants review

CSE 373: AVL trees. Warmup: Warmup. Interlude: Exploring the balance invariant. AVL Trees: Invariants. AVL tree invariants review rmup CSE 7: AVL trs rmup: ht is n invrint? Mihl L Friy, Jn 9, 0 ht r th AVL tr invrints, xtly? Disuss with your nighor. AVL Trs: Invrints Intrlu: Exploring th ln invrint Cor i: xtr invrint to BSTs tht

More information

FSA. CmSc 365 Theory of Computation. Finite State Automata and Regular Expressions (Chapter 2, Section 2.3) ALPHABET operations: U, concatenation, *

FSA. CmSc 365 Theory of Computation. Finite State Automata and Regular Expressions (Chapter 2, Section 2.3) ALPHABET operations: U, concatenation, * CmSc 365 Thory of Computtion Finit Stt Automt nd Rgulr Exprssions (Chptr 2, Sction 2.3) ALPHABET oprtions: U, conctntion, * otin otin Strings Form Rgulr xprssions dscri Closd undr U, conctntion nd * (if

More information

How much air is required by the people in this lecture theatre during this lecture?

How much air is required by the people in this lecture theatre during this lecture? 3 NTEGRATON tgrtio is us to swr qustios rltig to Ar Volum Totl qutity such s: Wht is th wig r of Boig 747? How much will this yr projct cost? How much wtr os this rsrvoir hol? How much ir is rquir y th

More information

Paths. Connectivity. Euler and Hamilton Paths. Planar graphs.

Paths. Connectivity. Euler and Hamilton Paths. Planar graphs. Pths.. Eulr n Hmilton Pths.. Pth D. A pth rom s to t is squn o gs {x 0, x 1 }, {x 1, x 2 },... {x n 1, x n }, whr x 0 = s, n x n = t. D. Th lngth o pth is th numr o gs in it. {, } {, } {, } {, } {, } {,

More information

Seven-Segment Display Driver

Seven-Segment Display Driver 7-Smnt Disply Drivr, Ron s in 7-Smnt Disply Drivr, Ron s in Prolm 62. 00 0 0 00 0000 000 00 000 0 000 00 0 00 00 0 0 0 000 00 0 00 BCD Diits in inry Dsin Drivr Loi 4 inputs, 7 outputs 7 mps, h with 6 on

More information

T H E S C I E N C E B E H I N D T H E A R T

T H E S C I E N C E B E H I N D T H E A R T A t t R u r s - L x C t I. xtr turs t Lx Ct Rurs. Rr qurtr s s r t surt strutur. Ts Att Rurs rv ut us, s srt t tr t rtt rt yur t w yu ru. T uqu Lx st ut rv ss ts ss t t y rt t tys t r ts w wr rtts. Atrx

More information

Steady-state tracking & sys. types

Steady-state tracking & sys. types Sty-tt trcking & y. ty Unity fck control: um CL tl lnt r C y - r - o.l. y y r ol ol o.l. m m n n n N N N N N, N,, ut N N, m, ol.. clo-loo: y r ol.. trcking rror: r y r ty-tt trcking: t r ol.. ol.. For

More information

Integration Continued. Integration by Parts Solving Definite Integrals: Area Under a Curve Improper Integrals

Integration Continued. Integration by Parts Solving Definite Integrals: Area Under a Curve Improper Integrals Intgrtion Continud Intgrtion y Prts Solving Dinit Intgrls: Ar Undr Curv Impropr Intgrls Intgrtion y Prts Prticulrly usul whn you r trying to tk th intgrl o som unction tht is th product o n lgric prssion

More information

Does the Order Matter?

Does the Order Matter? LESSON 6 Does the Order Mtter? LEARNING OBJECTIVES Tody I : writing out exponent ultipliction. So tht I cn: develop rules for exponents. I ll know I hve it when I cn: solve proble like ( b) = b 5 0. Opening

More information

Section 10.2 Angles and Triangles

Section 10.2 Angles and Triangles 117 Ojective #1: Section 10.2 nges n Tringes Unerstning efinitions of ifferent types of nges. In the intersection of two ines, the nges tht re cttycorner fro ech other re vertic nges. Vertic nges wi hve

More information

minimize c'x subject to subject to subject to

minimize c'x subject to subject to subject to z ' sut to ' M ' M N uostrd N z ' sut to ' z ' sut to ' sl vrls vtor of : vrls surplus vtor of : uostrd s s s s s s z sut to whr : ut ost of :out of : out of ( ' gr of h food ( utrt : rqurt for h utrt

More information

CSE 373. Graphs 1: Concepts, Depth/Breadth-First Search reading: Weiss Ch. 9. slides created by Marty Stepp

CSE 373. Graphs 1: Concepts, Depth/Breadth-First Search reading: Weiss Ch. 9. slides created by Marty Stepp CSE 373 Grphs 1: Conpts, Dpth/Brth-First Srh ring: Wiss Ch. 9 slis rt y Mrty Stpp http://www.s.wshington.u/373/ Univrsity o Wshington, ll rights rsrv. 1 Wht is grph? 56 Tokyo Sttl Soul 128 16 30 181 140

More information

V={A,B,C,D,E} E={ (A,D),(A,E),(B,D), (B,E),(C,D),(C,E)}

V={A,B,C,D,E} E={ (A,D),(A,E),(B,D), (B,E),(C,D),(C,E)} Introution Computr Sin & Enginring 423/823 Dsign n Anlysis of Algorithms Ltur 03 Elmntry Grph Algorithms (Chptr 22) Stphn Sott (Apt from Vinohnrn N. Vriym) I Grphs r strt t typs tht r pplil to numrous

More information

Chapter 16. 1) is a particular point on the graph of the function. 1. y, where x y 1

Chapter 16. 1) is a particular point on the graph of the function. 1. y, where x y 1 Prctic qustions W now tht th prmtr p is dirctl rltd to th mplitud; thrfor, w cn find tht p. cos d [ sin ] sin sin Not: Evn though ou might not now how to find th prmtr in prt, it is lws dvisl to procd

More information

V={A,B,C,D,E} E={ (A,D),(A,E),(B,D), (B,E),(C,D),(C,E)}

V={A,B,C,D,E} E={ (A,D),(A,E),(B,D), (B,E),(C,D),(C,E)} s s of s Computr Sin & Enginring 423/823 Dsign n Anlysis of Ltur 03 (Chptr 22) Stphn Sott (Apt from Vinohnrn N. Vriym) s of s s r strt t typs tht r pplil to numrous prolms Cn ptur ntitis, rltionships twn

More information

Practice Final Exam. 3.) What is the 61st term of the sequence 7, 11, 15, 19,...?

Practice Final Exam. 3.) What is the 61st term of the sequence 7, 11, 15, 19,...? Discrt mth Prctic Fl Em.) Fd 4 (i ) i=.) Fd i= 6 i.) Wht is th 6st trm th squnc 7,, 5, 9,...? 4.) Wht s th 57th trm, 6,, 4,...? 5.) Wht s th sum th first 60 trms th squnc, 5, 7, 9,...? 6.) Suppos st A

More information

Planar convex hulls (I)

Planar convex hulls (I) Covx Hu Covxty Gv st P o ots 2D, tr ovx u s t sst ovx oyo tt ots ots o P A oyo P s ovx or y, P, t st s try P. Pr ovx us (I) Coutto Gotry [s 3250] Lur To Bowo Co ovx o-ovx 1 2 3 Covx Hu Covx Hu Covx Hu

More information

Walk Like a Mathematician Learning Task:

Walk Like a Mathematician Learning Task: Gori Dprtmnt of Euction Wlk Lik Mthmticin Lrnin Tsk: Mtrics llow us to prform mny usful mthmticl tsks which orinrily rquir lr numbr of computtions. Som typs of problms which cn b on fficintly with mtrics

More information

Let's start with an example:

Let's start with an example: Finite Automt Let's strt with n exmple: Here you see leled circles tht re sttes, nd leled rrows tht re trnsitions. One of the sttes is mrked "strt". One of the sttes hs doule circle; this is terminl stte

More information

Divided. diamonds. Mimic the look of facets in a bracelet that s deceptively deep RIGHT-ANGLE WEAVE. designed by Peggy Brinkman Matteliano

Divided. diamonds. Mimic the look of facets in a bracelet that s deceptively deep RIGHT-ANGLE WEAVE. designed by Peggy Brinkman Matteliano RIGHT-ANGLE WEAVE Dv mons Mm t look o ts n rlt tt s ptvly p sn y Py Brnkmn Mttlno Dv your mons nto trnls o two or our olors. FCT-SCON0216_BNB66 2012 Klm Pulsn Co. Ts mtrl my not rprou n ny orm wtout prmsson

More information

Outline. 1 Introduction. 2 Min-Cost Spanning Trees. 4 Example

Outline. 1 Introduction. 2 Min-Cost Spanning Trees. 4 Example Outlin Computr Sin 33 Computtion o Minimum-Cost Spnnin Trs Prim's Alorithm Introution Mik Joson Dprtmnt o Computr Sin Univrsity o Clry Ltur #33 3 Alorithm Gnrl Constrution Mik Joson (Univrsity o Clry)

More information

UniversitaireWiskundeCompetitie. Problem 2005/4-A We have k=1. Show that for every q Q satisfying 0 < q < 1, there exists a finite subset K N so that

UniversitaireWiskundeCompetitie. Problem 2005/4-A We have k=1. Show that for every q Q satisfying 0 < q < 1, there exists a finite subset K N so that Problemen/UWC NAW 5/7 nr juni 006 47 Problemen/UWC UniversitireWiskundeCompetitie Edition 005/4 For Session 005/4 we received submissions from Peter Vndendriessche, Vldislv Frnk, Arne Smeets, Jn vn de

More information

along the vector 5 a) Find the plane s coordinate after 1 hour. b) Find the plane s coordinate after 2 hours. c) Find the plane s coordinate

along the vector 5 a) Find the plane s coordinate after 1 hour. b) Find the plane s coordinate after 2 hours. c) Find the plane s coordinate L8 VECTOR EQUATIONS OF LINES HL Mth - Sntowski Vector eqution of line 1 A plne strts journey t the point (4,1) moves ech hour long the vector. ) Find the plne s coordinte fter 1 hour. b) Find the plne

More information

d e c b a d c b a d e c b a a c a d c c e b

d e c b a d c b a d e c b a a c a d c c e b FLAT PEYOTE STITCH Bin y mkin stoppr -- sw trou n pull it lon t tr until it is out 6 rom t n. Sw trou t in witout splittin t tr. You soul l to sli it up n own t tr ut it will sty in pl wn lt lon. Evn-Count

More information

C D o F. 30 o F. Wall String. 53 o. F y A B C D E. m 2. m 1. m a. v Merry-go round. Phy 231 Sp 03 Homework #8 Page 1 of 4

C D o F. 30 o F. Wall String. 53 o. F y A B C D E. m 2. m 1. m a. v Merry-go round. Phy 231 Sp 03 Homework #8 Page 1 of 4 Phy 231 Sp 3 Hoework #8 Pge 1 of 4 8-1) rigid squre object of negligible weight is cted upon by the forces 1 nd 2 shown t the right, which pull on its corners The forces re drwn to scle in ters of the

More information

Outline. Computer Science 331. Computation of Min-Cost Spanning Trees. Costs of Spanning Trees in Weighted Graphs

Outline. Computer Science 331. Computation of Min-Cost Spanning Trees. Costs of Spanning Trees in Weighted Graphs Outlin Computr Sin 33 Computtion o Minimum-Cost Spnnin Trs Prim s Mik Joson Dprtmnt o Computr Sin Univrsity o Clry Ltur #34 Introution Min-Cost Spnnin Trs 3 Gnrl Constrution 4 5 Trmintion n Eiiny 6 Aitionl

More information

Closure Properties of Regular Languages

Closure Properties of Regular Languages Closure Properties of Regulr Lnguges Regulr lnguges re closed under mny set opertions. Let L 1 nd L 2 e regulr lnguges. (1) L 1 L 2 (the union) is regulr. (2) L 1 L 2 (the conctention) is regulr. (3) L

More information

MA 15910, Lessons 2a and 2b Introduction to Functions Algebra: Sections 3.5 and 7.4 Calculus: Sections 1.2 and 2.1

MA 15910, Lessons 2a and 2b Introduction to Functions Algebra: Sections 3.5 and 7.4 Calculus: Sections 1.2 and 2.1 MA 15910, Lessons nd Introduction to Functions Alger: Sections 3.5 nd 7.4 Clculus: Sections 1. nd.1 Representing n Intervl Set of Numers Inequlity Symol Numer Line Grph Intervl Nottion ) (, ) ( (, ) ]

More information

Aquauno Video 6 Plus Page 1

Aquauno Video 6 Plus Page 1 Connt th timr to th tp. Aquuno Vio 6 Plus Pg 1 Usr mnul 3 lik! For Aquuno Vio 6 (p/n): 8456 For Aquuno Vio 6 Plus (p/n): 8413 Opn th timr unit y prssing th two uttons on th sis, n fit 9V lklin ttry. Whn

More information

More Foundations. Undirected Graphs. Degree. A Theorem. Graphs, Products, & Relations

More Foundations. Undirected Graphs. Degree. A Theorem. Graphs, Products, & Relations Mr Funtins Grphs, Pruts, & Rltins Unirt Grphs An unirt grph is pir f 1. A st f ns 2. A st f gs (whr n g is st f tw ns*) Friy, Sptmr 2, 2011 Ring: Sipsr 0.2 ginning f 0.4; Stughtn 1.1.5 ({,,,,}, {{,}, {,},

More information

Unit 2 Exponents Study Guide

Unit 2 Exponents Study Guide Unit Eponents Stud Guide 7. Integer Eponents Prt : Zero Eponents Algeric Definition: 0 where cn e n non-zero vlue 0 ecuse 0 rised to n power less thn or equl to zero is n undefined vlue. Eple: 0 If ou

More information

Nondeterminism and Nodeterministic Automata

Nondeterminism and Nodeterministic Automata Nondeterminism nd Nodeterministic Automt 61 Nondeterminism nd Nondeterministic Automt The computtionl mchine models tht we lerned in the clss re deterministic in the sense tht the next move is uniquely

More information

Domine Dominus Noster Motetto a V voci

Domine Dominus Noster Motetto a V voci Dn Dns Nstr Mttt V vc And Gbrl (c. 1533-155) Prm Prs O Lrd r Lrd, hw dbl s thy n th whl rth! Fr thy mgfcnc s lvtd bv th hvns. Ot f th mth f fnts nd f cklgs th hst prfctd ps, bcs f thy ns, tht th ght dstry

More information

On Hamiltonian Tetrahedralizations Of Convex Polyhedra

On Hamiltonian Tetrahedralizations Of Convex Polyhedra O Ht Ttrrzts O Cvx Pyr Frs C 1 Q-Hu D 2 C A W 3 1 Dprtt Cputr S T Uvrsty H K, H K, C. E: @s.u. 2 R & TV Trsss Ctr, Hu, C. E: q@163.t 3 Dprtt Cputr S, Mr Uvrsty Nwu St. J s, Nwu, C A1B 35. E: w@r.s.u. Astrt

More information

DUET WITH DIAMONDS COLOR SHIFTING BRACELET By Leslie Rogalski

DUET WITH DIAMONDS COLOR SHIFTING BRACELET By Leslie Rogalski Dut with Dimons Brlt DUET WITH DIAMONDS COLOR SHIFTING BRACELET By Lsli Roglski Photo y Anrw Wirth Supruo DUETS TM from BSmith rt olor shifting fft tht mks your work tk on lif of its own s you mov! This

More information

Gilbert the Green Tree Frog

Gilbert the Green Tree Frog Gbrt th Gr Tr Frog A org Kpr Kd book Wrtt by Stph Jk Iutrtd by T Eor ONCE UPON A TIME thr w frog md Gbrt. Gbrt w Gr Tr Frog. H fmy w gr. H hom w gr. Ad omtm v h food w gr. Gbrt w ck d trd of bg o gr th

More information

CSCI 340: Computational Models. Kleene s Theorem. Department of Computer Science

CSCI 340: Computational Models. Kleene s Theorem. Department of Computer Science CSCI 340: Computtionl Models Kleene s Theorem Chpter 7 Deprtment of Computer Science Unifiction In 1954, Kleene presented (nd proved) theorem which (in our version) sttes tht if lnguge cn e defined y ny

More information

Wave Phenomena Physics 15c

Wave Phenomena Physics 15c Wv hnon hyscs 5c cur 4 Coupl Oscllors! H& con 4. Wh W D s T " u forc oscllon " olv h quon of oon wh frcon n foun h sy-s soluon " Oscllon bcos lr nr h rsonnc frquncy " hs chns fro 0 π/ π s h frquncy ncrss

More information

Graphs. CSC 1300 Discrete Structures Villanova University. Villanova CSC Dr Papalaskari

Graphs. CSC 1300 Discrete Structures Villanova University. Villanova CSC Dr Papalaskari Grphs CSC 1300 Disrt Struturs Villnov Univrsity Grphs Grphs r isrt struturs onsis?ng of vr?s n gs tht onnt ths vr?s. Grphs n us to mol: omputr systms/ntworks mthm?l rl?ons logi iruit lyout jos/prosss f

More information

Handout 11. Energy Bands in Graphene: Tight Binding and the Nearly Free Electron Approach

Handout 11. Energy Bands in Graphene: Tight Binding and the Nearly Free Electron Approach Hdout rg ds Grh: Tght dg d th Nrl Fr ltro roh I ths ltur ou wll lr: rg Th tght bdg thod (otd ) Th -bds grh FZ C 407 Srg 009 Frh R Corll Uvrst Grh d Crbo Notubs: ss Grh s two dsol sgl to lr o rbo tos rrgd

More information

4 7x =250; 5 3x =500; Read section 3.3, 3.4 Announcements: Bell Ringer: Use your calculator to solve

4 7x =250; 5 3x =500; Read section 3.3, 3.4 Announcements: Bell Ringer: Use your calculator to solve Dte: 3/14/13 Objective: SWBAT pply properties of exponentil functions nd will pply properties of rithms. Bell Ringer: Use your clcultor to solve 4 7x =250; 5 3x =500; HW Requests: Properties of Log Equtions

More information

Date: Use the code to write each homophone. The first one has been for you. Handwriting and Vocabulary L1

Date: Use the code to write each homophone. The first one has been for you. Handwriting and Vocabulary L1 Wco to E pnisns g! x Hping you chid buid ssnti skis is sy! Ths tch-ppovd ctivitis hv bn spciy dvopd to k ning both ccssib nd njoyb. On ch pg, you find: hoophons Focus ski Th focus of ch ctivity pg is cy

More information

The Properties of Stars

The Properties of Stars 10/11/010 The Properties of Strs sses Using Newton s Lw of Grvity to Determine the ss of Celestil ody ny two prticles in the universe ttrct ech other with force tht is directly proportionl to the product

More information

Computer Graphics. Viewing & Projections

Computer Graphics. Viewing & Projections Vw & Ovrvw rr : rss r t -vw trsrt: st st, rr w.r.t. r rqurs r rr (rt syst) rt: 2 trsrt st, rt trsrt t 2D rqurs t r y rt rts ss Rr P usuy st try trsrt t wr rts t rs t surs trsrt t r rts u rt w.r.t. vw vu

More information

Winter 2016 COMP-250: Introduction to Computer Science. Lecture 23, April 5, 2016

Winter 2016 COMP-250: Introduction to Computer Science. Lecture 23, April 5, 2016 Wintr 2016 COMP-250: Introduction to Computr Scinc Lctur 23, April 5, 2016 Commnt out input siz 2) Writ ny lgorithm tht runs in tim Θ(n 2 log 2 n) in wors cs. Explin why this is its running tim. I don

More information

Decimals DECIMALS.

Decimals DECIMALS. Dimls DECIMALS www.mthltis.o.uk ow os it work? Solutions Dimls P qustions Pl vlu o imls 0 000 00 000 0 000 00 0 000 00 0 000 00 0 000 tnths or 0 thousnths or 000 hunrths or 00 hunrths or 00 0 tn thousnths

More information

Graphs. Graphs. Graphs: Basic Terminology. Directed Graphs. Dr Papalaskari 1

Graphs. Graphs. Graphs: Basic Terminology. Directed Graphs. Dr Papalaskari 1 CSC 00 Disrt Struturs : Introuon to Grph Thory Grphs Grphs CSC 00 Disrt Struturs Villnov Univrsity Grphs r isrt struturs onsisng o vrs n gs tht onnt ths vrs. Grphs n us to mol: omputr systms/ntworks mthml

More information

Math 154B Elementary Algebra-2 nd Half Spring 2015

Math 154B Elementary Algebra-2 nd Half Spring 2015 Mth 154B Elementry Alger- nd Hlf Spring 015 Study Guide for Exm 4, Chpter 9 Exm 4 is scheduled for Thursdy, April rd. You my use " x 5" note crd (oth sides) nd scientific clcultor. You re expected to know

More information

3 x x x 1 3 x a a a 2 7 a Ba 1 NOW TRY EXERCISES 89 AND a 2/ Evaluate each expression.

3 x x x 1 3 x a a a 2 7 a Ba 1 NOW TRY EXERCISES 89 AND a 2/ Evaluate each expression. SECTION. Eponents nd Rdicls 7 B 7 7 7 7 7 7 7 NOW TRY EXERCISES 89 AND 9 7. EXERCISES CONCEPTS. () Using eponentil nottion, we cn write the product s. In the epression 3 4,the numer 3 is clled the, nd

More information

5/7/13. Part 10. Graphs. Theorem Theorem Graphs Describing Precedence. Outline. Theorem 10-1: The Handshaking Theorem

5/7/13. Part 10. Graphs. Theorem Theorem Graphs Describing Precedence. Outline. Theorem 10-1: The Handshaking Theorem Thorm 10-1: Th Hnshkin Thorm Lt G=(V,E) n unirt rph. Thn Prt 10. Grphs CS 200 Alorithms n Dt Struturs v V (v) = 2 E How mny s r thr in rph with 10 vrtis h of r six? 10 * 6 /2= 30 1 Thorm 10-2 An unirt

More information

Campsites are approximately 20 wide x 50 deep. Campsites must be paid for when the site is staked.

Campsites are approximately 20 wide x 50 deep. Campsites must be paid for when the site is staked. SHOTGUN MPSITE OOTE (SUNDY, SEPTEMBE 23) LST EVENT O 2018 SUPE SHOE WEEKEND (SEPTEMBE 28 30) NIGHT O DESTUTION. PHOTOS! I h Spr Sh p. Th rf w d 2:00 PM r h Sh r d h f f f (d f f f) dh h prf p. O hr, yr.

More information

The Mathematics of Harmonic Oscillators

The Mathematics of Harmonic Oscillators Th Mhcs of Hronc Oscllors Spl Hronc Moon In h cs of on-nsonl spl hronc oon (SHM nvolvng sprng wh sprng consn n wh no frcon, you rv h quon of oon usng Nwon's scon lw: con wh gvs: 0 Ths s sos wrn usng h

More information

> DC < D CO LU > Z> CJ LU

> DC < D CO LU > Z> CJ LU C C FNS TCNCAL NFRMATN CNTR [itpfttiiknirike?fi-'.;t C'JM.V TC hs determined n \ _\}. L\\ tht this Technicl cment hs the istribtin Sttement checked belw. The crnt distribtin fr this dcment cn be telind

More information

ELEG 413 Lecture #6. Mark Mirotznik, Ph.D. Professor The University of Delaware

ELEG 413 Lecture #6. Mark Mirotznik, Ph.D. Professor The University of Delaware LG 43 Lctur #6 Mrk Mirtnik, Ph.D. Prfssr Th Univrsity f Dlwr mil: mirtni@c.udl.du Wv Prpgtin nd Plritin TM: Trnsvrs lctrmgntic Wvs A md is prticulr fild cnfigurtin. Fr givn lctrmgntic bundry vlu prblm,

More information

Last time: introduced our first computational model the DFA.

Last time: introduced our first computational model the DFA. Lctur 7 Homwork #7: 2.2.1, 2.2.2, 2.2.3 (hnd in c nd d), Misc: Givn: M, NFA Prov: (q,xy) * (p,y) iff (q,x) * (p,) (follow proof don in clss tody) Lst tim: introducd our first computtionl modl th DFA. Tody

More information

Fingerprint idea. Assume:

Fingerprint idea. Assume: Fingerprint ide Assume: We cn compute fingerprint f(p) of P in O(m) time. If f(p) f(t[s.. s+m 1]), then P T[s.. s+m 1] We cn compre fingerprints in O(1) We cn compute f = f(t[s+1.. s+m]) from f(t[s.. s+m

More information

INF5820/INF9820 LANGUAGE TECHNOLOGICAL APPLICATIONS. Jan Tore Lønning, Lecture 4, 14 Sep

INF5820/INF9820 LANGUAGE TECHNOLOGICAL APPLICATIONS. Jan Tore Lønning, Lecture 4, 14 Sep INF5820/INF9820 LANGUAGE TECHNOLOGICAL ALICATIONS Jn Tor Lønning Lctur 4 4 Sp. 206 tl@ii.uio.no Tody 2 Sttisticl chin trnsltion: Th noisy chnnl odl Word-bsd Trining IBM odl 3 SMT xpl 4 En kokk lgd n rtt

More information

Solutions for HW11. Exercise 34. (a) Use the recurrence relation t(g) = t(g e) + t(g/e) to count the number of spanning trees of v 1

Solutions for HW11. Exercise 34. (a) Use the recurrence relation t(g) = t(g e) + t(g/e) to count the number of spanning trees of v 1 Solutions for HW Exris. () Us th rurrn rltion t(g) = t(g ) + t(g/) to ount th numr of spnning trs of v v v u u u Rmmr to kp multipl gs!! First rrw G so tht non of th gs ross: v u v Rursing on = (v, u ):

More information

CSC Design and Analysis of Algorithms. Example: Change-Making Problem

CSC Design and Analysis of Algorithms. Example: Change-Making Problem CSC 801- Dsign n Anlysis of Algorithms Ltur 11 Gry Thniqu Exmpl: Chng-Mking Prolm Givn unlimit mounts of oins of nomintions 1 > > m, giv hng for mount n with th lst numr of oins Exmpl: 1 = 25, 2 =10, =

More information

The Death of Stars - II.

The Death of Stars - II. Th Dath of Stars - II. Larning Objctivs! How can w us H-R diagrams to masur th ag of star clustrs (and hnc th ag of our Univrs)?! Why do high and low mass stars volv diffrntly? How ar havy lmnts such as

More information

Math 61 : Discrete Structures Final Exam Instructor: Ciprian Manolescu. You have 180 minutes.

Math 61 : Discrete Structures Final Exam Instructor: Ciprian Manolescu. You have 180 minutes. Nm: UCA ID Numr: Stion lttr: th 61 : Disrt Struturs Finl Exm Instrutor: Ciprin nolsu You hv 180 minuts. No ooks, nots or lultors r llow. Do not us your own srth ppr. 1. (2 points h) Tru/Fls: Cirl th right

More information

Chapter 6 Continuous Random Variables and Distributions

Chapter 6 Continuous Random Variables and Distributions Chpter 6 Continuous Rndom Vriles nd Distriutions Mny economic nd usiness mesures such s sles investment consumption nd cost cn hve the continuous numericl vlues so tht they cn not e represented y discrete

More information

Nefertiti. Echoes of. Regal components evoke visions of the past MULTIPLE STITCHES. designed by Helena Tang-Lim

Nefertiti. Echoes of. Regal components evoke visions of the past MULTIPLE STITCHES. designed by Helena Tang-Lim MULTIPLE STITCHES Nrtiti Ehos o Rgl omponnts vok visions o th pst sign y Hln Tng-Lim Us vrity o stiths to rt this rgl yt wrl sign. Prt sping llows squr s to mk roun omponnts tht rp utiully. FCT-SC-030617-07

More information

Converting Regular Expressions to Discrete Finite Automata: A Tutorial

Converting Regular Expressions to Discrete Finite Automata: A Tutorial Converting Regulr Expressions to Discrete Finite Automt: A Tutoril Dvid Christinsen 2013-01-03 This is tutoril on how to convert regulr expressions to nondeterministic finite utomt (NFA) nd how to convert

More information

Lecture contents. Bloch theorem k-vector Brillouin zone Almost free-electron model Bands Effective mass Holes. NNSE 508 EM Lecture #9

Lecture contents. Bloch theorem k-vector Brillouin zone Almost free-electron model Bands Effective mass Holes. NNSE 508 EM Lecture #9 Lctur contnts Bloch thorm -vctor Brillouin zon Almost fr-lctron modl Bnds ffctiv mss Hols Trnsltionl symmtry: Bloch thorm On-lctron Schrödingr qution ch stt cn ccommo up to lctrons: If Vr is priodic function:

More information

Instructions for Section 1

Instructions for Section 1 Instructions for Sction 1 Choos th rspons tht is corrct for th qustion. A corrct nswr scors 1, n incorrct nswr scors 0. Mrks will not b dductd for incorrct nswrs. You should ttmpt vry qustion. No mrks

More information

What else can you do?

What else can you do? Wht else cn you do? ngle sums The size of specil ngle types lernt erlier cn e used to find unknown ngles. tht form stright line dd to 180c. lculte the size of + M, if L is stright line M + L = 180c( stright

More information

A 1 A 2. a) Find the wavelength of the radio waves. Since c = f, then = c/f = (3x10 8 m/s) / (30x10 6 Hz) = 10m.

A 1 A 2. a) Find the wavelength of the radio waves. Since c = f, then = c/f = (3x10 8 m/s) / (30x10 6 Hz) = 10m. 1. Young s doubl-slit xprint undrlis th instrunt landing syst at ost airports and is usd to guid aircraft to saf landings whn th visibility is poor. Suppos that a pilot is trying to align hr plan with

More information

Polygons POLYGONS.

Polygons POLYGONS. Polgons PLYGNS www.mthltis.o.uk ow os it work? Solutions Polgons Pg qustions Polgons Polgon Not polgon Polgon Not polgon Polgon Not polgon Polgon Not polgon f g h Polgon Not polgon Polgon Not polgon Polgon

More information

We partition C into n small arcs by forming a partition of [a, b] by picking s i as follows: a = s 0 < s 1 < < s n = b.

We partition C into n small arcs by forming a partition of [a, b] by picking s i as follows: a = s 0 < s 1 < < s n = b. Mth 255 - Vector lculus II Notes 4.2 Pth nd Line Integrls We begin with discussion of pth integrls (the book clls them sclr line integrls). We will do this for function of two vribles, but these ides cn

More information

1. For each of the following theorems, give a two or three sentence sketch of how the proof goes or why it is not true.

1. For each of the following theorems, give a two or three sentence sketch of how the proof goes or why it is not true. York University CSE 2 Unit 3. DFA Clsses Converting etween DFA, NFA, Regulr Expressions, nd Extended Regulr Expressions Instructor: Jeff Edmonds Don t chet y looking t these nswers premturely.. For ech

More information

R. 7.5 E. R. 8 E. ! ( y R. S a Clackamas County. . Sa. Zi gzag R. S almon R. U.S. Forest Service 63. acka m a. Wasco. County. Jefferson. County.

R. 7.5 E. R. 8 E. ! ( y R. S a Clackamas County. . Sa. Zi gzag R. S almon R. U.S. Forest Service 63. acka m a. Wasco. County. Jefferson. County. T 2 N r o T 1 N T 1 T 2 B d r C r lo B L t t dr vr Wh t E Wh o c r C l T 27 ch C r L r c t f C r T 4 Z z t h E T 3 H o od y d Clc l 36 C 4 N t T 3 E C r l E N 17 E H o od u u ll B ull u T 1 B 3 vr M H

More information

Riemann Sums and Riemann Integrals

Riemann Sums and Riemann Integrals Riemnn Sums nd Riemnn Integrls Jmes K. Peterson Deprtment of Biologicl Sciences nd Deprtment of Mthemticl Sciences Clemson University August 26, 203 Outline Riemnn Sums Riemnn Integrls Properties Abstrct

More information

The Z transform techniques

The Z transform techniques h Z trnfor tchniqu h Z trnfor h th rol in dicrt yt tht th Lplc trnfor h in nlyi of continuou yt. h Z trnfor i th principl nlyticl tool for ingl-loop dicrt-ti yt. h Z trnfor h Z trnfor i to dicrt-ti yt

More information

CS 373, Spring Solutions to Mock midterm 1 (Based on first midterm in CS 273, Fall 2008.)

CS 373, Spring Solutions to Mock midterm 1 (Based on first midterm in CS 273, Fall 2008.) CS 373, Spring 29. Solutions to Mock midterm (sed on first midterm in CS 273, Fll 28.) Prolem : Short nswer (8 points) The nswers to these prolems should e short nd not complicted. () If n NF M ccepts

More information

Designing finite automata II

Designing finite automata II Designing finite utomt II Prolem: Design DFA A such tht L(A) consists of ll strings of nd which re of length 3n, for n = 0, 1, 2, (1) Determine wht to rememer out the input string Assign stte to ech of

More information

b.) v d =? Example 2 l = 50 m, D = 1.0 mm, E = 6 V, " = 1.72 #10 $8 % & m, and r = 0.5 % a.) R =? c.) V ab =? a.) R eq =?

b.) v d =? Example 2 l = 50 m, D = 1.0 mm, E = 6 V,  = 1.72 #10 $8 % & m, and r = 0.5 % a.) R =? c.) V ab =? a.) R eq =? xmpl : An 8-gug oppr wr hs nomnl mtr o. mm. Ths wr rrs onstnt urrnt o.67 A to W lmp. Th nsty o r ltrons s 8.5 x 8 ltrons pr u mtr. Fn th mgntu o. th urrnt nsty. th rt vloty xmpl D. mm,.67 A, n N 8.5" 8

More information

Name Ima Sample ASU ID

Name Ima Sample ASU ID Nme Im Smple ASU ID 2468024680 CSE 355 Test 1, Fll 2016 30 Septemer 2016, 8:35-9:25.m., LSA 191 Regrding of Midterms If you elieve tht your grde hs not een dded up correctly, return the entire pper to

More information