SCIENCE Student Book. 5th Grade Unit 3

Size: px
Start display at page:

Download "SCIENCE Student Book. 5th Grade Unit 3"

Transcription

1 SCIENCE Studnt Book 5th Grad Unit 3

2 Unit 3 ANIMALS: LIFE CYCLES SCIENCE 503 ANIMALS: LIFE CYCLES Introduction 3 1. Invrtbrats...5 Lif Cycls of Invrtbrats 9 On-Clld, Animal-Lik Protists 14 Egg-Laying Invrtbrats 17 Slf Tst Vrtbrats Lif Cycls of Vrtbrats 33 Egg-Laying Vrtbrats 35 Liv-Baring Vrtbrats 45 Slf Tst 2 50 LIFEPAC Tst Pull-out 1

3 ANIMALS: LIFE CYCLES Unit 3 Author: Barry G. Burrus, M.Div, M.A., B.S. Editor: Brian Ring Illustrations: Brian Ring Mdia Crdits: Pag 3: Lnorlux, istock, Thinkstock; 5: Bussarakam, istock, Thinkstock; 7: ALsik, istock, Thinkstock; Amng Wu, istock, Thinkstock; 9: Coprid, istock, Thinkstock; 13: PlazaCamman, istock, Thinkstock; 18: Comstock, Stockbyt, Thinkstock; 26: Dorling Kindrsly, Thinkstock; 32: Saddako, istock, Thinkstock; 33: thrry, istock, Thinkstock; 34: idizimag, istock, Thinkstock; 35: skarb, istock, Thinkstock; 36: randimal, istock,thinkstock; 39: italiansight, istock,thinkstock; 40: Comstock, Thinkstock; 45: MR1805, istock, Thinkstock; 47: Purstock, Thinkstock. 804 N. 2nd Av. E. Rock Rapids, IA MM by Alpha Omga Publications, Inc. All rights rsrvd. LIFEPAC is a rgistrd tradmark of Alpha Omga Publications, Inc. All tradmarks and/or srvic marks rfrncd in this matrial ar th proprty of thir rspctiv ownrs. Alpha Omga Publications, Inc. maks no claim of ownrship to any tradmarks and/or srvic marks othr than thir own and thir affiliats, and maks no claim of affiliation to any companis whos tradmarks may b listd in this matrial, othr than thir own. 2

4 Unit 3 ANIMALS: LIFE CYCLES ANIMALS: LIFE CYCLES God has cratd a rich varity of animals. In th Book of Gnsis, w rad: And God said, Lt th watrs bring forth abundantly th moving cratur that hath lif, and fowl that may fly abov th arth in th opn firmamnt of havn. And God cratd grat whals, and vry living cratur that movth, which th watrs brought forth abundantly, aftr thir kind, and vry wingd fowl aftr his kind: and God saw that it was good. And God blssd thm, saying, b fruitful, and multiply, and fill th watrs in th sas, and lt fowl multiply in th arth. And th vning and th morning wr th fifth day. And God said, Lt th arth bring forth th living cratur aftr his kind, cattl, and crping thing, and bast of th arth aftr his kind: and it was so. And God mad th bast of th arth aftr his kind, and cattl aftr thir kind, and vry thing that crpth upon th arth aftr his kind: and God saw that it was good. (Gnsis 1:20-25) Fish, birds, inscts, lizards, cattl, and bars ar all xampls of th animals that God has cratd. In this LIFEPAC, you will xplor th rich varity of animals found in th watrs and on th arth. You will also larn about som on-clld, animal-lik protists such as amoba and paramcium. You will xamin aspcts of th lif cycls of ths living things. You will larn about som similaritis and diffrncs among various animals and protists. You will also larn about thir common structurs and th ways thy rproduc. Finally, you will hav an opportunity to obsrv som of ths living things clos-up during xprimnts! 3

5 ANIMALS: LIFE CYCLES Unit 3 Objctivs Rad ths objctivs. Ths objctivs tll what you should b abl to do whn you hav compltd this LIFEPAC. Each sction will list according to th numbrs blow what objctivs will b mt in that sction. Whn you hav finishd this LIFEPAC, you should b abl to: 1. Dscrib th lif cycls of invrtbrats. 2. Explain th diffrncs btwn th lif cycls of invrtbrats. 3. Dscrib th lif cycls of vrtbrats. 4. Explain th diffrncs btwn th lif cycls of vrtbrats. 5. Nam th groups to which th animals blong. 6. Show th rlationship of th structurs of animals to thir rproduction in a lif cycl. 4

6 Unit 3 ANIMALS: LIFE CYCLES 1. INVERTEBRATES In th prvious LIFEPAC, Scinc 502, you larnd that God has cratd a grat varity of living things. You larnd that scintists classify all living things into 5 kingdoms: animals, plants, fungi, protists, and monrans. In th prvious LIFEPAC, you studid th lif cycls of plants, fungi, protists, and monrans. In this LIFEPAC, you will larn about th lif cycls, structurs, and rproduction of animals. W will also covr a coupl of xampls of on-clld, animal-lik protists in this LIFEPAC. W will covr ths protists bcaus, lik almost all animals, thy ar abl to mov about in thir nvironmnts. God has cratd such a rich varity of animals that no on knows for sur how many kinds of animals thr ar! Scintists hav classifid and namd ovr on and a half million diffrnt kinds of animals. Howvr, many scintists bliv that thr may b from two million to as many as fifty million diffrnt kinds of animals. Many nw kinds of animals ar discovrd, namd, and classifid ach yar. Th world of animals is xciting! Th study of animals is calld zoology, and scintists who study animals ar calld zoologists. Objctivs Rviw ths objctivs. Whn you hav compltd this sction, you should b abl to: 1. Dscrib th lif cycls of invrtbrats. 2. Explain th diffrncs btwn th lif cycls of invrtbrats. 5. Nam th groups to which th animals blong. 6. Show th rlationship of th structurs of animals to thir rproduction in a lif cycl. Sction 1 5

7 ANIMALS: LIFE CYCLES Unit 3 Vocabulary Study ths nw words. Larning th manings of ths words is a good study habit and will improv your undrstanding of this LIFEPAC. amoba ( mē b ). A microscopic, on-clld protist. carnivors (kär n vorz). Animals that at only othr animals. Thy ar also calld mat-atrs. xtnds (k stndz ). Strtchs out or rachs out. fluks (flüks). Flatworms of a crtain typ. fragmntation (frag m n tā sh n). A mthod of asxual rproduction in animals by th division of th body into two or mor pics. gills (gilz). Th parts of a fish body that tak oxygn from th watr. hrbivors (hr b vorz). Animals that at only plants. host (hōst). An animal that has anothr animal living in or on it. invrtbrats (in vr t br ts). Animals that do not hav backbons. Inscts, jllyfish, snails, spidrs, and worms ar xampls of invrtbrats. larva (lär v ). Th worm-lik form of an arly stag in th lif cycl of som inscts. larva (lär vē). Plural form of larva. maggot (mag t). Th larva of a fly. mollusks (mol sks). Animals with soft bodis. Adults oftn grow hard shlls. A snail is an xampl of a mollusk. nymph (nimf). Th part of crtain insct lif cycls whr th young animal has no wings or rproductiv organs. octopus (ok t p s). A mollusk with a soft body and ight long arms. omnivors (om n vorz). Animals that at both plants and animals. paramcium (par mē s um). A on-clld, animal-lik protist that has a spcial shap. parasits (par ē sīts). Animals that liv on or in othr animals. Thy gt thir food from th hosts. protozoans (prō t zō nz). A larg group of on-clld protists. pupa (pyü p ). Th form of crtain inscts btwn th tim thy ar larva and adults. pupa (pyü pē). Plural for pupa. squid (skwid). A mollusk that livs in th sa. tsts (ts tēz). Th body parts of mal animals whr sprm is formd. varity (v rī tē). Diffrnt kinds or typs. vrtbrats (vėr t brits). Animals that hav backbons. Birds, fish, rptils, and mammals ar xampls of vrtbrats. zoology (zō ol gē). Th scinc of th study of animals. Not: All vocabulary words in this LIFEPAC appar in boldfac print th first tim thy ar usd. If you ar unsur of th maning whn you ar rading, study th dfinitions givn. Pronunciation Ky: hat, āg, cãr, fär; lt, ēqual, tėrm; it, īc; hot, ōpn, ôrdr; oil; out; cup, pu t, rül; child; long; thin; /ŦH/ for thn; /zh/ for masur; /u/ or / / rprsnts /a/ in about, // in takn, /i/ in pncil, /o/ in lmon, and /u/ in circus. 6 Sction 1

8 Unit 3 ANIMALS: LIFE CYCLES Lik plants, animals com in many shaps and sizs. Most kinds of animals ar lss than an inch long. Som ar so tiny that thy can only b sn with a microscop. Othr animals ar vry larg, lik th lphant, th giraff, and th blu whal. As you larnd in prvious LIFEPACs in this sris, animals and plants ar dpndnt on on anothr. Plants dpnd on th carbon dioxid givn off by animals and human bings. In turn, animals and human bings dpnd upon plants for oxygn and food. As you larnd, this cycl of lif is calld th carbon cycl. In addition, som plants dpnd upon animals to rproduc. For xampl, bs and birds carry polln from plant to plant so that th plants might b frtilizd. Animals diffr from plants in thir ability to mov around in thir nvironmnt. Most plants ar fixd on on plac by roots or root-lik structurs. Howvr, almost all animals can mov around from on location to anothr. Thr ar many ways to classify th diffrnt kinds of animals. For xampl, som animals liv on th land, whil othrs liv in watr. Som animals ar cold-bloodd, whil othrs ar warm-bloodd. Cold-bloodd animals ar warm whn thir surroundings ar warm or cool whn thir surroundings ar cool. Warmbloodd animals, howvr, almost always hav th sam body tmpratur rgardlss of th tmpratur of thir surroundings. Rptils, lik snaks, ar cold-bloodd; thir body tmpratur is basd on thir surroundings. Th sidwindr snak (abov) movs sidways in ordr to mov forward. Animals can b classifid according to what thy at. Animals that only at plants ar calld hrbivors. Cows and giraffs ar xampls of hrbivors. Animals that at only othr animals ar calld carnivors or matatrs. Lions, sharks, and dogs ar carnivors. Animals that at both plants and animals ar calld omnivors. Bars ar omnivors. Dolphins ar warm-bloodd mammals. Thy rquir air to brath, unlik fish. Animals can also b classifid according to whthr or not thy hav backbons. Animals that do not hav backbons ar calld invrtbrats. Th vast majority of animals ar invrtbrats. Inscts, jllyfish, snails, spidrs, and worms ar xampls of invrtbrats. Animals that do hav a backbon ar calld vrtbrats. Birds, fish, rptils, and mammals ar xampls of vrtbrats. In this LIFEPAC, w will study animals by classifying thm as ithr invrtbrats or vrtbrats. In this sction of th LIFEPAC, you will larn about invrtbrats. In th nxt sction, you will xplor vrtbrats. Sction 1 7

9 ANIMALS: LIFE CYCLES Unit 3 Complt ths statmnts. 1.1 Scintists classify all living things into kingdoms. 1.2 Th study of animals is calld. 1.3 Scintists hav namd and classifid ovr diffrnt kinds of animals. 1.4 animals ar warm whn thir surroundings ar warm and cool whn thir surroundings ar cool. 1.5 Animals that at both plants and othr animals ar calld. 1.6 Animals that do not hav backbons ar calld. 1.7 Animals diffr from plants in thir ability to in thir nvironmnts. What is your favorit animal? Why? Look up som information on this animal in a book or ncyclopdia, th library, or th Intrnt. Thn, writ a short papr (lss than on pag) about your favorit animal. Includ som information about whr th animal livs, what it ats, how it braths, and any othr things that you find intrsting about your favorit animal. Lt your tachr rad about your favorit animal whn you hav finishd. Tachr chck: Initials Dat 8 Sction 1

10 Unit 3 ANIMALS: LIFE CYCLES Lif Cycls of Invrtbrats In th prvious LIFEPAC Scinc 502, you larnd that living things go through lif cycls. Thr ar various lif stags in a lif cycl of living things; for xampl, bginning, growth, adulthood, and nd. Animals go through lif stags, too. Thy also bgin, grow, and bcom adults. For xampl, considr th arthworm. Th arthworm has no backbon, so it is an invrtbrat. Th arthworm bgins lif as a tiny, frtilizd gg. Aftr hatching from th gg, it grows into a matur worm. Whn it rachs maturity, it mats with anothr arthworm and lays many nw ggs. Finally, th arthworm gts old and dis. Th arthworm is just on of many typs of worms. Worms hav soft, slndr bodis and no backbons or lgs. Othr xampls of worms bsids th arthworm ar flatworms, roundworms, and lchs. Othr worms may hav lif cycls lik th arthworm. Thy may diffr, howvr, in th numbr of offspring that thy produc. Othr worms may rproduc mor tims or fwr tims. All worms ar invrtbrats. Yt, not all invrtbrats hav lif stags lik thos of th arthworm. You will now larn som things about th various lif stags of invrtbrats. Answr ths qustions. 1.8 What is a lif cycl of a living thing? (You may nd to rfr to th Scinc 502 LIFEPAC, Sction I to hlp you answr this qustion.) 1.9 Why is an arthworm an invrtbrat? Sction 1 9

11 ANIMALS: LIFE CYCLES Unit 3 Bginning stag. Lik almost all living things, th first stag in th lif cycl of invrtbrats bgins with rproduction. Invrtbrats can rproduc in on of two ways: (1) asxual rproduction, and (2) sxual rproduction. In asxual rproduction, only on parnt is ndd to produc an offspring. In sxual rproduction, two parnts on mal and on fmal ar ndd to produc offspring. Most animals and invrtbrats rproduc through sxual rproduction. Asxual rproduction only taks on parnt to produc an offspring. This happns in two ways: (1) fragmntation, or (2) budding. Fragmntation is usd by invrtbrats such as planarians and som othr flatworms. In this mthod of rproduction, a singl parnt usually divids into two pics, on with th had and th othr with th tail! Each sction thn grows th parts that ar missing and bcoms a compltly nw individual animal. Budding occurs whn th animal producs small projctions, calld buds, from its sid. (You larnd about this procss for clls and plants in th prvious LIFEPACs in this sris.) Invrtbrats known as hydras and som sa anmons rproduc by budding. Th buds dvlop into tiny copis of th parnt. Evntually, th buds grow larg nough to dtach from th parnt and bcom a nw individual animal. Fragmntation of Flatworm Sxual rproduction is usd by most animals Budding and invrtbrats. In this mthod, a mal of Sa Anmon sprm units with a fmal gg cll to Asxual rproduction produc a frtilizd gg. It is at this point that a nw animal lif bgins. Th mans of frtilization can ithr occur outsid th fmal body or within th fmal body. In sxual rproduction, th bginning stag of th lif cycl starts with a singl cll. This cll is producd through frtilization of a fmal gg cll with a mal sprm cll. Aftr it is frtilizd, th gg cll bgins growing and rproducing. This is th nxt stag in th lif cycl of th invrtbrat: th growth stag. 10 Sction 1

12 Unit 3 ANIMALS: LIFE CYCLES Match ths itms asxual rproduction 1.11 sxual rproduction 1.12 fragmntation 1.13 budding 1.14 frtilization a. th rsult of a mal sprm combining with a fmal gg b. a singl parnt divids into two or mor pics c. only on parnt ndd to produc offspring d. two parnts, mal and fmal, ndd to produc offspring. producs small projctions from on parnt which split off to form offspring f. th procss of cll division Growth stag. Sxual rproduction can occur ithr within or without th fmal body; that is, th sprm may ithr rach th gg insid th fmal body or outsid th fmal body. If frtilization of th gg occurs within th fmal body, th frtilizd gg is thn laid outsid th fmal body. If th frtilization took plac outsid th body, th frtilizd gg rmains outsid th fmal s body. Now an mbryo bgins to form within th frtilizd gg. This occurs through th procss of mitosis, th division of clls. (Rcall that you larnd about mitosis in prvious LIFEPACs in this sris.) Each frtilizd gg contains som food for th growing mbryo. Growth of th mbryo insid th gg is th first part of th growth stag. As soon as th nw animal can liv outsid th gg, it hatchs from th gg. Young Silvrfish Eggs (mbryo insid nourishd within th gg) Adult Silvrfish Growth stags of silvrfish Sction 1 11

13 ANIMALS: LIFE CYCLES Unit 3 Othr invrtbrats go through a diffrnt procss of growth aftr hatching from an gg. Thy ar hatchd in larva form. (You will larn mor about this latr in this sction.) Larva do not look lik thir parnts. Thy turn into pupa form bfor bcoming adults. Larva and som pupa gt thir own food as thy grow. Som othr invrtbrats hav an vn diffrnt procss occur during thir growth stag. Aftr hatching from an gg, th nw invrtbrat is calld a nymph. (You will larn mor about this latr in this sction.) Th nymph looks somwhat lik th parnt invrtbrat, but som parts ar missing. Nymphs ar abl to gt thir own food for continud growth. As thy grow, thy bgin to form th missing parts of thir bodis that will allow thm to bcom adult invrtbrats. Answr tru or fals An mbryo forms insid a frtilizd fmal gg of invrtbrats Embryos must sarch for thir own food outsid th gg Aftr hatching, th baby of som invrtbrats looks lik a miniatur adult Som invrtbrats hatch in larva form and bcom a pupa bfor bcoming an adult A nymph looks somwhat lik a parnt invrtbrat, but som body parts ar missing. Adult stag. Th adult stag of an invrtbrat is rachd whn it grows to full siz and is abl to rproduc. It looks vry much lik its parnts. Its form will chang vry littl during th adult stag. It can bgin to rproduc. Som invrtbrats will rproduc many tims during thir adult stag. Th gg-laying fmal invrtbrat may produc many ggs at on tim. Most of ths ggs may b frtilizd by sprm from th mal invrtbrat. Th nw frtilizd ggs ar thn dpositd outsid th body of th fmal if thy wr not alrady outsid th body. Nw animals ar formd just lik th parnt bgan. Ths hatch into babis. Th babis grow. Lif for that spcis continus. 12 Sction 1

14 Unit 3 ANIMALS: LIFE CYCLES SELF TEST 1 Match ths itms (ach answr, 3 points) Th body has no rgular shap Adult grows a hard shll Adult is long, thin, and soft Adult has six lgs Som hav a pupa form. a. mollusk b. worm c. insct d. amoba. paramcium 1.06 On cll. Adult has a rgular shap Many ar parasits during growth and adult stags Adult has gills A nymph grows wings About on million diffrnt kinds. Writ tru or fals (ach answr, 3 points) Amobas grow from ggs Embryos must sarch for thir own food outsid th gg A tapworm is a parasit Som worms grow from larva Som inscts do not go through th pupa and larva forms Sprm is producd in th tsts of an animal Eggs must b frtilizd insid th fmal s body A paramcium grows from a nymph A spidr is an insct A larva shds its skin as it grows. Sction 1 29

15 ANIMALS: LIFE CYCLES Unit 3 Writ th corrct lttr in ach blank (ach answr, 2 points) Th study of animals is calld. a. botany b. zoology c. microbiology Animals that at only plants ar calld. a. carnivors b. hrbivors c. omnivors A lif cycl can b compltd in lss than a day by. a. worms b. mollusks c. paramciums A looks lik th parnt, but dosn t hav wings or rproductiv organs. a. nymph b. larva c. pupa A parasit. a. livs alon b. ats mostly blood c. livs in or on othr animals An animal without a backbon is calld. a. a wak animal b. a vrtbrat c. an invrtbrat An gg cll is mad frtil by. a. mitosis b. a sprm cll c. an amoba Maggot is anothr nam for. a. a fly larva b. nymph c. pupa An invrtbrat that has both mal and fmal parts is th. a. larva b. paramcium c. arthworm Animals that hav six lgs ar. a. spidrs b. vrtbrats c. inscts 30 Sction 1

16 Unit 3 ANIMALS: LIFE CYCLES Put ths vnts of a lif cycl in propr ordr (ach vnt, 3 points). wings grow gg is laid an gg cll is frtilizd adulthood nymph is hatchd from gg Complt this activity (this answr, 5 points) Dscrib th lif cycl of a mollusk. Tachr chck: Initials Scor Dat Sction 1 31

17 SCI_Gr3-5 SCI0503 Jan 16 Printing 804 N. 2nd Av. E. Rock Rapids, IA ISBN

SCIENCE Student Book. 3rd Grade Unit 2

SCIENCE Student Book. 3rd Grade Unit 2 SCIENCE Studnt Book 3rd Grad Unit 2 Unit 2 PLANTS SCIENCE 302 PLANTS Introduction 3 1. Plant Parts...4 Roots 6 Stms 8 Lavs 10 Food Storag Parts 11 Slf Tst 1 15 2. Plant Growth... 17 Watr and Minrals 18

More information

SCIENCE Student Book. 5th Grade Unit 5

SCIENCE Student Book. 5th Grade Unit 5 SCIENCE Studnt Book 5th Grad Unit 5 Unit 5 TRANSFORMATION OF ENERGY SCIENCE 505 TRANSFORMATION OF ENERGY Introduction 3 1. Enrgy and Work...4 Enrgy 6 Work 13 Slf Tst 1 17 2. Work from Enrgy... 20 Hat Enrgy

More information

SCIENCE Student Book. 3rd Grade Unit 9

SCIENCE Student Book. 3rd Grade Unit 9 SCIENCE Studnt Book 3rd Grad Unit 9 Unit 9 HEAT ENERGY SCIENCE 309 HEAT ENERGY Introduction 3 1. Whr Hat Enrgy Coms From...4 Friction 6 Fir 9 Elctricity 14 Our Bodis 18 Th Sun 21 Slf Tst 1 25 2. What Hat

More information

Higher order derivatives

Higher order derivatives Robrto s Nots on Diffrntial Calculus Chaptr 4: Basic diffrntiation ruls Sction 7 Highr ordr drivativs What you nd to know alrady: Basic diffrntiation ruls. What you can larn hr: How to rpat th procss of

More information

ph People Grade Level: basic Duration: minutes Setting: classroom or field site

ph People Grade Level: basic Duration: minutes Setting: classroom or field site ph Popl Adaptd from: Whr Ar th Frogs? in Projct WET: Curriculum & Activity Guid. Bozman: Th Watrcours and th Council for Environmntal Education, 1995. ph Grad Lvl: basic Duration: 10 15 minuts Stting:

More information

First derivative analysis

First derivative analysis Robrto s Nots on Dirntial Calculus Chaptr 8: Graphical analysis Sction First drivativ analysis What you nd to know alrady: How to us drivativs to idntiy th critical valus o a unction and its trm points

More information

Summer Reading Activities!

Summer Reading Activities! HOOT FLUSH SCAT CHOMP From Bstslling Author Summr Rading Activitis! Flush Word Find Can you find all 14 words in th puzzl blow? S W I M E N J L P H S P A R R D A Z A G A Z E I B H O T L V S C N U D H I

More information

Fungi Algae Yeast... 46

Fungi Algae Yeast... 46 SCIENCE 502 PLANTS: LIFE CYCLES CONTENTS Introduction............................ 1 I. CLASSIFYING LIVING THINGS AND PLANTS 4 Kinds of Plants......................... 6 Parts of Plants..........................

More information

A central nucleus. Protons have a positive charge Electrons have a negative charge

A central nucleus. Protons have a positive charge Electrons have a negative charge Atomic Structur Lss than ninty yars ago scintists blivd that atoms wr tiny solid sphrs lik minut snookr balls. Sinc thn it has bn discovrd that atoms ar not compltly solid but hav innr and outr parts.

More information

6.1 Integration by Parts and Present Value. Copyright Cengage Learning. All rights reserved.

6.1 Integration by Parts and Present Value. Copyright Cengage Learning. All rights reserved. 6.1 Intgration by Parts and Prsnt Valu Copyright Cngag Larning. All rights rsrvd. Warm-Up: Find f () 1. F() = ln(+1). F() = 3 3. F() =. F() = ln ( 1) 5. F() = 6. F() = - Objctivs, Day #1 Studnts will b

More information

Alpha and beta decay equation practice

Alpha and beta decay equation practice Alpha and bta dcay quation practic Introduction Alpha and bta particls may b rprsntd in quations in svral diffrnt ways. Diffrnt xam boards hav thir own prfrnc. For xampl: Alpha Bta α β alpha bta Dspit

More information

SCIENCE Student Book. 3rd Grade Unit 8

SCIENCE Student Book. 3rd Grade Unit 8 SCIENCE Studnt Book 3rd Grad Unit 8 Unit 8 ROCKS AND THEIR CHANGE SCIENCE 308 ROCKS AND THEIR CHANGE Introduction 3 1. How Rocks Ar Formd...4 By Hat 6 By Prssur 15 Slf Tst 1 25 2. How Rocks Ar Changd...

More information

September 23, Honors Chem Atomic structure.notebook. Atomic Structure

September 23, Honors Chem Atomic structure.notebook. Atomic Structure Atomic Structur Topics covrd Atomic structur Subatomic particls Atomic numbr Mass numbr Charg Cations Anions Isotops Avrag atomic mass Practic qustions atomic structur Sp 27 8:16 PM 1 Powr Standards/ Larning

More information

Differential Equations

Differential Equations Prfac Hr ar m onlin nots for m diffrntial quations cours that I tach hr at Lamar Univrsit. Dspit th fact that ths ar m class nots, th should b accssibl to anon wanting to larn how to solv diffrntial quations

More information

The Matrix Exponential

The Matrix Exponential Th Matrix Exponntial (with xrciss) by Dan Klain Vrsion 28928 Corrctions and commnts ar wlcom Th Matrix Exponntial For ach n n complx matrix A, dfin th xponntial of A to b th matrix () A A k I + A + k!

More information

The Matrix Exponential

The Matrix Exponential Th Matrix Exponntial (with xrciss) by D. Klain Vrsion 207.0.05 Corrctions and commnts ar wlcom. Th Matrix Exponntial For ach n n complx matrix A, dfin th xponntial of A to b th matrix A A k I + A + k!

More information

ECE602 Exam 1 April 5, You must show ALL of your work for full credit.

ECE602 Exam 1 April 5, You must show ALL of your work for full credit. ECE62 Exam April 5, 27 Nam: Solution Scor: / This xam is closd-book. You must show ALL of your work for full crdit. Plas rad th qustions carfully. Plas chck your answrs carfully. Calculators may NOT b

More information

MA 262, Spring 2018, Final exam Version 01 (Green)

MA 262, Spring 2018, Final exam Version 01 (Green) MA 262, Spring 218, Final xam Vrsion 1 (Grn) INSTRUCTIONS 1. Switch off your phon upon ntring th xam room. 2. Do not opn th xam booklt until you ar instructd to do so. 3. Bfor you opn th booklt, fill in

More information

u x v x dx u x v x v x u x dx d u x v x u x v x dx u x v x dx Integration by Parts Formula

u x v x dx u x v x v x u x dx d u x v x u x v x dx u x v x dx Integration by Parts Formula 7. Intgration by Parts Each drivativ formula givs ris to a corrsponding intgral formula, as w v sn many tims. Th drivativ product rul yilds a vry usful intgration tchniqu calld intgration by parts. Starting

More information

Lecture 37 (Schrödinger Equation) Physics Spring 2018 Douglas Fields

Lecture 37 (Schrödinger Equation) Physics Spring 2018 Douglas Fields Lctur 37 (Schrödingr Equation) Physics 6-01 Spring 018 Douglas Filds Rducd Mass OK, so th Bohr modl of th atom givs nrgy lvls: E n 1 k m n 4 But, this has on problm it was dvlopd assuming th acclration

More information

Give the letter that represents an atom (6) (b) Atoms of A and D combine to form a compound containing covalent bonds.

Give the letter that represents an atom (6) (b) Atoms of A and D combine to form a compound containing covalent bonds. 1 Th diagram shows th lctronic configurations of six diffrnt atoms. A B C D E F (a) You may us th Priodic Tabl on pag 2 to hlp you answr this qustion. Answr ach part by writing on of th lttrs A, B, C,

More information

u r du = ur+1 r + 1 du = ln u + C u sin u du = cos u + C cos u du = sin u + C sec u tan u du = sec u + C e u du = e u + C

u r du = ur+1 r + 1 du = ln u + C u sin u du = cos u + C cos u du = sin u + C sec u tan u du = sec u + C e u du = e u + C Tchniqus of Intgration c Donald Kridr and Dwight Lahr In this sction w ar going to introduc th first approachs to valuating an indfinit intgral whos intgrand dos not hav an immdiat antidrivativ. W bgin

More information

Search sequence databases 3 10/25/2016

Search sequence databases 3 10/25/2016 Sarch squnc databass 3 10/25/2016 Etrm valu distribution Ø Suppos X is a random variabl with probability dnsity function p(, w sampl a larg numbr S of indpndnt valus of X from this distribution for an

More information

A=P=E M-A=N Alpha particle Beta Particle. Periodic table

A=P=E M-A=N Alpha particle Beta Particle. Periodic table Nam Pr. Atomic Structur/Nuclar Chmistry (Ch. 3 & 21) OTHS Acadmic Chmistry Objctivs: Undrstand th xprimntal dsign and conclusions usd in th dvlopmnt of modrn atomic thory, including Dalton's Postulats,

More information

Differentiation of Exponential Functions

Differentiation of Exponential Functions Calculus Modul C Diffrntiation of Eponntial Functions Copyright This publication Th Northrn Albrta Institut of Tchnology 007. All Rights Rsrvd. LAST REVISED March, 009 Introduction to Diffrntiation of

More information

Where k is either given or determined from the data and c is an arbitrary constant.

Where k is either given or determined from the data and c is an arbitrary constant. Exponntial growth and dcay applications W wish to solv an quation that has a drivativ. dy ky k > dx This quation says that th rat of chang of th function is proportional to th function. Th solution is

More information

General Notes About 2007 AP Physics Scoring Guidelines

General Notes About 2007 AP Physics Scoring Guidelines AP PHYSICS C: ELECTRICITY AND MAGNETISM 2007 SCORING GUIDELINES Gnral Nots About 2007 AP Physics Scoring Guidlins 1. Th solutions contain th most common mthod of solving th fr-rspons qustions and th allocation

More information

1 Minimum Cut Problem

1 Minimum Cut Problem CS 6 Lctur 6 Min Cut and argr s Algorithm Scribs: Png Hui How (05), Virginia Dat: May 4, 06 Minimum Cut Problm Today, w introduc th minimum cut problm. This problm has many motivations, on of which coms

More information

Chapter 6 Folding. Folding

Chapter 6 Folding. Folding Chaptr 6 Folding Wintr 1 Mokhtar Abolaz Folding Th folding transformation is usd to systmatically dtrmin th control circuits in DSP architctur whr multipl algorithm oprations ar tim-multiplxd to a singl

More information

Calculus concepts derivatives

Calculus concepts derivatives All rasonabl fforts hav bn mad to mak sur th nots ar accurat. Th author cannot b hld rsponsibl for any damags arising from th us of ths nots in any fashion. Calculus concpts drivativs Concpts involving

More information

Math 34A. Final Review

Math 34A. Final Review Math A Final Rviw 1) Us th graph of y10 to find approimat valus: a) 50 0. b) y (0.65) solution for part a) first writ an quation: 50 0. now tak th logarithm of both sids: log() log(50 0. ) pand th right

More information

Addition of angular momentum

Addition of angular momentum Addition of angular momntum April, 07 Oftn w nd to combin diffrnt sourcs of angular momntum to charactriz th total angular momntum of a systm, or to divid th total angular momntum into parts to valuat

More information

4. Money cannot be neutral in the short-run the neutrality of money is exclusively a medium run phenomenon.

4. Money cannot be neutral in the short-run the neutrality of money is exclusively a medium run phenomenon. PART I TRUE/FALSE/UNCERTAIN (5 points ach) 1. Lik xpansionary montary policy, xpansionary fiscal policy rturns output in th mdium run to its natural lvl, and incrass prics. Thrfor, fiscal policy is also

More information

(1) Then we could wave our hands over this and it would become:

(1) Then we could wave our hands over this and it would become: MAT* K285 Spring 28 Anthony Bnoit 4/17/28 Wk 12: Laplac Tranform Rading: Kohlr & Johnon, Chaptr 5 to p. 35 HW: 5.1: 3, 7, 1*, 19 5.2: 1, 5*, 13*, 19, 45* 5.3: 1, 11*, 19 * Pla writ-up th problm natly and

More information

GEOMETRICAL PHENOMENA IN THE PHYSICS OF SUBATOMIC PARTICLES. Eduard N. Klenov* Rostov-on-Don, Russia

GEOMETRICAL PHENOMENA IN THE PHYSICS OF SUBATOMIC PARTICLES. Eduard N. Klenov* Rostov-on-Don, Russia GEOMETRICAL PHENOMENA IN THE PHYSICS OF SUBATOMIC PARTICLES Eduard N. Klnov* Rostov-on-Don, Russia Th articl considrs phnomnal gomtry figurs bing th carrirs of valu spctra for th pairs of th rmaining additiv

More information

Problem Set 6 Solutions

Problem Set 6 Solutions 6.04/18.06J Mathmatics for Computr Scinc March 15, 005 Srini Dvadas and Eric Lhman Problm St 6 Solutions Du: Monday, March 8 at 9 PM in Room 3-044 Problm 1. Sammy th Shark is a financial srvic providr

More information

SCIENCE Student Book. 3rd Grade Unit 7

SCIENCE Student Book. 3rd Grade Unit 7 SCIENCE Student Book 3rd Grade Unit 7 Unit 7 TIMES AND SEASONS SCIENCE 307 TIMES AND SEASONS Introduction 3 1. How the Earth Moves...5 The Earth Rotates 7 Day and Night 14 The Earth Revolves 18 Self Test

More information

4 x 4, and. where x is Town Square

4 x 4, and. where x is Town Square Accumulation and Population Dnsity E. A city locatd along a straight highway has a population whos dnsity can b approimatd by th function p 5 4 th distanc from th town squar, masurd in mils, whr 4 4, and

More information

A Propagating Wave Packet Group Velocity Dispersion

A Propagating Wave Packet Group Velocity Dispersion Lctur 8 Phys 375 A Propagating Wav Packt Group Vlocity Disprsion Ovrviw and Motivation: In th last lctur w lookd at a localizd solution t) to th 1D fr-particl Schrödingr quation (SE) that corrsponds to

More information

MEMORIAL UNIVERSITY OF NEWFOUNDLAND

MEMORIAL UNIVERSITY OF NEWFOUNDLAND MEMORIAL UNIVERSITY OF NEWFOUNDLAND DEPARTMENT OF MATHEMATICS AND STATISTICS Midtrm Examination Statistics 2500 001 Wintr 2003 Nam: Studnt No: St by Dr. H. Wang OFFICE USE ONLY Mark: Instructions: 1. Plas

More information

Brief Introduction to Statistical Mechanics

Brief Introduction to Statistical Mechanics Brif Introduction to Statistical Mchanics. Purpos: Ths nots ar intndd to provid a vry quick introduction to Statistical Mchanics. Th fild is of cours far mor vast than could b containd in ths fw pags.

More information

PHA 5127 Answers Homework 2 Fall 2001

PHA 5127 Answers Homework 2 Fall 2001 PH 5127 nswrs Homwork 2 Fall 2001 OK, bfor you rad th answrs, many of you spnt a lot of tim on this homwork. Plas, nxt tim if you hav qustions plas com talk/ask us. Thr is no nd to suffr (wll a littl suffring

More information

What are those βs anyway? Understanding Design Matrix & Odds ratios

What are those βs anyway? Understanding Design Matrix & Odds ratios Ral paramtr stimat WILD 750 - Wildlif Population Analysis of 6 What ar thos βs anyway? Undrsting Dsign Matrix & Odds ratios Rfrncs Hosmr D.W.. Lmshow. 000. Applid logistic rgrssion. John Wily & ons Inc.

More information

EEO 401 Digital Signal Processing Prof. Mark Fowler

EEO 401 Digital Signal Processing Prof. Mark Fowler EEO 401 Digital Signal Procssing Prof. Mark Fowlr Dtails of th ot St #19 Rading Assignmnt: Sct. 7.1.2, 7.1.3, & 7.2 of Proakis & Manolakis Dfinition of th So Givn signal data points x[n] for n = 0,, -1

More information

Principles of Humidity Dalton s law

Principles of Humidity Dalton s law Principls of Humidity Dalton s law Air is a mixtur of diffrnt gass. Th main gas componnts ar: Gas componnt volum [%] wight [%] Nitrogn N 2 78,03 75,47 Oxygn O 2 20,99 23,20 Argon Ar 0,93 1,28 Carbon dioxid

More information

Gradebook & Midterm & Office Hours

Gradebook & Midterm & Office Hours Your commnts So what do w do whn on of th r's is 0 in th quation GmM(1/r-1/r)? Do w nd to driv all of ths potntial nrgy formulas? I don't undrstand springs This was th first lctur I actually larnd somthing

More information

CS 361 Meeting 12 10/3/18

CS 361 Meeting 12 10/3/18 CS 36 Mting 2 /3/8 Announcmnts. Homwork 4 is du Friday. If Friday is Mountain Day, homwork should b turnd in at my offic or th dpartmnt offic bfor 4. 2. Homwork 5 will b availabl ovr th wknd. 3. Our midtrm

More information

Propositional Logic. Combinatorial Problem Solving (CPS) Albert Oliveras Enric Rodríguez-Carbonell. May 17, 2018

Propositional Logic. Combinatorial Problem Solving (CPS) Albert Oliveras Enric Rodríguez-Carbonell. May 17, 2018 Propositional Logic Combinatorial Problm Solving (CPS) Albrt Olivras Enric Rodríguz-Carbonll May 17, 2018 Ovrviw of th sssion Dfinition of Propositional Logic Gnral Concpts in Logic Rduction to SAT CNFs

More information

Mor Tutorial at www.dumblittldoctor.com Work th problms without a calculator, but us a calculator to chck rsults. And try diffrntiating your answrs in part III as a usful chck. I. Applications of Intgration

More information

The van der Waals interaction 1 D. E. Soper 2 University of Oregon 20 April 2012

The van der Waals interaction 1 D. E. Soper 2 University of Oregon 20 April 2012 Th van dr Waals intraction D. E. Sopr 2 Univrsity of Orgon 20 pril 202 Th van dr Waals intraction is discussd in Chaptr 5 of J. J. Sakurai, Modrn Quantum Mchanics. Hr I tak a look at it in a littl mor

More information

Partial Derivatives: Suppose that z = f(x, y) is a function of two variables.

Partial Derivatives: Suppose that z = f(x, y) is a function of two variables. Chaptr Functions o Two Variabls Applid Calculus 61 Sction : Calculus o Functions o Two Variabls Now that ou hav som amiliarit with unctions o two variabls it s tim to start appling calculus to hlp us solv

More information

That is, we start with a general matrix: And end with a simpler matrix:

That is, we start with a general matrix: And end with a simpler matrix: DIAGON ALIZATION OF THE STR ESS TEN SOR INTRO DUCTIO N By th us of Cauchy s thorm w ar abl to rduc th numbr of strss componnts in th strss tnsor to only nin valus. An additional simplification of th strss

More information

1 Isoparametric Concept

1 Isoparametric Concept UNIVERSITY OF CALIFORNIA BERKELEY Dpartmnt of Civil Enginring Spring 06 Structural Enginring, Mchanics and Matrials Profssor: S. Govindj Nots on D isoparamtric lmnts Isoparamtric Concpt Th isoparamtric

More information

1. In the given figure PQRS is a parallelogram. Find the coordinates of R.

1. In the given figure PQRS is a parallelogram. Find the coordinates of R. Tst Assss Achiv Class : 9 CLASS : 9 Mathmatics 1. In th givn figur PQRS is a paralllogram. Find th coordinats of R. Y S(2, 3) R O P(1, 0) Q(5, 0) X (5, 2) (5, 3) (6, 2) (6, 3) 2. Th prpndicular distanc

More information

Chapter 8: Electron Configurations and Periodicity

Chapter 8: Electron Configurations and Periodicity Elctron Spin & th Pauli Exclusion Principl Chaptr 8: Elctron Configurations and Priodicity 3 quantum numbrs (n, l, ml) dfin th nrgy, siz, shap, and spatial orintation of ach atomic orbital. To xplain how

More information

10. Limits involving infinity

10. Limits involving infinity . Limits involving infinity It is known from th it ruls for fundamntal arithmtic oprations (+,-,, ) that if two functions hav finit its at a (finit or infinit) point, that is, thy ar convrgnt, th it of

More information

INTEGRATION BY PARTS

INTEGRATION BY PARTS Mathmatics Rvision Guids Intgration by Parts Pag of 7 MK HOME TUITION Mathmatics Rvision Guids Lvl: AS / A Lvl AQA : C Edcl: C OCR: C OCR MEI: C INTEGRATION BY PARTS Vrsion : Dat: --5 Eampls - 6 ar copyrightd

More information

Unit 6: Solving Exponential Equations and More

Unit 6: Solving Exponential Equations and More Habrman MTH 111 Sction II: Eonntial and Logarithmic Functions Unit 6: Solving Eonntial Equations and Mor EXAMPLE: Solv th quation 10 100 for. Obtain an act solution. This quation is so asy to solv that

More information

CS 6353 Compiler Construction, Homework #1. 1. Write regular expressions for the following informally described languages:

CS 6353 Compiler Construction, Homework #1. 1. Write regular expressions for the following informally described languages: CS 6353 Compilr Construction, Homwork #1 1. Writ rgular xprssions for th following informally dscribd languags: a. All strings of 0 s and 1 s with th substring 01*1. Answr: (0 1)*01*1(0 1)* b. All strings

More information

Chapter 3 Exponential and Logarithmic Functions. Section a. In the exponential decay model A. Check Point Exercises

Chapter 3 Exponential and Logarithmic Functions. Section a. In the exponential decay model A. Check Point Exercises Chaptr Eponntial and Logarithmic Functions Sction. Chck Point Erciss. a. A 87. Sinc is yars aftr, whn t, A. b. A A 87 k() k 87 k 87 k 87 87 k.4 Thus, th growth function is A 87 87.4t.4t.4t A 87..4t 87.4t

More information

REGISTER!!! The Farmer and the Seeds (a parable of scientific reasoning) Class Updates. The Farmer and the Seeds. The Farmer and the Seeds

REGISTER!!! The Farmer and the Seeds (a parable of scientific reasoning) Class Updates. The Farmer and the Seeds. The Farmer and the Seeds How dos light intract with mattr? And what dos (this say about) mattr? REGISTER!!! If Schrödingr s Cat walks into a forst, and no on is around to obsrv it, is h rally in th forst? sourc unknown Phys 1010

More information

Probability Translation Guide

Probability Translation Guide Quick Guid to Translation for th inbuilt SWARM Calculator If you s information looking lik this: Us this statmnt or any variant* (not th backticks) And this is what you ll s whn you prss Calculat Th chancs

More information

Addition of angular momentum

Addition of angular momentum Addition of angular momntum April, 0 Oftn w nd to combin diffrnt sourcs of angular momntum to charactriz th total angular momntum of a systm, or to divid th total angular momntum into parts to valuat th

More information

Background: We have discussed the PIB, HO, and the energy of the RR model. In this chapter, the H-atom, and atomic orbitals.

Background: We have discussed the PIB, HO, and the energy of the RR model. In this chapter, the H-atom, and atomic orbitals. Chaptr 7 Th Hydrogn Atom Background: W hav discussd th PIB HO and th nrgy of th RR modl. In this chaptr th H-atom and atomic orbitals. * A singl particl moving undr a cntral forc adoptd from Scott Kirby

More information

COMPUTER GENERATED HOLOGRAMS Optical Sciences 627 W.J. Dallas (Monday, April 04, 2005, 8:35 AM) PART I: CHAPTER TWO COMB MATH.

COMPUTER GENERATED HOLOGRAMS Optical Sciences 627 W.J. Dallas (Monday, April 04, 2005, 8:35 AM) PART I: CHAPTER TWO COMB MATH. C:\Dallas\0_Courss\03A_OpSci_67\0 Cgh_Book\0_athmaticalPrliminaris\0_0 Combath.doc of 8 COPUTER GENERATED HOLOGRAS Optical Scincs 67 W.J. Dallas (onday, April 04, 005, 8:35 A) PART I: CHAPTER TWO COB ATH

More information

Chemical Physics II. More Stat. Thermo Kinetics Protein Folding...

Chemical Physics II. More Stat. Thermo Kinetics Protein Folding... Chmical Physics II Mor Stat. Thrmo Kintics Protin Folding... http://www.nmc.ctc.com/imags/projct/proj15thumb.jpg http://nuclarwaponarchiv.org/usa/tsts/ukgrabl2.jpg http://www.photolib.noaa.gov/corps/imags/big/corp1417.jpg

More information

cycle that does not cross any edges (including its own), then it has at least

cycle that does not cross any edges (including its own), then it has at least W prov th following thorm: Thorm If a K n is drawn in th plan in such a way that it has a hamiltonian cycl that dos not cross any dgs (including its own, thn it has at last n ( 4 48 π + O(n crossings Th

More information

Estimation of apparent fraction defective: A mathematical approach

Estimation of apparent fraction defective: A mathematical approach Availabl onlin at www.plagiarsarchlibrary.com Plagia Rsarch Library Advancs in Applid Scinc Rsarch, 011, (): 84-89 ISSN: 0976-8610 CODEN (USA): AASRFC Estimation of apparnt fraction dfctiv: A mathmatical

More information

Ch. 24 Molecular Reaction Dynamics 1. Collision Theory

Ch. 24 Molecular Reaction Dynamics 1. Collision Theory Ch. 4 Molcular Raction Dynamics 1. Collision Thory Lctur 16. Diffusion-Controlld Raction 3. Th Matrial Balanc Equation 4. Transition Stat Thory: Th Eyring Equation 5. Transition Stat Thory: Thrmodynamic

More information

Aim To manage files and directories using Linux commands. 1. file Examines the type of the given file or directory

Aim To manage files and directories using Linux commands. 1. file Examines the type of the given file or directory m E x. N o. 3 F I L E M A N A G E M E N T Aim To manag ils and dirctoris using Linux commands. I. F i l M a n a g m n t 1. il Examins th typ o th givn il or dirctory i l i l n a m > ( o r ) < d i r c t

More information

Fourier Transforms and the Wave Equation. Key Mathematics: More Fourier transform theory, especially as applied to solving the wave equation.

Fourier Transforms and the Wave Equation. Key Mathematics: More Fourier transform theory, especially as applied to solving the wave equation. Lur 7 Fourir Transforms and th Wav Euation Ovrviw and Motivation: W first discuss a fw faturs of th Fourir transform (FT), and thn w solv th initial-valu problm for th wav uation using th Fourir transform

More information

Math-3. Lesson 5-6 Euler s Number e Logarithmic and Exponential Modeling (Newton s Law of Cooling)

Math-3. Lesson 5-6 Euler s Number e Logarithmic and Exponential Modeling (Newton s Law of Cooling) Math-3 Lsson 5-6 Eulr s Numbr Logarithmic and Eponntial Modling (Nwton s Law of Cooling) f ( ) What is th numbr? is th horizontal asymptot of th function: 1 1 ~ 2.718... On my 3rd submarin (USS Springfild,

More information

Sundials and Linear Algebra

Sundials and Linear Algebra Sundials and Linar Algbra M. Scot Swan July 2, 25 Most txts on crating sundials ar dirctd towards thos who ar solly intrstd in making and using sundials and usually assums minimal mathmatical background.

More information

Homework #3. 1 x. dx. It therefore follows that a sum of the

Homework #3. 1 x. dx. It therefore follows that a sum of the Danil Cannon CS 62 / Luan March 5, 2009 Homwork # 1. Th natural logarithm is dfind by ln n = n 1 dx. It thrfor follows that a sum of th 1 x sam addnd ovr th sam intrval should b both asymptotically uppr-

More information

COHORT MBA. Exponential function. MATH review (part2) by Lucian Mitroiu. The LOG and EXP functions. Properties: e e. lim.

COHORT MBA. Exponential function. MATH review (part2) by Lucian Mitroiu. The LOG and EXP functions. Properties: e e. lim. MTH rviw part b Lucian Mitroiu Th LOG and EXP functions Th ponntial function p : R, dfind as Proprtis: lim > lim p Eponntial function Y 8 6 - -8-6 - - X Th natural logarithm function ln in US- log: function

More information

Dealing with quantitative data and problem solving life is a story problem! Attacking Quantitative Problems

Dealing with quantitative data and problem solving life is a story problem! Attacking Quantitative Problems Daling with quantitati data and problm soling lif is a story problm! A larg portion of scinc inols quantitati data that has both alu and units. Units can sa your butt! Nd handl on mtric prfixs Dimnsional

More information

0 +1e Radionuclides - can spontaneously emit particles and radiation which can be expressed by a nuclear equation.

0 +1e Radionuclides - can spontaneously emit particles and radiation which can be expressed by a nuclear equation. Radioactivity Radionuclids - can spontanously mit particls and radiation which can b xprssd by a nuclar quation. Spontanous Emission: Mass and charg ar consrvd. 4 2α -β Alpha mission Bta mission 238 92U

More information

Note If the candidate believes that e x = 0 solves to x = 0 or gives an extra solution of x = 0, then withhold the final accuracy mark.

Note If the candidate believes that e x = 0 solves to x = 0 or gives an extra solution of x = 0, then withhold the final accuracy mark. . (a) Eithr y = or ( 0, ) (b) Whn =, y = ( 0 + ) = 0 = 0 ( + ) = 0 ( )( ) = 0 Eithr = (for possibly abov) or = A 3. Not If th candidat blivs that = 0 solvs to = 0 or givs an tra solution of = 0, thn withhold

More information

y = 2xe x + x 2 e x at (0, 3). solution: Since y is implicitly related to x we have to use implicit differentiation: 3 6y = 0 y = 1 2 x ln(b) ln(b)

y = 2xe x + x 2 e x at (0, 3). solution: Since y is implicitly related to x we have to use implicit differentiation: 3 6y = 0 y = 1 2 x ln(b) ln(b) 4. y = y = + 5. Find th quation of th tangnt lin for th function y = ( + ) 3 whn = 0. solution: First not that whn = 0, y = (1 + 1) 3 = 8, so th lin gos through (0, 8) and thrfor its y-intrcpt is 8. y

More information

Seebeck and Peltier Effects

Seebeck and Peltier Effects Sbck and Pltir Effcts Introduction Thrmal nrgy is usually a byproduct of othr forms of nrgy such as chmical nrgy, mchanical nrgy, and lctrical nrgy. Th procss in which lctrical nrgy is transformd into

More information

HISTORY & GEOGRAPHY STUDENT BOOK

HISTORY & GEOGRAPHY STUDENT BOOK HISTORY & GEOGRAPHY STUDENT BOOK 3rd Grad Unit 9 Unit 9 PACIFIC STATES HISTORY & GEOGRAPHY 309 PACIFIC STATES Introduction 3 1. Pacific Gography...5 Stats in th Pacific Rgion 6 Gographical Faturs 8 Wathr

More information

Construction of asymmetric orthogonal arrays of strength three via a replacement method

Construction of asymmetric orthogonal arrays of strength three via a replacement method isid/ms/26/2 Fbruary, 26 http://www.isid.ac.in/ statmath/indx.php?modul=prprint Construction of asymmtric orthogonal arrays of strngth thr via a rplacmnt mthod Tian-fang Zhang, Qiaoling Dng and Alok Dy

More information

(Upside-Down o Direct Rotation) β - Numbers

(Upside-Down o Direct Rotation) β - Numbers Amrican Journal of Mathmatics and Statistics 014, 4(): 58-64 DOI: 10593/jajms0140400 (Upsid-Down o Dirct Rotation) β - Numbrs Ammar Sddiq Mahmood 1, Shukriyah Sabir Ali,* 1 Dpartmnt of Mathmatics, Collg

More information

EXST Regression Techniques Page 1

EXST Regression Techniques Page 1 EXST704 - Rgrssion Tchniqus Pag 1 Masurmnt rrors in X W hav assumd that all variation is in Y. Masurmnt rror in this variabl will not ffct th rsults, as long as thy ar uncorrlatd and unbiasd, sinc thy

More information

Quasi-Classical States of the Simple Harmonic Oscillator

Quasi-Classical States of the Simple Harmonic Oscillator Quasi-Classical Stats of th Simpl Harmonic Oscillator (Draft Vrsion) Introduction: Why Look for Eignstats of th Annihilation Oprator? Excpt for th ground stat, th corrspondnc btwn th quantum nrgy ignstats

More information

The following information relates to Questions 1 to 4:

The following information relates to Questions 1 to 4: Th following information rlats to Qustions 1 to 4: QUESTIN 1 Th lctrolyt usd in this ful cll is D watr carbonat ions hydrogn ions hydroxid ions QUESTIN 2 Th product formd in th ful cll is D hydrogn gas

More information

Chapter 13 GMM for Linear Factor Models in Discount Factor form. GMM on the pricing errors gives a crosssectional

Chapter 13 GMM for Linear Factor Models in Discount Factor form. GMM on the pricing errors gives a crosssectional Chaptr 13 GMM for Linar Factor Modls in Discount Factor form GMM on th pricing rrors givs a crosssctional rgrssion h cas of xcss rturns Hors rac sting for charactristic sting for pricd factors: lambdas

More information

Molecules and Covalent Bond

Molecules and Covalent Bond Molculs and ovalnt ond Qustion Papr 1 Lvl IGSE Subjct hmistry (0620/0971) Exam oard ambridg Intrnational Examinations (IE) Topic toms, lmnts and compounds Sub-Topic Molculs and covalnt bonds ooklt Qustion

More information

Davisson Germer experiment

Davisson Germer experiment Announcmnts: Davisson Grmr xprimnt Homwork st 5 is today. Homwork st 6 will b postd latr today. Mad a good guss about th Nobl Priz for 2013 Clinton Davisson and Lstr Grmr. Davisson won Nobl Priz in 1937.

More information

4037 ADDITIONAL MATHEMATICS

4037 ADDITIONAL MATHEMATICS CAMBRIDGE INTERNATIONAL EXAMINATIONS GCE Ordinary Lvl MARK SCHEME for th Octobr/Novmbr 0 sris 40 ADDITIONAL MATHEMATICS 40/ Papr, maimum raw mark 80 This mark schm is publishd as an aid to tachrs and candidats,

More information

Sec 2.3 Modeling with First Order Equations

Sec 2.3 Modeling with First Order Equations Sc.3 Modling with First Ordr Equations Mathmatical modls charactriz physical systms, oftn using diffrntial quations. Modl Construction: Translating physical situation into mathmatical trms. Clarly stat

More information

In the table below, write the coordinates of each point in the figure. Point x-coordinate y-coordinate A 0 3 B 3 3 C 3 5 D 3 8 E 5 5 F 6 3 G 3 1

In the table below, write the coordinates of each point in the figure. Point x-coordinate y-coordinate A 0 3 B 3 3 C 3 5 D 3 8 E 5 5 F 6 3 G 3 1 1 TASK 1.1.1: PATTY PAPER TRANSFORMATIONS Solutions 10 D C E A B F G -5 5 10 - - In th tabl blow, writ th s of ach pot th figur. x- y- A 0 3 B 3 3 C 3 5 D 3 E 5 5 F 3 G 3 1 1. On patty papr, trac th figur

More information

are given in the table below. t (hours)

are given in the table below. t (hours) CALCULUS WORKSHEET ON INTEGRATION WITH DATA Work th following on notbook papr. Giv dcimal answrs corrct to thr dcimal placs.. A tank contains gallons of oil at tim t = hours. Oil is bing pumpd into th

More information

Electrochemistry L E O

Electrochemistry L E O Rmmbr from CHM151 A rdox raction in on in which lctrons ar transfrrd lctrochmistry L O Rduction os lctrons xidation G R ain lctrons duction W can dtrmin which lmnt is oxidizd or rducd by assigning oxidation

More information

Function Spaces. a x 3. (Letting x = 1 =)) a(0) + b + c (1) = 0. Row reducing the matrix. b 1. e 4 3. e 9. >: (x = 1 =)) a(0) + b + c (1) = 0

Function Spaces. a x 3. (Letting x = 1 =)) a(0) + b + c (1) = 0. Row reducing the matrix. b 1. e 4 3. e 9. >: (x = 1 =)) a(0) + b + c (1) = 0 unction Spacs Prrquisit: Sction 4.7, Coordinatization n this sction, w apply th tchniqus of Chaptr 4 to vctor spacs whos lmnts ar functions. Th vctor spacs P n and P ar familiar xampls of such spacs. Othr

More information

orbiting electron turns out to be wrong even though it Unfortunately, the classical visualization of the

orbiting electron turns out to be wrong even though it Unfortunately, the classical visualization of the Lctur 22-1 Byond Bohr Modl Unfortunatly, th classical visualization of th orbiting lctron turns out to b wrong vn though it still givs us a simpl way to think of th atom. Quantum Mchanics is ndd to truly

More information

Problem Statement. Definitions, Equations and Helpful Hints BEAUTIFUL HOMEWORK 6 ENGR 323 PROBLEM 3-79 WOOLSEY

Problem Statement. Definitions, Equations and Helpful Hints BEAUTIFUL HOMEWORK 6 ENGR 323 PROBLEM 3-79 WOOLSEY Problm Statmnt Suppos small arriv at a crtain airport according to Poisson procss with rat α pr hour, so that th numbr of arrivals during a tim priod of t hours is a Poisson rv with paramtr t (a) What

More information

Strongly Connected Components

Strongly Connected Components Strongly Connctd Componnts Lt G = (V, E) b a dirctd graph Writ if thr is a path from to in G Writ if and is an quivalnc rlation: implis and implis s quivalnc classs ar calld th strongly connctd componnts

More information

A. Limits and Horizontal Asymptotes ( ) f x f x. f x. x "±# ( ).

A. Limits and Horizontal Asymptotes ( ) f x f x. f x. x ±# ( ). A. Limits and Horizontal Asymptots What you ar finding: You can b askd to find lim x "a H.A.) problm is asking you find lim x "# and lim x "$#. or lim x "±#. Typically, a horizontal asymptot algbraically,

More information

The Death of Stars - I.

The Death of Stars - I. Th Dath of Stars - I. Larning Objctivs! B abl to sktch th H-R diagram and includ stars by siz, sctral ty, liftim, color, mass, magnitud, tmratur and luminosity, rlativ to our Sun! Comar Rd Dwarfs to our

More information