Lesson 8.1 Areas of Rectangles and Parallelograms

Size: px
Start display at page:

Download "Lesson 8.1 Areas of Rectangles and Parallelograms"

Transcription

1 Leon 8.1 e of Rectngle nd Pllelogm 1. Find the e of the hded egion.. Find the e of the hded egion. 17 cm 9 cm 5 cm 8 cm 1.5 cm 13 cm cm cm 3. Rectngle D h e 684 m nd width 44 m. Find it length. 4. Find. 5. The ectngle nd the que hve equl e. The ectngle i 1 ft b 1 ft 4 in. 15 cm Wht i the peimete of the entie hegon in feet? 6 cm 39 cm 6. Dw pllelogm with e 85 cm nd n ngle with meue 40. I ou pllelogm unique? If not, dw diffeent one. 7. Find the e of PQRS. 8. Find the e of DEF. S( 4, 5) P( 4, 3) R(7, 1) (4, ) F (15, 7)E (, ) D(1, 7) Q(7, 9) (4, 5) (, 5) 9. n ce i equl to 43,560 ft. 4-ce ectngul ptue h 50-foot ide tht i 40 feet fom the neet od. To the neet foot, wht i the ditnce fom the od to the f fence?. ection of lnd i que piece of lnd 1 mile on ide. How mn ce e in ection? (1 mile 580 feet) 11. Dn bu piece of cpet tht meue 0 que d. Will he be ble to completel cove ectngul floo tht meue 1 ft 6 in. b 16 ft 6 in.? Eplin wh o wh not. Dicoveing Geomet Pctice You Skill HPTER 8 49

2 Leon 8. e of Tingle, Tpezoid, nd Kite 1. Find the e of the hded egion.. D i pllelogm, DE i kite, 1 cm D 18 cm, nd E cm. Find the e of DE. 0 cm D 3. e 16 in.. b cm, 8 cm, nd cm. Find D. b 16 in. 9 in. 5. concve kite (dt) h digonl meuing 13 cm nd 19 cm. Wht i it e? 6. The hded e i wht fction of the 7. Eplin wh the e of thi tingle lge pllelogm? cnnot be gete thn 7. E D midegment of tingle divide the tingle into tingle nd tpezoid. If the oiginl tingle h e 64 in., wht i the e of the tpezoid? 9. TP i tngent to cicle M nd N. TP 16 cm. The diu of N i 7 cm nd the diu of M i. Find the e of NMPT. T P N M. Find the e of TRI. 11. Find the e of HEXGN. I (1, 1) E (4, 6) X (7, 4) (0, 6) R ( 1, 3) H T (6, 0) (0, 1) N G (3, ) (7, ) 50 HPTER 8 Dicoveing Geomet Pctice You Skill

3 Leon 8.3 e Poblem 1. bundle of hdwood flooing contin 14 1 ft nd cot $ How much will it cot to bu flooing fo the kitchen nd fmil oom? You hould bu 5% et to ccount fo wte.. Fo Wold Pece D celebtion the tudent t bot Junio/Senio High School e mking 6-m-b-8-m flg. Ech of the i gde will cete motif to hono the people of the i inhbited continent. Sketch thee poible w to divide the flg: one into i conguent tingle; one into i tingle with equl e but none conguent; nd one into i conguent tpezoid. Give meuement o mking on ou ketche o ech cl know it h equl e. 3. Olive h evolutionized the pizz indut b intoducing que pizz. She need to chge $8.40 to ecove he cot on 1-inch (on ide) pizz. She then dd 5% nd ound up to the net multiple of qute. With thi picing cheme, wht hould Olive chge fo 16-inch pizz? 3 ft 13 ft 7 ft 3 ft 4 ft 18 ft Tile 18 ft Fieplce nd heth 4 ft Kitchen Fmil oom 6 ft 14 ft 4. et igtime ke h bked the wold lget chocolte cke. It i 600 cm b 400 cm b 180 cm high. et wnt to ppl foting to the fou ide nd the top. How mn lite of foting doe he need if 1 lite of foting cove bout 100 cm? 5. Jeome i mking mll metl kite pin to ell t the chool fi. Ech kite h n e of nd one digonl of 8 cm, which i divided b the othe digonl into cm nd 6 cm pt. The heet metl come in 7-cm-b-4-cm ectngle. How mn kite pin cn Jeome cut fom one heet? Wht pecentge of wte doe he hve? Dw cutting ptten Jeome could ue. 6. Kit nd Kt e building kite fo the big kite fetivl. Kit h led cut hi tick fo the digonl. He wnt to poition P o tht he will hve mimum kite e. He k Kt fo dvice. Wht hould Kt tell him? P Dicoveing Geomet Pctice You Skill HPTER 8 51

4 Leon 8.4 e of Regul Polgon In Eecie 1 3, the polgon e egul cm nd. 4. cm nd 3. 6 cm nd 14.5 cm. 197 cm cm. p 1-gon 4. In egul n-gon, 4.8 cm, 7., nd cm. Find n. 5. egul hegon with ide 8 cm h n e of ppoimtel 166 cm. Wht e the dimete of the incibed nd the cicumcibed cicle? In Eecie 6 8, dw ech egul polgon o tht it h peimete 0 cm. Ue the Regul Polgon e onjectue nd centimete ule to find the ppoimte e of ech polgon. 6. Pentgon 7. Octgon 8. Decgon 9. Ue comp nd tightedge to contuct egul octgon nd it pothem. Ue centimete ule to meue it ide length nd pothem nd the Regul Polgon e onjectue to find it ppoimte e.. Find the e of the hded egion between the que nd the egul octgon. 5 cm. 3 cm. 11. op the 3.6 /3 6 teelltion below howing the polgon ound ech tpe of vete. egul hegon with 3 cm h.60 cm. n equiltel tingle with 3 cm h 0.87 cm. If ech ide in thi teelltion i 3 cm, find the ppoimte e of ech dul polgon. 5 HPTER 8 Dicoveing Geomet Pctice You Skill

5 Leon 8.5 e of icle In Eecie 1 3, leve ou nwe in tem of. 1. If d 6.,.. If 59 cm,. 3. If 36 cm,. In Eecie 4 11, ound ou nwe to the neet 0.01 unit. 4. If 7.8 cm,. 5. If ,. 6. If d 3.1,. Fo Eecie 7 nd 8, efe to the figue of cicle incibed in n equiltel tingle. 7. Find the e of the 8. Find the e of the incibed cicle. hded egion nd 1 e tngent line. D i que. Find the e of the hded egion. 1 (, 7) D (6, 1). hoe i tetheed on 0 ft ope. If the ope i lengthened to 5 ft, b wht pecentge doe the hoe gzing e incee? 11. The thee cicle e tngent. Find the e of the hded egion. 5 cm 1. unning tck i hped like ectngle with emicicle on ech of the hote ide. The ditnce ound the tck i 1 mile (580 ft). The tightw i twice long the width of the field. Wht i the e of the field encloed b the tck to the neet que foot? Width Stightw Field Dicoveing Geomet Pctice You Skill HPTER 8 53

6 Leon 8.6 n W You Slice It In Eecie 1 6, find the e of the hded egion. Round ou nwe to the neet 0.01 cm cm 3 cm cm, 6 cm, 6. nd 3 9 cm. 8 cm 1 cm cm Shded e i 0 cm. 8. Shded e i 1. Find 9. Shded e i 15 cm. Find. to the neet 0.01 cm. Find OT to the neet 0.01 cm. 144 S T Q O. Rul dog, Spot, i tied with 0 ft ope to the cente of the bck wll of the hed. See the digm below. Ove wht e cn Spot pl, to the neet que foot? U Shed 1 ft 0 ft 54 HPTER 8 Dicoveing Geomet Pctice You Skill

7 Leon 8.7 Sufce e In Eecie 1 7, find the ufce e of ech olid. ll qudiltel e ectngle, nd ll meuement e in centimete. Round ou nwe to the neet 0.1 cm. 1.. e i egul hegon. 3. 6, 5., nd l l oth be e que que hole in ound peg In ode to clculte the het lo of thi etunt, Kevin need to find the e of the ufce tht i epoed to the i. i emicicle. ll meuement e in feet. Round ou nwe to the neet 0.1 ft Il i building mueum dipl ce. The ide nd bottom will be plwood nd the top will be gl. Plwood come in 4-ft-b-8-ft heet. How mn heet of plwood will he need to bu? Eplin. Sketch cutting ptten tht will leve he with the lget ingle piece poible. 1_ ft 3 ft 3 ft 1 1_ ft ft Dicoveing Geomet Pctice You Skill HPTER 8 55

G.GMD.1 STUDENT NOTES WS #5 1 REGULAR POLYGONS

G.GMD.1 STUDENT NOTES WS #5 1 REGULAR POLYGONS G.GMD.1 STUDENT NOTES WS #5 1 REGULAR POLYGONS Regul polygon e of inteet to u becue we begin looking t the volume of hexgonl pim o Tethedl nd to do thee type of clcultion we need to be ble to olve fit

More information

Intro to Circle Geometry By Raymond Cheong

Intro to Circle Geometry By Raymond Cheong Into to Cicle Geomety By Rymond Cheong Mny poblems involving cicles cn be solved by constucting ight tingles then using the Pythgoen Theoem. The min chllenge is identifying whee to constuct the ight tingle.

More information

r (1+cos(θ)) sin(θ) C θ 2 r cos θ 2

r (1+cos(θ)) sin(θ) C θ 2 r cos θ 2 icles xmple 66: Rounding one ssume we hve cone of ngle θ, nd we ound it off with cuve of dius, how f wy fom the cone does the ound stt? nd wht is the chod length? (1+cos(θ)) sin(θ) θ 2 cos θ 2 xmple 67:

More information

(Ch. 22.5) 2. What is the magnitude (in pc) of a point charge whose electric field 50 cm away has a magnitude of 2V/m?

(Ch. 22.5) 2. What is the magnitude (in pc) of a point charge whose electric field 50 cm away has a magnitude of 2V/m? Em I Solutions PHY049 Summe 0 (Ch..5). Two smll, positively chged sphees hve combined chge of 50 μc. If ech sphee is epelled fom the othe by n electosttic foce of N when the sphees e.0 m pt, wht is the

More information

Maths Word Searches. List of Contents. Word Search 1. Word Search 2. Word Search 3. Word Search 4. Word Search 5. Word Search 6.

Maths Word Searches. List of Contents. Word Search 1. Word Search 2. Word Search 3. Word Search 4. Word Search 5. Word Search 6. Maths Word earches List of Contents Word earch 1 Word earch 2 Word earch 3 Word earch 4 Word earch 5 Word earch 6 Word earch 7 Word earch 8 Maths Word earch 1 The Word List at the bottom (from CE to TWO)

More information

AP Physics Gravity and Circular Motion

AP Physics Gravity and Circular Motion AP Phyic Gity nd icul Motion Newton theoy i ey iple. Gity i foce of ttction between ny two object tht he. Two object itting on dektop ttct ech othe with foce tht we cll gity. They don t go flying togethe

More information

4.4 VOLUME AND SURFACE AREA

4.4 VOLUME AND SURFACE AREA 160 CHAPTER 4 Geomety 4.4 VOLUME AND SURFACE AREA Textbook Refeence Section 8.4 CLAST OBJECTIVES Calculate volume and uface aea Infe fomula fo meauing geometic figue Select applicable fomula fo computing

More information

Orbits and Kepler s Laws

Orbits and Kepler s Laws Obits nd Keple s Lws This web pge intoduces some of the bsic ides of obitl dynmics. It stts by descibing the bsic foce due to gvity, then consides the ntue nd shpe of obits. The next section consides how

More information

N V V L. R a L I. Transformer Equation Notes

N V V L. R a L I. Transformer Equation Notes Tnsfome Eqution otes This file conts moe etile eivtion of the tnsfome equtions thn the notes o the expeiment 3 wite-up. t will help you to unestn wht ssumptions wee neee while eivg the iel tnsfome equtions

More information

32. The Tangency Problem of Apollonius.

32. The Tangency Problem of Apollonius. . The Tngeny olem of Apollonius. Constut ll iles tngent to thee given iles. This eleted polem ws posed y Apollinius of eg (. 60-70 BC), the getest mthemtiin of ntiquity fte Eulid nd Ahimedes. His mjo wok

More information

Curvature. (Com S 477/577 Notes) Yan-Bin Jia. Oct 8, 2015

Curvature. (Com S 477/577 Notes) Yan-Bin Jia. Oct 8, 2015 Cuvtue Com S 477/577 Notes Yn-Bin Ji Oct 8, 205 We wnt to find mesue of how cuved cuve is. Since this cuvtue should depend only on the shpe of the cuve, it should not be chnged when the cuve is epmetized.

More information

GRAVITATION 1. BASIC FORCES IN NATURE

GRAVITATION 1. BASIC FORCES IN NATURE GRAVITATION. BASIC ORCES IN NATURE POINTS TO REMEMBER. Bsing on the ntue nd eltive stength the bsic foces in ntue e clssified into fou ctegoies. They e ) Gvittionl foce ) Electomgnetic foce 3) Stong Nucle

More information

Summary: Vectors. This theorem is used to find any points (or position vectors) on a given line (direction vector). Two ways RT can be applied:

Summary: Vectors. This theorem is used to find any points (or position vectors) on a given line (direction vector). Two ways RT can be applied: Summ: Vectos ) Rtio Theoem (RT) This theoem is used to find n points (o position vectos) on given line (diection vecto). Two ws RT cn e pplied: Cse : If the point lies BETWEEN two known position vectos

More information

PROBLEMS 13 - APPLICATIONS OF DERIVATIVES Page 1

PROBLEMS 13 - APPLICATIONS OF DERIVATIVES Page 1 PROBLEMS - APPLICATIONS OF DERIVATIVES Pge ( ) Wter seeps out of conicl filter t the constnt rte of 5 cc / sec. When the height of wter level in the cone is 5 cm, find the rte t which the height decreses.

More information

Chapter 23 Electrical Potential

Chapter 23 Electrical Potential hpte Electicl Potentil onceptul Polems [SSM] A poton is moved to the left in unifom electic field tht points to the ight. Is the poton moving in the diection of incesing o decesing electic potentil? Is

More information

Geometry 7-1 Geometric Mean and the Pythagorean Theorem

Geometry 7-1 Geometric Mean and the Pythagorean Theorem Geometry 7-1 Geometric Men nd the Pythgoren Theorem. Geometric Men 1. Def: The geometric men etween two positive numers nd is the positive numer x where: = x. x Ex 1: Find the geometric men etween the

More information

AMPERE S LAW. by Kirby Morgan MISN-0-138

AMPERE S LAW. by Kirby Morgan MISN-0-138 MISN-0-138 AMPERE S LAW by Kiby Mogn 1. Usefullness................................................ 1 AMPERE S LAW 2. The Lw................................................... 1. The Integl Reltionship...............................

More information

Graphs on Logarithmic and Semilogarithmic Paper

Graphs on Logarithmic and Semilogarithmic Paper 0CH_PHClter_TMSETE_ 3//00 :3 PM Pge Grphs on Logrithmic nd Semilogrithmic Pper OBJECTIVES When ou hve completed this chpter, ou should be ble to: Mke grphs on logrithmic nd semilogrithmic pper. Grph empiricl

More information

Basically, logarithmic transformations ask, a number, to what power equals another number?

Basically, logarithmic transformations ask, a number, to what power equals another number? Wht i logrithm? To nwer thi, firt try to nwer the following: wht i x in thi eqution? 9 = 3 x wht i x in thi eqution? 8 = 2 x Biclly, logrithmic trnformtion k, number, to wht power equl nother number? In

More information

Exam in physics, El-grunder (Electromagnetism), 2014-03-26, kl 9.00-15.00

Exam in physics, El-grunder (Electromagnetism), 2014-03-26, kl 9.00-15.00 Umeå Univesitet, Fysik 1 Vitly Bychkov Em in physics, El-gunde (Electomgnetism, 14--6, kl 9.-15. Hjälpmedel: Students my use ny book(s. Mino notes in the books e lso llowed. Students my not use thei lectue

More information

AREA OF A SURFACE OF REVOLUTION

AREA OF A SURFACE OF REVOLUTION AREA OF A SURFACE OF REVOLUTION h cut r πr h A surfce of revolution is formed when curve is rotted bout line. Such surfce is the lterl boundr of solid of revolution of the tpe discussed in Sections 7.

More information

Skills Needed for Success in Calculus 1

Skills Needed for Success in Calculus 1 Skills Needed fo Success in Calculus Thee is much appehension fom students taking Calculus. It seems that fo man people, "Calculus" is snonmous with "difficult." Howeve, an teache of Calculus will tell

More information

Polynomial Functions. Polynomial functions in one variable can be written in expanded form as ( )

Polynomial Functions. Polynomial functions in one variable can be written in expanded form as ( ) Polynomil Functions Polynomil functions in one vrible cn be written in expnded form s n n 1 n 2 2 f x = x + x + x + + x + x+ n n 1 n 2 2 1 0 Exmples of polynomils in expnded form re nd 3 8 7 4 = 5 4 +

More information

1.- L a m e j o r o p c ió n e s c l o na r e l d i s co ( s e e x p li c a r á d es p u é s ).

1.- L a m e j o r o p c ió n e s c l o na r e l d i s co ( s e e x p li c a r á d es p u é s ). PROCEDIMIENTO DE RECUPERACION Y COPIAS DE SEGURIDAD DEL CORTAFUEGOS LINUX P ar a p od e r re c u p e ra r nu e s t r o c o rt a f u e go s an t e un d es a s t r e ( r ot u r a d e l di s c o o d e l a

More information

Random Variables and Distribution Functions

Random Variables and Distribution Functions Topic 7 Rndom Vibles nd Distibution Functions 7.1 Intoduction Fom the univese of possible infomtion, we sk question. To ddess this question, we might collect quntittive dt nd ognize it, fo emple, using

More information

EASY RECEPTION TASKS FOR USE IN THE LITERACY HOUR. S t e p h e n s t e. Jigsaw names of self and friends.

EASY RECEPTION TASKS FOR USE IN THE LITERACY HOUR. S t e p h e n s t e. Jigsaw names of self and friends. EASY RECEPTION TASKS FOR USE IN THE LITERACY HOUR Own Nme Tk Mtching letter underneth nme crd. S t e p h e n t e B e n Mtching mgnetic letter under nme crd p t t h o n Jigw nme of elf nd friend. T r c

More information

1. Find the zeros Find roots. Set function = 0, factor or use quadratic equation if quadratic, graph to find zeros on calculator

1. Find the zeros Find roots. Set function = 0, factor or use quadratic equation if quadratic, graph to find zeros on calculator AP Clculus Finl Review Sheet When you see the words. This is wht you think of doing. Find the zeros Find roots. Set function =, fctor or use qudrtic eqution if qudrtic, grph to find zeros on clcultor.

More information

Use Geometry Expressions to create a more complex locus of points. Find evidence for equivalence using Geometry Expressions.

Use Geometry Expressions to create a more complex locus of points. Find evidence for equivalence using Geometry Expressions. Lerning Objectives Loci nd Conics Lesson 3: The Ellipse Level: Preclculus Time required: 120 minutes In this lesson, students will generlize their knowledge of the circle to the ellipse. The prmetric nd

More information

Chapter 30: Magnetic Fields Due to Currents

Chapter 30: Magnetic Fields Due to Currents d Chapte 3: Magnetic Field Due to Cuent A moving electic chage ceate a magnetic field. One of the moe pactical way of geneating a lage magnetic field (.1-1 T) i to ue a lage cuent flowing though a wie.

More information

Mathematics. Vectors. hsn.uk.net. Higher. Contents. Vectors 128 HSN23100

Mathematics. Vectors. hsn.uk.net. Higher. Contents. Vectors 128 HSN23100 hsn.uk.net Higher Mthemtics UNIT 3 OUTCOME 1 Vectors Contents Vectors 18 1 Vectors nd Sclrs 18 Components 18 3 Mgnitude 130 4 Equl Vectors 131 5 Addition nd Subtrction of Vectors 13 6 Multipliction by

More information

Vectors. The magnitude of a vector is its length, which can be determined by Pythagoras Theorem. The magnitude of a is written as a.

Vectors. The magnitude of a vector is its length, which can be determined by Pythagoras Theorem. The magnitude of a is written as a. Vectors mesurement which onl descries the mgnitude (i.e. size) of the oject is clled sclr quntit, e.g. Glsgow is 11 miles from irdrie. vector is quntit with mgnitude nd direction, e.g. Glsgow is 11 miles

More information

10 AREA AND VOLUME 1. Before you start. Objectives

10 AREA AND VOLUME 1. Before you start. Objectives 10 AREA AND VOLUME 1 The Tower of Pis is circulr bell tower. Construction begn in the 1170s, nd the tower strted lening lmost immeditely becuse of poor foundtion nd loose soil. It is 56.7 metres tll, with

More information

Solution to Problem Set 1

Solution to Problem Set 1 CSE 5: Introduction to the Theory o Computtion, Winter A. Hevi nd J. Mo Solution to Prolem Set Jnury, Solution to Prolem Set.4 ). L = {w w egin with nd end with }. q q q q, d). L = {w w h length t let

More information

Tallahassee Community College PERIMETER

Tallahassee Community College PERIMETER Tallahassee Community College 47 PERIMETER The perimeter of a plane figure is the distance around it. Perimeter is measured in linear units because we are finding the total of the lengths of the sides

More information

VEHICLE PLANAR DYNAMICS BICYCLE MODEL

VEHICLE PLANAR DYNAMICS BICYCLE MODEL Auptions -Do, VEHE PANA DYNAMS BYE MODE o tel, (esued o instntneous cente o ottion O) o Yw, (wt Globl Ais) ongitudinl elocit is ued to be constnt. Sll slip ngles, i.e. ties opete in the line egion. No

More information

10.6 Applications of Quadratic Equations

10.6 Applications of Quadratic Equations 10.6 Applictions of Qudrtic Equtions In this section we wnt to look t the pplictions tht qudrtic equtions nd functions hve in the rel world. There re severl stndrd types: problems where the formul is given,

More information

Physics 43 Homework Set 9 Chapter 40 Key

Physics 43 Homework Set 9 Chapter 40 Key Physics 43 Homework Set 9 Chpter 4 Key. The wve function for n electron tht is confined to x nm is. Find the normliztion constnt. b. Wht is the probbility of finding the electron in. nm-wide region t x

More information

Binary Representation of Numbers Autar Kaw

Binary Representation of Numbers Autar Kaw Binry Representtion of Numbers Autr Kw After reding this chpter, you should be ble to: 1. convert bse- rel number to its binry representtion,. convert binry number to n equivlent bse- number. In everydy

More information

Bayesian Updating with Continuous Priors Class 13, 18.05, Spring 2014 Jeremy Orloff and Jonathan Bloom

Bayesian Updating with Continuous Priors Class 13, 18.05, Spring 2014 Jeremy Orloff and Jonathan Bloom Byesin Updting with Continuous Priors Clss 3, 8.05, Spring 04 Jeremy Orloff nd Jonthn Bloom Lerning Gols. Understnd prmeterized fmily of distriutions s representing continuous rnge of hypotheses for the

More information

Quick Reference Guide: Reset Password

Quick Reference Guide: Reset Password Quick Reference Guide: Reset Pssword How to reset pssword This Quick Reference Guide shows you how to reset your pssword if you hve forgotten it. There re three wys to reset your SingPss pssword: 1) Online

More information

Example A rectangular box without lid is to be made from a square cardboard of sides 18 cm by cutting equal squares from each corner and then folding

Example A rectangular box without lid is to be made from a square cardboard of sides 18 cm by cutting equal squares from each corner and then folding 1 Exmple A rectngulr box without lid is to be mde from squre crdbord of sides 18 cm by cutting equl squres from ech corner nd then folding up the sides. 1 Exmple A rectngulr box without lid is to be mde

More information

Operations with Polynomials

Operations with Polynomials 38 Chpter P Prerequisites P.4 Opertions with Polynomils Wht you should lern: Write polynomils in stndrd form nd identify the leding coefficients nd degrees of polynomils Add nd subtrct polynomils Multiply

More information

Lesson 4.1 Triangle Sum Conjecture

Lesson 4.1 Triangle Sum Conjecture Lesson 4.1 ringle um onjecture Nme eriod te n ercises 1 9, determine the ngle mesures. 1. p, q 2., y 3., b 31 82 p 98 q 28 53 y 17 79 23 50 b 4. r, s, 5., y 6. y t t s r 100 85 100 y 30 4 7 y 31 7. s 8.

More information

Quantity Formula Meaning of variables. 5 C 1 32 F 5 degrees Fahrenheit, 1 bh A 5 area, b 5 base, h 5 height. P 5 2l 1 2w

Quantity Formula Meaning of variables. 5 C 1 32 F 5 degrees Fahrenheit, 1 bh A 5 area, b 5 base, h 5 height. P 5 2l 1 2w 1.4 Rewite Fomulas and Equations Befoe You solved equations. Now You will ewite and evaluate fomulas and equations. Why? So you can apply geometic fomulas, as in Ex. 36. Key Vocabulay fomula solve fo a

More information

Quick Reference Guide: One-time Account Update

Quick Reference Guide: One-time Account Update Quick Reference Guide: One-time Account Updte How to complete The Quick Reference Guide shows wht existing SingPss users need to do when logging in to the enhnced SingPss service for the first time. 1)

More information

Or more simply put, when adding or subtracting quantities, their uncertainties add.

Or more simply put, when adding or subtracting quantities, their uncertainties add. Propgtion of Uncertint through Mthemticl Opertions Since the untit of interest in n eperiment is rrel otined mesuring tht untit directl, we must understnd how error propgtes when mthemticl opertions re

More information

15.6. The mean value and the root-mean-square value of a function. Introduction. Prerequisites. Learning Outcomes. Learning Style

15.6. The mean value and the root-mean-square value of a function. Introduction. Prerequisites. Learning Outcomes. Learning Style The men vlue nd the root-men-squre vlue of function 5.6 Introduction Currents nd voltges often vry with time nd engineers my wish to know the verge vlue of such current or voltge over some prticulr time

More information

Excel Invoice Format. SupplierWebsite - Excel Invoice Upload. Data Element Definition UCLA Supplier website (Rev. July 9, 2013)

Excel Invoice Format. SupplierWebsite - Excel Invoice Upload. Data Element Definition UCLA Supplier website (Rev. July 9, 2013) Excel Invoice Format Excel Column Name Cell Format Notes Campus* Supplier Number* Invoice Number* Order Number* Invoice Date* Total Invoice Amount* Total Sales Tax Amount* Discount Amount Discount Percent

More information

LECTURE #05. Learning Objective. To describe the geometry in and around a unit cell in terms of directions and planes.

LECTURE #05. Learning Objective. To describe the geometry in and around a unit cell in terms of directions and planes. LECTURE #05 Chpter 3: Lttice Positions, Directions nd Plnes Lerning Objective To describe the geometr in nd round unit cell in terms of directions nd plnes. 1 Relevnt Reding for this Lecture... Pges 64-83.

More information

Tangent Properties. Line m is a tangent to circle O. Point T is the point of tangency.

Tangent Properties. Line m is a tangent to circle O. Point T is the point of tangency. CONDENSED LESSON 6.1 Tangent Properties In this lesson you will Review terms associated with circles Discover how a tangent to a circle and the radius to the point of tangency are related Make a conjecture

More information

Worked Examples. v max =?

Worked Examples. v max =? Exaple iction + Unifo Cicula Motion Cicula Hill A ca i diing oe a ei-cicula hill of adiu. What i the fatet the ca can die oe the top of the hill without it tie lifting off of the gound? ax? (1) Copehend

More information

Level D - Form 1 - Applied Mathematics: Measurement

Level D - Form 1 - Applied Mathematics: Measurement Level D - Form 1 - Applied Mathematics: Measurement Sample Question What time does this clock show? A 1:20 B 1:23 C 2:23 D 2:43 Level D - Form 1 - Applied Mathematics: Measurement 1. A movie begins at

More information

Multiplication and Division - Left to Right. Addition and Subtraction - Left to Right.

Multiplication and Division - Left to Right. Addition and Subtraction - Left to Right. Order of Opertions r of Opertions Alger P lese Prenthesis - Do ll grouped opertions first. E cuse Eponents - Second M D er Multipliction nd Division - Left to Right. A unt S hniqu Addition nd Sutrction

More information

Answer, Key Homework 10 David McIntyre 1

Answer, Key Homework 10 David McIntyre 1 Answer, Key Homework 10 Dvid McIntyre 1 This print-out should hve 22 questions, check tht it is complete. Multiple-choice questions my continue on the next column or pge: find ll choices efore mking your

More information

Answer, Key Homework 6 David McIntyre 45123 Mar 25, 2004 1

Answer, Key Homework 6 David McIntyre 45123 Mar 25, 2004 1 Answe, Key Homewok 6 vid McInye 4513 M 5, 004 1 This pin-ou should hve 0 quesions. Muliple-choice quesions my coninue on he nex column o pge find ll choices befoe mking you selecion. The due ime is Cenl

More information

(1) continuity equation: 0. momentum equation: u v g (2) u x. 1 a

(1) continuity equation: 0. momentum equation: u v g (2) u x. 1 a Comment on The effect of vible viscosity on mied convection het tnsfe long veticl moving sufce by M. Ali [Intentionl Jounl of Theml Sciences, 006, Vol. 45, pp. 60-69] Asteios Pntoktos Associte Pofesso

More information

Experiment 6: Friction

Experiment 6: Friction Experiment 6: Friction In previous lbs we studied Newton s lws in n idel setting, tht is, one where friction nd ir resistnce were ignored. However, from our everydy experience with motion, we know tht

More information

Review Problems for the Final of Math 121, Fall 2014

Review Problems for the Final of Math 121, Fall 2014 Review Problems for the Finl of Mth, Fll The following is collection of vrious types of smple problems covering sections.,.5, nd.7 6.6 of the text which constitute only prt of the common Mth Finl. Since

More information

Angles 2.1. Exercise 2.1... Find the size of the lettered angles. Give reasons for your answers. a) b) c) Example

Angles 2.1. Exercise 2.1... Find the size of the lettered angles. Give reasons for your answers. a) b) c) Example 2.1 Angles Reognise lternte n orresponing ngles Key wors prllel lternte orresponing vertilly opposite Rememer, prllel lines re stright lines whih never meet or ross. The rrows show tht the lines re prllel

More information

PROBLEM 4.1 SOLUTION. Knowing that the couple shown acts in a vertical plane, determine the stress at (a) point A, (b) point B.

PROBLEM 4.1 SOLUTION. Knowing that the couple shown acts in a vertical plane, determine the stress at (a) point A, (b) point B. PROBLEM.1 Knowing tht the couple shown cts in verticl plne, determine the stress t () point A, (b) point B. SOLUTON () (b) For rectngle: For cross sectionl re: 1 = bh 1 1 = 1 + + = ()(1.5) + ()(5.5) +

More information

Continuous Compounding and Annualization

Continuous Compounding and Annualization Continuous Compounding and Annualization Philip A. Viton Januay 11, 2006 Contents 1 Intoduction 1 2 Continuous Compounding 2 3 Pesent Value with Continuous Compounding 4 4 Annualization 5 5 A Special Poblem

More information

9 CONTINUOUS DISTRIBUTIONS

9 CONTINUOUS DISTRIBUTIONS 9 CONTINUOUS DISTIBUTIONS A rndom vrible whose vlue my fll nywhere in rnge of vlues is continuous rndom vrible nd will be ssocited with some continuous distribution. Continuous distributions re to discrete

More information

Chapter 22 The Electric Field II: Continuous Charge Distributions

Chapter 22 The Electric Field II: Continuous Charge Distributions Chpte The lectic Field II: Continuous Chge Distibutions Conceptul Poblems [SSM] Figue -7 shows n L-shped object tht hs sides which e equl in length. Positive chge is distibuted unifomly long the length

More information

Math 135 Circles and Completing the Square Examples

Math 135 Circles and Completing the Square Examples Mth 135 Circles nd Completing the Squre Exmples A perfect squre is number such tht = b 2 for some rel number b. Some exmples of perfect squres re 4 = 2 2, 16 = 4 2, 169 = 13 2. We wish to hve method for

More information

Numerical Methods of Approximating Definite Integrals

Numerical Methods of Approximating Definite Integrals 6 C H A P T E R Numericl Methods o Approimting Deinite Integrls 6. APPROXIMATING SUMS: L n, R n, T n, AND M n Introduction Not only cn we dierentite ll the bsic unctions we ve encountered, polynomils,

More information

UNIT CIRCLE TRIGONOMETRY

UNIT CIRCLE TRIGONOMETRY UNIT CIRCLE TRIGONOMETRY The Unit Cicle is the cicle centeed at the oigin with adius unit (hence, the unit cicle. The equation of this cicle is + =. A diagam of the unit cicle is shown below: + = - - -

More information

How To Set Up A Network For Your Business

How To Set Up A Network For Your Business Why Network is n Essentil Productivity Tool for Any Smll Business TechAdvisory.org SME Reports sponsored by Effective technology is essentil for smll businesses looking to increse their productivity. Computer

More information

Area. GABLES 411: Gables Citywalk/Waterford Square a

Area. GABLES 411: Gables Citywalk/Waterford Square a Are GABLES 411: Gbles Citywlk/Wterford Squre Where is the closest post office? 3740 Greenbrir St. Houston, TX 0.5 Miles (713) 528-5875 Where is the closest grocery store? Whole Foods, 2955 Kirby Dr. Houston,

More information

16. Mean Square Estimation

16. Mean Square Estimation 6 Me Sque stmto Gve some fomto tht s elted to uow qutty of teest the poblem s to obt good estmte fo the uow tems of the obseved dt Suppose epeset sequece of dom vbles bout whom oe set of obsevtos e vlble

More information

CURVES ANDRÉ NEVES. that is, the curve α has finite length. v = p q p q. a i.e., the curve of smallest length connecting p to q is a straight line.

CURVES ANDRÉ NEVES. that is, the curve α has finite length. v = p q p q. a i.e., the curve of smallest length connecting p to q is a straight line. CURVES ANDRÉ NEVES 1. Problems (1) (Ex 1 of 1.3 of Do Crmo) Show tht the tngent line to the curve α(t) (3t, 3t 2, 2t 3 ) mkes constnt ngle with the line z x, y. (2) (Ex 6 of 1.3 of Do Crmo) Let α(t) (e

More information

SPECIAL PRODUCTS AND FACTORIZATION

SPECIAL PRODUCTS AND FACTORIZATION MODULE - Specil Products nd Fctoriztion 4 SPECIAL PRODUCTS AND FACTORIZATION In n erlier lesson you hve lernt multipliction of lgebric epressions, prticulrly polynomils. In the study of lgebr, we come

More information

12. Rolling, Torque, and Angular Momentum

12. Rolling, Torque, and Angular Momentum 12. olling, Toque, and Angula Momentum 1 olling Motion: A motion that is a combination of otational and tanslational motion, e.g. a wheel olling down the oad. Will only conside olling with out slipping.

More information

GFI EventsMnge vs Netikus.net EventSenty GFI Softwe www.gfi.com GFI EventsMnge vs Netikus.net EventSenty GFI EventsMnge EventSenty Who we e Suppot fo MS SQL Seve Suppot fo MSDE / MS SQL Expess Suppot fo

More information

Lecture 5. Inner Product

Lecture 5. Inner Product Lecture 5 Inner Product Let us strt with the following problem. Given point P R nd line L R, how cn we find the point on the line closest to P? Answer: Drw line segment from P meeting the line in right

More information

Small Business Networking

Small Business Networking Why network is n essentil productivity tool for ny smll business Effective technology is essentil for smll businesses looking to increse the productivity of their people nd processes. Introducing technology

More information

The remaining two sides of the right triangle are called the legs of the right triangle.

The remaining two sides of the right triangle are called the legs of the right triangle. 10 MODULE 6. RADICAL EXPRESSIONS 6 Pythgoren Theorem The Pythgoren Theorem An ngle tht mesures 90 degrees is lled right ngle. If one of the ngles of tringle is right ngle, then the tringle is lled right

More information

Vectors 2. 1. Recap of vectors

Vectors 2. 1. Recap of vectors Vectors 2. Recp of vectors Vectors re directed line segments - they cn be represented in component form or by direction nd mgnitude. We cn use trigonometry nd Pythgors theorem to switch between the forms

More information

PROF. BOYAN KOSTADINOV NEW YORK CITY COLLEGE OF TECHNOLOGY, CUNY

PROF. BOYAN KOSTADINOV NEW YORK CITY COLLEGE OF TECHNOLOGY, CUNY MAT 0630 INTERNET RESOURCES, REVIEW OF CONCEPTS AND COMMON MISTAKES PROF. BOYAN KOSTADINOV NEW YORK CITY COLLEGE OF TECHNOLOGY, CUNY Contents 1. ACT Compss Prctice Tests 1 2. Common Mistkes 2 3. Distributive

More information

Math 314, Homework Assignment 1. 1. Prove that two nonvertical lines are perpendicular if and only if the product of their slopes is 1.

Math 314, Homework Assignment 1. 1. Prove that two nonvertical lines are perpendicular if and only if the product of their slopes is 1. Mth 4, Homework Assignment. Prove tht two nonverticl lines re perpendiculr if nd only if the product of their slopes is. Proof. Let l nd l e nonverticl lines in R of slopes m nd m, respectively. Suppose

More information

Lesson 2.1 Inductive Reasoning

Lesson 2.1 Inductive Reasoning Lesson.1 Inutive Resoning Nme Perio Dte For Eerises 1 7, use inutive resoning to fin the net two terms in eh sequene. 1. 4, 8, 1, 16,,. 400, 00, 100, 0,,,. 1 8, 7, 1, 4,, 4.,,, 1, 1, 0,,. 60, 180, 10,

More information

Mechanics 1: Work, Power and Kinetic Energy

Mechanics 1: Work, Power and Kinetic Energy Mechanics 1: Wok, Powe and Kinetic Eneg We fist intoduce the ideas of wok and powe. The notion of wok can be viewed as the bidge between Newton s second law, and eneg (which we have et to define and discuss).

More information

Ratio and Proportion

Ratio and Proportion Rtio nd Proportion Rtio: The onept of rtio ours frequently nd in wide vriety of wys For exmple: A newspper reports tht the rtio of Repulins to Demorts on ertin Congressionl ommittee is 3 to The student/fulty

More information

Section 7-4 Translation of Axes

Section 7-4 Translation of Axes 62 7 ADDITIONAL TOPICS IN ANALYTIC GEOMETRY Section 7-4 Trnsltion of Aes Trnsltion of Aes Stndrd Equtions of Trnslted Conics Grphing Equtions of the Form A 2 C 2 D E F 0 Finding Equtions of Conics In the

More information

VOLUME of Rectangular Prisms Volume is the measure of occupied by a solid region.

VOLUME of Rectangular Prisms Volume is the measure of occupied by a solid region. Math 6 NOTES 7.5 Name VOLUME of Rectangular Prisms Volume is the measure of occupied by a solid region. **The formula for the volume of a rectangular prism is:** l = length w = width h = height Study Tip:

More information

ú Ó Á É é ú ú É ú Á Á ú É É É ú É Ó É ó É Á ú ú ó Á Á ú Ó ú Ó ú É Á ú Á ú ó ú Á ú Á É Á Á Ó É Á ú ú é ú ú ú ú Á ú ó ú Ó Á Á Á Á ú ú ú é É ó é ó ú ú ú É é ú ú ú óú ú ú Ó Á ú ö é É ú ú ú úé ú ú É É Á É

More information

The Casino Experience. Let us entertain you

The Casino Experience. Let us entertain you The Csio Expeiee Let us eteti you The Csio Expeiee If you e lookig fo get ight out, Csio Expeiee is just fo you. 10 The Stight Flush Expeiee 25 pe peso This is get itodutio to gmig tht sves you moey Kik

More information

Coordinate Systems L. M. Kalnins, March 2009

Coordinate Systems L. M. Kalnins, March 2009 Coodinate Sstems L. M. Kalnins, Mach 2009 Pupose of a Coodinate Sstem The pupose of a coodinate sstem is to uniquel detemine the position of an object o data point in space. B space we ma liteall mean

More information

Pythagorean Theorem: 9. x 2 2

Pythagorean Theorem: 9. x 2 2 Geometry Chapter 8 - Right Triangles.7 Notes on Right s Given: any 3 sides of a Prove: the is acute, obtuse, or right (hint: use the converse of Pythagorean Theorem) If the (longest side) 2 > (side) 2

More information

Introduction to Integration Part 2: The Definite Integral

Introduction to Integration Part 2: The Definite Integral Mthemtics Lerning Centre Introduction to Integrtion Prt : The Definite Integrl Mr Brnes c 999 Universit of Sdne Contents Introduction. Objectives...... Finding Ares 3 Ares Under Curves 4 3. Wht is the

More information

www.mathsbox.org.uk e.g. f(x) = x domain x 0 (cannot find the square root of negative values)

www.mathsbox.org.uk e.g. f(x) = x domain x 0 (cannot find the square root of negative values) www.mthsbo.org.uk CORE SUMMARY NOTES Functions A function is rule which genertes ectl ONE OUTPUT for EVERY INPUT. To be defined full the function hs RULE tells ou how to clculte the output from the input

More information

Area and Perimeter. Name: Class: Date: Short Answer

Area and Perimeter. Name: Class: Date: Short Answer Name: Class: Date: ID: A Area and Perimeter Short Answer 1. The squares on this grid are 1 centimeter long and 1 centimeter wide. Outline two different figures with an area of 12 square centimeters and

More information

How To Draw A Similar Figure From A Different Perspective

How To Draw A Similar Figure From A Different Perspective Chapter 6 Similarity of Figures 6.1 Similar Polygons 6.2 Determining if two Polygons are Similar 6.3 Drawing Similar Polygons 6.4 Similar Triangles 21 Name: 6.1 Similar Polygons A. What makes something

More information

Small Business Networking

Small Business Networking Why network is n essentil productivity tool for ny smll business Effective technology is essentil for smll businesses looking to increse the productivity of their people nd business. Introducing technology

More information

End of term: TEST A. Year 4. Name Class Date. Complete the missing numbers in the sequences below.

End of term: TEST A. Year 4. Name Class Date. Complete the missing numbers in the sequences below. End of term: TEST A You will need penil nd ruler. Yer Nme Clss Dte Complete the missing numers in the sequenes elow. 8 30 3 28 2 9 25 00 75 25 2 Put irle round ll of the following shpes whih hve 3 shded.

More information

Small Business Cloud Services

Small Business Cloud Services Smll Business Cloud Services Summry. We re thick in the midst of historic se-chnge in computing. Like the emergence of personl computers, grphicl user interfces, nd mobile devices, the cloud is lredy profoundly

More information

MATH STUDENT BOOK. 6th Grade Unit 8

MATH STUDENT BOOK. 6th Grade Unit 8 MATH STUDENT BOOK 6th Grade Unit 8 Unit 8 Geometry and Measurement MATH 608 Geometry and Measurement INTRODUCTION 3 1. PLANE FIGURES 5 PERIMETER 5 AREA OF PARALLELOGRAMS 11 AREA OF TRIANGLES 17 AREA OF

More information

Small Business Networking

Small Business Networking Why network is n essentil productivity tool for ny smll business Effective technology is essentil for smll businesses looking to increse the productivity of their people nd business. Introducing technology

More information

4a 4ab b 4 2 4 2 5 5 16 40 25. 5.6 10 6 (count number of places from first non-zero digit to

4a 4ab b 4 2 4 2 5 5 16 40 25. 5.6 10 6 (count number of places from first non-zero digit to . Simplify: 0 4 ( 8) 0 64 ( 8) 0 ( 8) = (Ode of opeations fom left to ight: Paenthesis, Exponents, Multiplication, Division, Addition Subtaction). Simplify: (a 4) + (a ) (a+) = a 4 + a 0 a = a 7. Evaluate

More information

Factoring Polynomials

Factoring Polynomials Fctoring Polynomils Some definitions (not necessrily ll for secondry school mthemtics): A polynomil is the sum of one or more terms, in which ech term consists of product of constnt nd one or more vribles

More information