Area of a Parallelogram

13 PERIMETER AND AREA OF 2D SHAPES

13 PERIMETER AND AREA OF D SHAPES 13.1 You can find te perimeter of sapes Key Points Te perimeter of a two-dimensional (D) sape is te total distance around te edge of te sape. l To work out te perimeter

Determine the perimeter of a triangle using algebra Find the area of a triangle using the formula

Student Name: Date: Contact Person Name: Pone Number: Lesson 0 Perimeter, Area, and Similarity of Triangles Objectives Determine te perimeter of a triangle using algebra Find te area of a triangle using

1.6. Analyse Optimum Volume and Surface Area. Maximum Volume for a Given Surface Area. Example 1. Solution

1.6 Analyse Optimum Volume and Surface Area Estimation and oter informal metods of optimizing measures suc as surface area and volume often lead to reasonable solutions suc as te design of te tent in tis

ACT Math Facts & Formulas

Numbers, Sequences, Factors Integers:..., -3, -2, -1, 0, 1, 2, 3,... Rationals: fractions, tat is, anyting expressable as a ratio of integers Reals: integers plus rationals plus special numbers suc as

SAT Subject Math Level 1 Facts & Formulas

Numbers, Sequences, Factors Integers:..., -3, -2, -1, 0, 1, 2, 3,... Reals: integers plus fractions, decimals, and irrationals ( 2, 3, π, etc.) Order Of Operations: Aritmetic Sequences: PEMDAS (Parenteses

New Vocabulary volume

-. Plan Objectives To find te volume of a prism To find te volume of a cylinder Examples Finding Volume of a Rectangular Prism Finding Volume of a Triangular Prism 3 Finding Volume of a Cylinder Finding

Perimeter, Area and Volume of Regular Shapes

Perimeter, Area and Volume of Regular Sapes Perimeter of Regular Polygons Perimeter means te total lengt of all sides, or distance around te edge of a polygon. For a polygon wit straigt sides tis is te

Lecture 10: What is a Function, definition, piecewise defined functions, difference quotient, domain of a function

Lecture 10: Wat is a Function, definition, piecewise defined functions, difference quotient, domain of a function A function arises wen one quantity depends on anoter. Many everyday relationsips between

Instantaneous Rate of Change:

Instantaneous Rate of Cange: Last section we discovered tat te average rate of cange in F(x) can also be interpreted as te slope of a scant line. Te average rate of cange involves te cange in F(x) over

Math Test Sections. The College Board: Expanding College Opportunity

Taking te SAT I: Reasoning Test Mat Test Sections Te materials in tese files are intended for individual use by students getting ready to take an SAT Program test; permission for any oter use must be sougt

Volumes of Pyramids and Cones. Use the Pythagorean Theorem to find the value of the variable. h 2 m. 1.5 m 12 in. 8 in. 2.5 m

-5 Wat You ll Learn To find te volume of a pramid To find te volume of a cone... And W To find te volume of a structure in te sape of a pramid, as in Eample Volumes of Pramids and Cones Ceck Skills You

Derivatives Math 120 Calculus I D Joyce, Fall 2013

Derivatives Mat 20 Calculus I D Joyce, Fall 203 Since we ave a good understanding of its, we can develop derivatives very quickly. Recall tat we defined te derivative f x of a function f at x to be te

Areas of Polygons. Goal. At-Home Help. 1. A hockey team chose this logo for their uniforms.

-NEM-WBAns-CH // : PM Page Areas of Polygons Estimate and measure the area of polygons.. A hockey team chose this logo for their uniforms. A grid is like an area ruler. Each full square on the grid has

Convert between units of area and determine the scale factor of two similar figures.

CHAPTER 5 Units of Area c GOAL Convert between units of area and determine the scale factor of two. You will need a ruler centimetre grid paper a protractor a calculator Learn about the Math The area of

2 Limits and Derivatives

2 Limits and Derivatives 2.7 Tangent Lines, Velocity, and Derivatives A tangent line to a circle is a line tat intersects te circle at exactly one point. We would like to take tis idea of tangent line

Chapter 10: Refrigeration Cycles

Capter 10: efrigeration Cycles Te vapor compression refrigeration cycle is a common metod for transferring eat from a low temperature to a ig temperature. Te above figure sows te objectives of refrigerators

Section 2.3 Solving Right Triangle Trigonometry

Section.3 Solving Rigt Triangle Trigonometry Eample In te rigt triangle ABC, A = 40 and c = 1 cm. Find a, b, and B. sin 40 a a c 1 a 1sin 40 7.7cm cos 40 b c b 1 b 1cos40 9.cm A 40 1 b C B a B = 90 - A

Projective Geometry. Projective Geometry

Euclidean versus Euclidean geometry describes sapes as tey are Properties of objects tat are uncanged by rigid motions» Lengts» Angles» Parallelism Projective geometry describes objects as tey appear Lengts,

Research on the Anti-perspective Correction Algorithm of QR Barcode

Researc on te Anti-perspective Correction Algoritm of QR Barcode Jianua Li, Yi-Wen Wang, YiJun Wang,Yi Cen, Guoceng Wang Key Laboratory of Electronic Tin Films and Integrated Devices University of Electronic

M(0) = 1 M(1) = 2 M(h) = M(h 1) + M(h 2) + 1 (h > 1)

Insertion and Deletion in VL Trees Submitted in Partial Fulfillment of te Requirements for Dr. Eric Kaltofen s 66621: nalysis of lgoritms by Robert McCloskey December 14, 1984 1 ackground ccording to Knut

A strong credit score can help you score a lower rate on a mortgage

NET GAIN Scoring points for your financial future AS SEEN IN USA TODAY S MONEY SECTION, JULY 3, 2007 A strong credit score can elp you score a lower rate on a mortgage By Sandra Block Sales of existing

Calculating Perimeter

Calculating Perimeter and Area Formulas are equations used to make specific calculations. Common formulas (equations) include: P = 2l + 2w perimeter of a rectangle A = l + w area of a square or rectangle

Pressure. Pressure. Atmospheric pressure. Conceptual example 1: Blood pressure. Pressure is force per unit area:

Pressure Pressure is force per unit area: F P = A Pressure Te direction of te force exerted on an object by a fluid is toward te object and perpendicular to its surface. At a microscopic level, te force

FINITE DIFFERENCE METHODS

FINITE DIFFERENCE METHODS LONG CHEN Te best known metods, finite difference, consists of replacing eac derivative by a difference quotient in te classic formulation. It is simple to code and economic to

CALCULATING THE AREA OF A FLOWER BED AND CALCULATING NUMBER OF PLANTS NEEDED

This resource has been produced as a result of a grant awarded by LSIS. The grant was made available through the Skills for Life Support Programme in 2010. The resource has been developed by (managers

MATHEMATICS FOR ENGINEERING DIFFERENTIATION TUTORIAL 1 - BASIC DIFFERENTIATION

MATHEMATICS FOR ENGINEERING DIFFERENTIATION TUTORIAL 1 - BASIC DIFFERENTIATION Tis tutorial is essential pre-requisite material for anyone stuing mecanical engineering. Tis tutorial uses te principle of

Chapter 7 Numerical Differentiation and Integration

45 We ave a abit in writing articles publised in scientiþc journals to make te work as Þnised as possible, to cover up all te tracks, to not worry about te blind alleys or describe ow you ad te wrong idea

What You ll Learn. Why It s Important

These students are setting up a tent. How do the students know how to set up the tent? How is the shape of the tent created? How could students find the amount of material needed to make the tent? Why

3 Ans. 1 of my $30. 3 on. 1 on ice cream and the rest on 2011 MATHCOUNTS STATE COMPETITION SPRINT ROUND

0 MATHCOUNTS STATE COMPETITION SPRINT ROUND. boy scouts are accompanied by scout leaders. Eac person needs bottles of water per day and te trip is day. + = 5 people 5 = 5 bottles Ans.. Cammie as pennies,

Verifying Numerical Convergence Rates

1 Order of accuracy Verifying Numerical Convergence Rates We consider a numerical approximation of an exact value u. Te approximation depends on a small parameter, suc as te grid size or time step, and

Notes: Most of the material in this chapter is taken from Young and Freedman, Chap. 12.

Capter 6. Fluid Mecanics Notes: Most of te material in tis capter is taken from Young and Freedman, Cap. 12. 6.1 Fluid Statics Fluids, i.e., substances tat can flow, are te subjects of tis capter. But

Build your skills: Perimeter and area Part 1. Working out the perimeter and area of different shapes

Working out the perimeter and area of different shapes This task has two parts. Part 1 In this part, you can brush up your skills and find out about perimeter and area. Part 2 In the second part, you can

Developing Conceptual Understanding of Number. Set J: Perimeter and Area

Developing Conceptual Understanding of Number Set J: Perimeter and Area Carole Bilyk cbilyk@gov.mb.ca Wayne Watt wwatt@mts.net Perimeter and Area Vocabulary perimeter area centimetres right angle Notes

Average and Instantaneous Rates of Change: The Derivative

9.3 verage and Instantaneous Rates of Cange: Te Derivative 609 OBJECTIVES 9.3 To define and find average rates of cange To define te derivative as a rate of cange To use te definition of derivative to

Answers to Exercises. Answers to Exercises 24.

Answers to Eercises CAPTER 10 CAPTER 10 LESSON 10.1 CAPTER 10 CAPTER 24. Answers to Eercises 1. polyedron; polygonal; triangles 2. PQR, TUS. PQUT, QRSU, RPTS 4. QU,PT,RS 5. 6 cm 6. GYPTAN 7. point E 8.

Shell and Tube Heat Exchanger

Sell and Tube Heat Excanger MECH595 Introduction to Heat Transfer Professor M. Zenouzi Prepared by: Andrew Demedeiros, Ryan Ferguson, Bradford Powers November 19, 2009 1 Abstract 2 Contents Discussion

- 1 - Handout #22 May 23, 2012 Huffman Encoding and Data Compression. CS106B Spring 2012. Handout by Julie Zelenski with minor edits by Keith Schwarz

CS106B Spring 01 Handout # May 3, 01 Huffman Encoding and Data Compression Handout by Julie Zelenski wit minor edits by Keit Scwarz In te early 1980s, personal computers ad ard disks tat were no larger

Tangent Lines and Rates of Change

Tangent Lines and Rates of Cange 9-2-2005 Given a function y = f(x), ow do you find te slope of te tangent line to te grap at te point P(a, f(a))? (I m tinking of te tangent line as a line tat just skims

In other words the graph of the polynomial should pass through the points

Capter 3 Interpolation Interpolation is te problem of fitting a smoot curve troug a given set of points, generally as te grap of a function. It is useful at least in data analysis (interpolation is a form

SAT Math Facts & Formulas

Numbers, Sequences, Factors SAT Mat Facts & Formuas Integers:..., -3, -2, -1, 0, 1, 2, 3,... Reas: integers pus fractions, decimas, and irrationas ( 2, 3, π, etc.) Order Of Operations: Aritmetic Sequences:

10-3 Area of Parallelograms

0-3 Area of Parallelograms MAIN IDEA Find the areas of parallelograms. NYS Core Curriculum 6.A.6 Evaluate formulas for given input values (circumference, area, volume, distance, temperature, interest,

f(a + h) f(a) f (a) = lim

Lecture 7 : Derivative AS a Function In te previous section we defined te derivative of a function f at a number a (wen te function f is defined in an open interval containing a) to be f (a) 0 f(a + )

The use of visualization for learning and teaching mathematics

Te use of visualization for learning and teacing matematics Medat H. Raim Radcliffe Siddo Lakeead University Lakeead University Tunder Bay, Ontario Tunder Bay, Ontario CANADA CANADA mraim@lakeeadu.ca rsiddo@lakeeadu.ca

Math 113 HW #5 Solutions

Mat 3 HW #5 Solutions. Exercise.5.6. Suppose f is continuous on [, 5] and te only solutions of te equation f(x) = 6 are x = and x =. If f() = 8, explain wy f(3) > 6. Answer: Suppose we ad tat f(3) 6. Ten

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

Writing Mathematics Papers

Writing Matematics Papers Tis essay is intended to elp your senior conference paper. It is a somewat astily produced amalgam of advice I ave given to students in my PDCs (Mat 4 and Mat 9), so it s not

AUTUMN UNIT 3. first half. Perimeter. Centimetres and millimetres. Metres and centimetres. Area. 3D shapes PART 3 MEASURES AND PROPERTIES OF SHAPES

PART AUTUMN first half MEASURES AND PROPERTIES OF SHAPES SECTION Perimeter SECTION Centimetres and millimetres SECTION Metres and centimetres SECTION Key Stage National Strategy CROWN COPYRIGHT 00 Area

How To Ensure That An Eac Edge Program Is Successful

Introduction Te Economic Diversification and Growt Enterprises Act became effective on 1 January 1995. Te creation of tis Act was to encourage new businesses to start or expand in Newfoundland and Labrador.

Optimized Data Indexing Algorithms for OLAP Systems

Database Systems Journal vol. I, no. 2/200 7 Optimized Data Indexing Algoritms for OLAP Systems Lucian BORNAZ Faculty of Cybernetics, Statistics and Economic Informatics Academy of Economic Studies, Bucarest

Lesson 3.1 Factors and Multiples of Whole Numbers Exercises (pages 140 141)

Lesson 3.1 Factors and Multiples of Whole Numbers Exercises (pages 140 141) A 3. Multiply each number by 1, 2, 3, 4, 5, and 6. a) 6 1 = 6 6 2 = 12 6 3 = 18 6 4 = 24 6 5 = 30 6 6 = 36 So, the first 6 multiples

Geometry Unit 6 Areas and Perimeters

Geometry Unit 6 Areas and Perimeters Name Lesson 8.1: Areas of Rectangle (and Square) and Parallelograms How do we measure areas? Area is measured in square units. The type of the square unit you choose

Grade 12 Assessment Exemplars

Grade Assessment Eemplars Learning Outcomes and. Assignment : Functions - Memo. Investigation: Sequences and Series Memo/Rubric 5. Control Test: Number Patterns, Finance and Functions - Memo 7. Project:

Geometric Stratification of Accounting Data

Stratification of Accounting Data Patricia Gunning * Jane Mary Horgan ** William Yancey *** Abstract: We suggest a new procedure for defining te boundaries of te strata in igly skewed populations, usual

SAT Math Must-Know Facts & Formulas

SAT Mat Must-Know Facts & Formuas Numbers, Sequences, Factors Integers:..., -3, -2, -1, 0, 1, 2, 3,... Rationas: fractions, tat is, anyting expressabe as a ratio of integers Reas: integers pus rationas

The EOQ Inventory Formula

Te EOQ Inventory Formula James M. Cargal Matematics Department Troy University Montgomery Campus A basic problem for businesses and manufacturers is, wen ordering supplies, to determine wat quantity of

What You ll Learn. Why It s Important

What is a circle? Where do you see circles? What do you know about a circle? What might be useful to know about a circle? What You ll Learn Measure the radius, diameter, and circumference of a circle.

Binary Search Trees. Adnan Aziz. Heaps can perform extract-max, insert efficiently O(log n) worst case

Binary Searc Trees Adnan Aziz 1 BST basics Based on CLRS, C 12. Motivation: Heaps can perform extract-max, insert efficiently O(log n) worst case Has tables can perform insert, delete, lookup efficiently

Unit 8 Angles, 2D and 3D shapes, perimeter and area

Unit 8 Angles, 2D and 3D shapes, perimeter and area Five daily lessons Year 6 Spring term Recognise and estimate angles. Use a protractor to measure and draw acute and obtuse angles to Page 111 the nearest

Catalogue no. 12-001-XIE. Survey Methodology. December 2004

Catalogue no. 1-001-XIE Survey Metodology December 004 How to obtain more information Specific inquiries about tis product and related statistics or services sould be directed to: Business Survey Metods

Lateral and Surface Area of Right Prisms

CHAPTER A Lateral and Surface Area of Right Prisms c GOAL Calculate lateral area and surface area of right prisms. You will need a ruler a calculator Learn about the Math A prism is a polyhedron (solid

2.23 Gambling Rehabilitation Services. Introduction

2.23 Gambling Reabilitation Services Introduction Figure 1 Since 1995 provincial revenues from gambling activities ave increased over 56% from $69.2 million in 1995 to $108 million in 2004. Te majority

Area and Volume Equations

Area and Volume Equations MODULE 16? ESSENTIAL QUESTION How can you use area and volume equations to solve real-world problems? LESSON 16.1 Area of Quadrilaterals 6.8.B, 6.8.D LESSON 16. Area of Triangles

Chapter 11. Limits and an Introduction to Calculus. Selected Applications

Capter Limits and an Introduction to Calculus. Introduction to Limits. Tecniques for Evaluating Limits. Te Tangent Line Problem. Limits at Infinit and Limits of Sequences.5 Te Area Problem Selected Applications

Maximum and minimum problems. Information sheet. Think about

Maximum and minimum problems This activity is about using graphs to solve some maximum and minimum problems which occur in industry and in working life. The graphs can be drawn using a graphic calculator

Area of Parallelograms, Triangles, and Trapezoids (pages 314 318)

Area of Parallelograms, Triangles, and Trapezoids (pages 34 38) Any side of a parallelogram or triangle can be used as a base. The altitude of a parallelogram is a line segment perpendicular to the base

Can a Lump-Sum Transfer Make Everyone Enjoy the Gains. from Free Trade?

Can a Lump-Sum Transfer Make Everyone Enjoy te Gains from Free Trade? Yasukazu Icino Department of Economics, Konan University June 30, 2010 Abstract I examine lump-sum transfer rules to redistribute te

43 Perimeter and Area

43 Perimeter and Area Perimeters of figures are encountered in real life situations. For example, one might want to know what length of fence will enclose a rectangular field. In this section we will study

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

Calculating Area, Perimeter and Volume

Calculating Area, Perimeter and Volume You will be given a formula table to complete your math assessment; however, we strongly recommend that you memorize the following formulae which will be used regularly

GAP CLOSING. 2D Measurement GAP CLOSING. Intermeditate / Senior Facilitator s Guide. 2D Measurement

GAP CLOSING 2D Measurement GAP CLOSING 2D Measurement Intermeditate / Senior Facilitator s Guide 2-D Measurement Diagnostic...4 Administer the diagnostic...4 Using diagnostic results to personalize interventions...4

How To Find The Area Of A Shape

9 Areas and Perimeters This is is our next key Geometry unit. In it we will recap some of the concepts we have met before. We will also begin to develop a more algebraic approach to finding areas and perimeters.

Theoretical calculation of the heat capacity

eoretical calculation of te eat capacity Principle of equipartition of energy Heat capacity of ideal and real gases Heat capacity of solids: Dulong-Petit, Einstein, Debye models Heat capacity of metals

Unit 5 Length. Year 4. Five daily lessons. Autumn term Unit Objectives. Link Objectives

Unit 5 Length Five daily lessons Year 4 Autumn term Unit Objectives Year 4 Suggest suitable units and measuring equipment to Page 92 estimate or measure length. Use read and write standard metric units

Measurement Length, Area and Volume

Length, Area and Volume Data from international studies consistently indicate that students are weaker in the area of measurement than any other topic in the mathematics curriculum Thompson & Preston,

For Sale By Owner Program. We can help with our for sale by owner kit that includes:

Dawn Coen Broker/Owner For Sale By Owner Program If you want to sell your ome By Owner wy not:: For Sale Dawn Coen Broker/Owner YOUR NAME YOUR PHONE # Look as professional as possible Be totally prepared

NAFN NEWS SPRING2011 ISSUE 7. Welcome to the Spring edition of the NAFN Newsletter! INDEX. Service Updates Follow That Car! Turn Back The Clock

NAFN NEWS ISSUE 7 SPRING2011 Welcome to te Spring edition of te NAFN Newsletter! Spring is in te air at NAFN as we see several new services cropping up. Driving and transport emerged as a natural teme

Exercise 11.1. Q.1. A square and a rectangular field with measurements as given in the figure have the same perimeter. Which field has a larger area?

11 MENSURATION Exercise 11.1 Q.1. A square and a rectangular field with measurements as given in the figure have the same perimeter. Which field has a larger area? (a) Side = 60 m (Given) Perimeter of

UNIFORM FLOW. Key words Uniform flow; most economical cross-section; discharge; velocity; erosion; sedimentation

Capter UNIFORM FLOW.. Introduction.. Basic equations in uniform open-cannel flow.3. Most economical cross-section.4. Cannel wit compound cross-section.5. Permissible velocity against erosion and sedimentation

Computer Science and Engineering, UCSD October 7, 1999 Goldreic-Levin Teorem Autor: Bellare Te Goldreic-Levin Teorem 1 Te problem We æx a an integer n for te lengt of te strings involved. If a is an n-bit

An Introduction to Milankovitch Cycles

An Introduction to Milankovitc Cycles Wat Causes Glacial Cycles? Ricard McGeee kiloyear bp 45 4 35 3 5 15 1 5 4 - -4-6 -8 temperature -1 Note te period of about 1 kyr. Seminar on te Matematics of Climate

Volume of Right Prisms Objective To provide experiences with using a formula for the volume of right prisms.

Volume of Right Prisms Objective To provide experiences with using a formula for the volume of right prisms. www.everydaymathonline.com epresentations etoolkit Algorithms Practice EM Facts Workshop Game

GRADE SIX-CONTENT STANDARD #4 EXTENDED LESSON A Permission Granted. Making a Scale Drawing A.25

GRADE SIX-CONTENT STANDARD #4 EXTENDED LESSON A Permission Granted Making a Scale Drawing Introduction Objective Students will create a detailed scale drawing. Context Students have used tools to measure

10-4-10 Year 9 mathematics: holiday revision. 2 How many nines are there in fifty-four?

DAY 1 Mental questions 1 Multiply seven by seven. 49 2 How many nines are there in fifty-four? 54 9 = 6 6 3 What number should you add to negative three to get the answer five? 8 4 Add two point five to

Volume of a Cylinder

Volume of a Cylinder Focus on After this lesson, you will be able to φ determine the volume of a cylinder How much water do you use? You might be surprised. The water storage tank shown has a height of

Circumference and Area of a Circle

Overview Math Concepts Materials Students explore how to derive pi (π) as a ratio. Students also study the circumference and area of a circle using formulas. numbers and operations TI-30XS MultiView two-dimensional

GAP CLOSING. 2D Measurement. Intermediate / Senior Student Book

GAP CLOSING 2D Measurement Intermediate / Senior Student Book 2-D Measurement Diagnostic...3 Areas of Parallelograms, Triangles, and Trapezoids...6 Areas of Composite Shapes...14 Circumferences and Areas

Dear Grade 4 Families,

Dear Grade 4 Families, During the next few weeks, our class will be exploring geometry. Through daily activities, we will explore the relationship between flat, two-dimensional figures and solid, three-dimensional

E XPLORING QUADRILATERALS

E XPLORING QUADRILATERALS E 1 Geometry State Goal 9: Use geometric methods to analyze, categorize and draw conclusions about points, lines, planes and space. Statement of Purpose: The activities in this

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:

Heat Exchangers. Heat Exchanger Types. Heat Exchanger Types. Applied Heat Transfer Part Two. Topics of This chapter

Applied Heat Transfer Part Two Heat Excangers Dr. Amad RAMAZANI S.A. Associate Professor Sarif University of Tecnology انتقال حرارت کاربردی احمد رمضانی سعادت ا بادی Autumn, 1385 (2006) Ramazani, Heat Excangers

2.12 Student Transportation. Introduction

Introduction Figure 1 At 31 Marc 2003, tere were approximately 84,000 students enrolled in scools in te Province of Newfoundland and Labrador, of wic an estimated 57,000 were transported by scool buses.

Guide to Cover Letters & Thank You Letters

Guide to Cover Letters & Tank You Letters 206 Strebel Student Center (315) 792-3087 Fax (315) 792-3370 TIPS FOR WRITING A PERFECT COVER LETTER Te resume never travels alone. Eac time you submit your resume

MAIN IDEA The rectangle at the right has an area of 20 square units. The distance around the rectangle is 5 + 4 + 5 + 4, or 18 units.

1-9 Algebra: Area Formulas MAIN IDEA The rectangle at the right has an area of 20 square units. The distance around the rectangle is 5 + 4 + 5 + 4, or 1. Find the areas of rectangles and squares. New Vocabulary

Note nine: Linear programming CSE 101. 1 Linear constraints and objective functions. 1.1 Introductory example. Copyright c Sanjoy Dasgupta 1

Copyrigt c Sanjoy Dasgupta Figure. (a) Te feasible region for a linear program wit two variables (see tet for details). (b) Contour lines of te objective function: for different values of (profit). Te

Section 3.3. Differentiation of Polynomials and Rational Functions. Difference Equations to Differential Equations

Difference Equations to Differential Equations Section 3.3 Differentiation of Polynomials an Rational Functions In tis section we begin te task of iscovering rules for ifferentiating various classes of

Imperial Length Measurements

Unit I Measuring Length 1 Section 2.1 Imperial Length Measurements Goals Reading Fractions Reading Halves on a Measuring Tape Reading Quarters on a Measuring Tape Reading Eights on a Measuring Tape Reading

Investing in Roads: Pricing, Costs and New Capacity

Investing in Roads: Pricing, Costs and New Capacity Cristoper rcer Stepen Glaister Department of Civil and Environmental Engineering Imperial College London November 2006 Researc commissioned by te Independent

CHAPTER 8: DIFFERENTIAL CALCULUS

CHAPTER 8: DIFFERENTIAL CALCULUS 1. Rules of Differentiation As we ave seen, calculating erivatives from first principles can be laborious an ifficult even for some relatively simple functions. It is clearly

Recall from last time: Events are recorded by local observers with synchronized clocks. Event 1 (firecracker explodes) occurs at x=x =0 and t=t =0

1/27 Day 5: Questions? Time Dilation engt Contraction PH3 Modern Pysics P11 I sometimes ask myself ow it came about tat I was te one to deelop te teory of relatiity. Te reason, I tink, is tat a normal

College Planning Using Cash Value Life Insurance

College Planning Using Cas Value Life Insurance CAUTION: Te advisor is urged to be extremely cautious of anoter college funding veicle wic provides a guaranteed return of premium immediately if funded