Inverse, Joint, and Combined Variation Section 8.1 beginning on page 480.

Slides:

Advertisements

Similar presentations

Inverse, Joint, and Combined Variation

Advertisements

Lesson 12.1 Inverse Variation pg. 642

What You Will Learn Recognize and solve direct and joint variation problems Recognize and solve inverse variation problems.

Chapter 5 Section 1 variation.

Types of Variation Direct Variation: y varies directly as x. As x increases, y also increases. As x decreases, y also decreases. Equation for Direct.

Three Forms of an Equation of a Line

TODAY IN GEOMETRY…  Warm up: Writing equations of a circle  Learning Target : 11.4 You will find the arc length and circumferences of circles  Independent.

Variation Variation describes the relationship between two or more variables. Two variables, x and y, can vary directly or inversely. Three or more variables.

EXAMPLE 5 Write a joint variation equation The variable z varies jointly with x and y. Also, z = –75 when x = 3 and y = –5. Write an equation that relates.

Direct Variation: y varies directly as x (y is directly proportional to x), if there is a nonzero constant k such th at 3.7 – Variation The number k is.

Lesson 3-5 Example Example 1 What is the volume of the rectangular prism? 1.The length of the rectangular prism is 6 units. The width of the rectangular.

Rewrite Formulas and Equations

Volume of rectangular prisms. B V= Bh B = area of the base The base of a rectangular prism is a rectangle h The area of a rectangle is length times width.

ObjectivesExamples DefinitionActivity Prepared by: Michael Lacsina Val de Guzman.

Warm Up Solve each equation. 2.4 = x x = 1.8(24.8)

PAP Algebra 2 NOTES 9.4 TLW… Simplify and work problems dealing with direct, inverse, and joint variations.

Copyright © Cengage Learning. All rights reserved. Graphs; Equations of Lines; Functions; Variation 3.

Investigation 3: Inverse Variation

Variation Unit 13.

Notes Over 3.2 Equations and Formulas When using a formula, you must first know what each variable represents. Example The formula for the area of a square.

Chapter 10 Test Formula Review.  Find the circumference of a circle with a diameter of 10. Identify the formula needed for the following questions.

§ 6.8 Modeling Using Variation. Blitzer, Intermediate Algebra, 5e – Slide #2 Section 6.8 Variation Certain situations occur so frequently in applied situations.

Section – Ratio, Proportion, Variation The Vocabulary.

DIRECT, INVERSE, AND JOINT VARIATION Unit 3 English Casbarro.

Lesson 2.8, page 357 Modeling using Variation Objectives: To find equations of direct, inverse, and joint variation, and to solve applied problems involving.

2.8 Modeling Using Variation Pg. 364 #2-10 (evens), (evens) Objectives –Solve direct variation problems. –Solve inverse variation problems. –Solve.

Direct Variation Talking about the relationship between variables in a new way!!! Fun, Huh?

1 Algebra 2: Section 9.1 Inverse and Joint Variation.

DIRECT VARIATION In a DIRECT VARIATION, as one quantity increases, the other quantity increases. Equation of Direct Variation.

Certain situations exist where:  If one quantity increases, the other quantity also increases.  If one quantity increases, the other quantity decreases.

1.10 Variation.

Volume of prisms and cylinders

10-1 Inverse Variation 10-2 Rational Functions 10-3 Simplifying Rational Expressions 10-4 Multiplying and Dividing Rational Expressions 10-5 Adding and.

Sullivan Algebra and Trigonometry: Section 2.5 Variation Objectives Construct a Model Using Direct Variation Construct a Model Using Inverse Variation.

Surface area & volume UNIT 4. Prisms SECTION 1  Prism: three dimensional shape with two parallel sides  Bases: sides parallel to each other  Lateral.

Variation Functions Essential Questions

College Algebra 3.6 Polynomial and Rational Inequalities 3.7 Variation.

Direct Variation  Let x and y denote two quantities. Then y varies directly with x, or y is directly proportional to x, if there is a nonzero number.

Direct, Inverse & Joint Variation. Direct Variation The variables x & y vary directly: Direct  Divide BIGGER.

11-3: Direct and Inverse Variation

3-8 Solving Equations and Formulas Objective Students will be able to solve equations for given variables.

Joint and Combined Variation Review of Variations Direct Variation Inverse Variation Formula General Equation.

LESSON 12-1 INVERSE VARIATION Algebra I Ms. Turk Algebra I Ms. Turk.

9-1 Notes. Direct Variation: Two variables, y and x, vary directly if: y = If k is any nonzero constant. Example: The equation: y = 5x exhibits direct.

Algebra 2 Notes May 19, Warm-Ups Remembering Direct Variation If you need help remembering, refer to page 74 Example 4 y varies directly with x:

Variation Functions Section 5.1. Direct Variation.

9.1: Inverse and Joint Variation Objectives: Students will be able to… Write and use inverse variation models Write and use joint variation models.

Section 5.1 Direct, Inverse, and Joint Variation.

College Algebra K/DC Monday, 07 March 2016

Precalculus Section 6.4 Find and graph equations of hyperbolas Geometric definition of a hyperbola: A hyperbola is the set of all points in a plane such.

7.3 Ratio, Proportion, and Variation Part 2: Direct and Indirect Variation.

Direct Variation Equations

Notes Over 11.3 Using Direct and Inverse Variation When x is 4, y is 5. Find the equation that relates x and y in each case. Direct Variation Two quantities.

Direct, Inverse & Joint Variation Section 2.5. Direct Variation 2 variables X & Y show direct variation provided y = kx & k ≠ 0. The constant k is called.

Bellwork Find the inverse of the following functions

Section 5.1: Multipliying Polynomial Expressions by Monomials

CHAPTER 3 SECTION 7.

9.1 Inverse & Joint Variation

Variation Objectives: Construct a Model using Direct Variation

Equation of Direct Variation

Find volumes of cylinders.

10-7 Volume of Pyramids and Cones

Do Now: Graph the following: Y=3x.

Direct and Inverse VARIATION Section 8.1.

Rational Expressions and Equations

8.1 Model Inverse & Joint Variation

Volume of Prisms.

Use Formula An equation that involves several variables is called a formula or literal equation. To solve a literal equation, apply the process.

Company Name 7.1- Inverse Variation.

Presentation transcript:

Inverse, Joint, and Combined Variation Section 8.1 beginning on page 480

Making Connections

Examples You may be given enough information to write an equation and then have to state what time of variation is occurring between the values. Example 2 (pg. 482): Write an equation for the volume of the prism, and identify the type of variation and the constant of variation. Then find the volume of the prism if the length of the base is 4 inches and the width of the base is 2 inches.

Examples You might be told the type of variation, along with additional information (either k or values of x, y, and possibly z) and then have to write an equation and/or find additional values or x, y, and possibly z. Example 1 (pg. 482): The variable y varies inversely as x, and y=13.5 when x=4.5. Find the constant of variation, write an equation for the relationship, and find y when x is 0.5,1,1.5, and 2. What do we know? We have enough info to find k, and then write the equation. The point (4.5,13.5) From this equation, we know that if we divide each x value into 60.75, we will find the corresponding y – value. x y

Non-Linear Relationships This is a type of joint variation, specifically, direct variation. [I would accept either answer, but be able to justify them] Use the equation to find each area from the given values of x. x

The Tough Stuff Z varies jointly as x and y and inversely as w. Write the appropriate combined-variation equation, and find z for the given values of x, y, and w. Ex: z=54 when x=9,y=2, and w=1.5; x=1.5, y=2.4, and w=3. The variables that vary jointly (or directly) will be in the numerator along with k, and the vary inversely will be in the denominator. Use this info to write the combined variation equation: Use this equation and the given values of x, y, and w to find z

Basic Practice

Word Problem Practice 1)Write an equation for the volume of a rectangular prism whose base has a length of 12 inches. Identify the type of variation and the constant of variation. Find the volume of the prism if the width of the base is 2 inches and the height of the prism is 4 inches. 2)Write a formula for the area, A, of a circle whose radius is r. Identify the type of variation and the constant of variation. Find the area of the circle when r is 1.5, 2.5, and )The time, t, that it takes to travel a given distance, d, varies inversely as r, the rate of speed. A certain trip can be made in 7.5 hours at a rate of 60 miles per hour. Find the constant of variation, and write an inverse variation equation. Find t to the nearest tenth when r is 40, 45, 50, and 55. Joint Variation (or direct variation)