• Share
  • Email
  • Embed
  • Like
  • Save
  • Private Content
MATH 12 Week3 ratio
 

MATH 12 Week3 ratio

on

  • 996 views

 

Statistics

Views

Total Views
996
Views on SlideShare
996
Embed Views
0

Actions

Likes
0
Downloads
19
Comments
0

0 Embeds 0

No embeds

Accessibility

Categories

Upload Details

Uploaded via as Microsoft PowerPoint

Usage Rights

© All Rights Reserved

Report content

Flagged as inappropriate Flag as inappropriate
Flag as inappropriate

Select your reason for flagging this presentation as inappropriate.

Cancel
  • Full Name Full Name Comment goes here.
    Are you sure you want to
    Your message goes here
    Processing…
Post Comment
Edit your comment
  • Week 3 Day 1 Ratio, Variation and Proportion (Algebra and Trigonometry, Young 2nd Edition, page 304-313)
  • Week 3 Day 1
  • Week 3 Day 1
  • Week 3 Day 1
  • Week 3 Day 1
  • Week 3 Day 1
  • Week 3 Day 1
  • Week 3 Day 1
  • Week 3 Day 1
  • Week 3 Day 1
  • Week 3 Day 1
  • Week 3 Day 1
  • Week 3 Day 1
  • Week 3 Day 1
  • Week 3 Day 1
  • Week 3 Day 1
  • Week 3 Day 1
  • Week 3 Day 1
  • Week 3 Day 1

MATH 12 Week3 ratio MATH 12 Week3 ratio Presentation Transcript

  • RATIO, VARIATION AND PROPORTION
    MATH10
    ALGEBRA
    Week 3 Day 1 Ratio, Variation and Proportion (Algebra and Trigonometry, Young 2nd Edition, page 304-313)
  • Week 3 Day 1
    TODAY’S OBJECTIVE
    At the end of the lesson the students are expected to:
    Use ratio and proportion in solving problems involving them,
    Identify the different types of variation,
    Understand the difference between direct variation and inverse variation,
    Understand the difference between combined variation and joint variation, and
    Develop mathematical models using direct variation, inverse variation, combined variation and joint variation.
  • Week 3 Day 1
    Definition
    RATIO
    A ratio is an indicated quotient of two quantities. Every ratio is a fraction and all ratios can be described by means of a fraction. The ratio of x and y is written as x : y, it can also be represented as
    Thus,
  • Week 3 Day 1
    EXAMPLE
    1. Express the following ratios as simplified fractions:
    a) 5 : 20
    b)
    2. Write the following comparisons as ratios reduced to lowestterms. Use common units whenever possible.
    a) 4 students to 8 students
    b) 4 days to 3 weeks
    c) 5 feet to 2 yards
    d) About 10 out of 40 students took Math Plus
  • Week 3 Day 1
    Definition
    PROPORTION
    A proportion is a statement indicating the equality of two ratios.
    Thus, , , are proportions.
    In the proportion x : y = m : n, x and n are called the extremes, y and m are called the means.x and m are the called the antecedents, y and n are called the consequents.
    In the event that the means are equal, they are called the mean proportional.
  • Week 3 Day 1
    EXAMPLE
    1. Find the mean proportional of
    2. Determine the value of x in the following proportion:
    a) 2 : 5 = x : 20
    b)
  • Week 3 Day 1
    Definition
    VARIATION
    A variation is the name given to the study of the effects of changes among related quantities.
    Variation describes the relationship between variables.
  • Week 3 Day 1
    Direct Variation
    When one quantity is a constant multiple of another quantity, we say that the quantities are directlyproportional to one another .
    Let x and y represent two quantities. The following are equivalent statements:
    • y = kx, where k is a nonzero constant.
    • y varies directly with x.
    • y is directly proportional to x.
    The constant k is called the constant of variation or the constant of proportionality.
    Definition page 304
  • Week 3 Day 1
    EXAMPLE
    Write an equation that describes each variation.
    d is directly proportional to t. d=r when t=1.
    V is directly proportional to both l and w.V=6h when w=3 qndh=4.
    24. W is directly proportional to both R and the square of I. W=4 when R=100 and I=0.25.
    (Exercises page 309)
  • Week 3 Day 1
    EXAMPLE
    In the United States, the costs of electricity is directly proportional to the number of kilowatt hours (kWh) used. If a household in Tennessee on average used 3098 kWh per month and had an average monthly electric bill of $179.99, find a mathematical model that gives the cost of electricity in Tennessee in terms of the number of kWh used.(Example 1 page 304)
    2. Hooke’s Law states that the force needed to keep a spring stretched x units beyond its natural length is directly proportional x. Here the constant of proportionality is called a spring constant.
    Write Hooke’s Law as an equation.
    If a spring has a natural length of 10 cm and a force of 40 N is required to maintain the spring stretched to a length of 15 cm, find the spring constant.
    What force is needed to keep the spring stretched to a length of 14cm? ( Exercise 23 page 191 from Algebra & Trig. by Stewart, Redlin & Watson, 2nd edition)
  • Week 3 Day 1
    Direct Variation with Powers
    Let x and y represent two quantities. The following are equivalent statements:
    • , where k is a nonzero constant.
    • y varies directly with the nth power of x.
    • y is directly proportional to the nth power of x.
    Definition page 305
  • Week 3 Day 1
    EXAMPLE
    A brother and sister have weight (pounds) that varies as the cube of the cube of height (feet) and they share the same proportionality constant . The sister is 6 feet tall and weighs 170 pounds. Her brother is 6’4” tall. How much does he weigh?
    (Your Turn page 306)
  • Week 3 Day 1
    Inverse Variation
    Let x and y represent two quantities. The following are equivalent statements:
    • , where k is a nonzero constant.
    • yvaries inversely with x.
    • y is inversely proportional to x.
    The constant k is called the constant of variation or the constant of proportionality.
    Definition page 306
  • Week 3 Day 1
    EXAMPLE
    The number of potential buyers of a house decreases as the price of the house increases (see the graph on the below). If the number of potential buyers of a house in a particular city is inversely proportional to the price of the house, find a mathematical equation that describes the demand for the houses as it relates to the price. How many potential buyers will there be for a $2 million house? (Example 3 page 306)
    (100,1000)
    1000
    800
    Demand (number of potential buyers)
    600
    (200,500)
    400
    (400,250)
    200
    (600,167)
    200
    600
    800
    400
    Price of the house (in thousands of dollars)
  • Week 3 Day 1
    Inverse Variation with Powers
    Definition page 307
  • Week 3 Day 1
    Joint Variation and Combined Variation
    • When one quantity is proportional to the product of two or more other quantities, the variation is called joint variation.
    Example: Simple interest which is defined as
    • When direct variation and inverse variation occur at the same time, the variation is called combined variation.
    Example: Combined gas law in chemistry,
    Definition page 307
  • Week 3 Day 1
    EXAMPLE
    The gas in the headspace of a soda bottle has a volume of 9.0 ml, pressure of 2 atm (atmospheres), and a temperature of 298K (standard room temperature of 77⁰F). If the soda bottle is stored in a refrigerator, the temperature drops to approximately 279K (42⁰F). What is the pressure of the gas in the headspace once the bottle is chilled?
    (Example 4 page 308)
  • Week 3 Day 1
    SUMMARY
    Direct, inverse, joint and combined variation can be used to model the relationship between two quantities. For two quantities x and y we say that:
    Joint variation occurs when one quantity is directly proportional to two or more quantities.
    Combined variation occurs when one quantity is directly proportional to one or more quantities and inversely proportional to one or more other quantities.
  • Week 3 Day 1
    CLASSWORK
    #s page 20, 27,46,53 page 309-310
    HOMEWORK
    #s 22, 32, 33,36, 37, 39,40,42,43,47 page 309-313