1 / 13

DIRECT & INVERSE VARIATION

DIRECT & INVERSE VARIATION. Can you distinguish between the two?. Description. Two related quantities can vary in one of two ways: directly or inversely In direct variation, as one quantity increases, so does the other.

minowa
Télécharger la présentation

DIRECT & INVERSE VARIATION

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. DIRECT & INVERSEVARIATION Can you distinguish between the two?

  2. Description • Two related quantities can vary in one of two ways: directly or inversely • In direct variation, as one quantity increases, so does the other. • In inverse variation, as one quantity increases, the other one decreases. • In both types, there is a constant factor k which describes the variation.

  3. Direct Variation Examples • ΔABC’s side lengths are 3 – 4 – 5. • Δ XYZ’s side lengths are 12 – 16 – 20. • The scale factor k is 4. (12 ÷ 3 = 4) • This is direct variation. • A 5” × 7” photo is enlarged so that the short side is 8”. How long is the long side? (Solve with proportion) • 5 : 7 = 8 : 11.2 (direct variation)

  4. Inverse Variation Examples • At sea level, the air pressure is 14.7 pounds per square inch. • At 9,000 feet altitude above sea level, the air pressure is 10.5 psi. • At 25,000 ft altitude, it’s 5.46 psi. • This is an example of inverse variation. • Source: www.engineeringtoolbox.com

  5. Do YOU Know Which is Which? • For each pair of quantities, state Direct if it is an example of direct variation, or Inverse if it is an example of inverse variation. • If the two quantities are not related, print “Not Related.” • Ready?

  6. How Are They Related? 1. Depth of the water vs. Water pressure • DIRECT 2. Altitude above sea level vs. Air pressure • INVERSE 3. Speed of the car vs. Time it takes to get there • INVERSE

  7. How Related? • Price of coconuts in Tahiti vs. Number of alligators in Florida • NOT RELATED • Time you spend studying for test vs. Score you make on test. • Usually it’s DIRECT, although at some point sleep will help you more

  8. How Related? • Distance from light source vs. Brightness of the light • INVERSE. Light varies inversely with the square of the distance. • Ratio of side lengths of two similar figures and ratio of their areas. • DIRECT. The area ratio is the square of the side length ratio.

  9. How Related? • Amount of taxable income vs. Amount of income tax owed. • DIRECT • Amount of paycheck deductions vs. Amount of take-home pay • INVERSE • Restaurant bill vs. Server’s tip • DIRECT

  10. How Related? • How much a photograph is enlarged vs. Picture quality • INVERSE. Picture will get grainier. • State Population vs. # of Electoral Votes • DIRECT…of course, some states are “more equal” than others

  11. How Related? • Amount of evidence against defendant vs. Likelihood of acquittal (“not guilty”) • INVERSE • Color of a car vs. How fast it goes • NOT RELATED • How much you adore your current boyfriend/girlfriend vs. How much your parents like him / her. • Usually….INVERSE

  12. Rectangular Garden • Suppose you have 400 feet of fence with which to enclose a rectangular garden. • L is length of garden, and W is the width. • The perimeter can be expressed as this equation: 2(L + W) = 400 or L + W = 200 • The area is L × W • As L increases, what happens to W? • It decreases. This is an inverse variation.

  13. Rectangular Garden • P = 400. Suppose L = 120. W = ? • L + w = 200 200 – 120 = 80 W = 80 • Area of garden is 120 × 80 = 9600 ft² • What dimensions maximize the area of the garden? • If garden is a square: L = W = 100 ft. • Area = 100 × 100 = 10,000 ft² • What dimensions make it “golden?”

More Related