2.1­2.2 Notes.notebook
February 19, 2013
Lesson 2.1 and 2.2 Direct and Indirect Variation
Feb 19­6:26 AM
Feb 19­6:28 AM
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2.1­2.2 Notes.notebook
February 19, 2013
Feb 19­6:30 AM
Feb 19­6:30 AM
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2.1­2.2 Notes.notebook
February 19, 2013
Feb 19­6:30 AM
Directions: Choose “directly” or “inversely” to complete each sentence.
The weight of a newspaper varies _________________ as the number of pages it contains.
The speed of a runner varies _________________ as the time it takes her to travel a given distance.
The number of desks that can fit in a classroom varies _________________ as the size of the desks.
The area of a circle varies _________________ as the square of its radius.
The perceived loudness of a radio varies _________________ as the square of the listener’s distance from the speakers.
Feb 19­6:31 AM
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2.1­2.2 Notes.notebook
February 19, 2013
Example #1
The time t required to do a job varies inversely as the number of workers w. It takes 5 hours for 8 cement finishers to do a job. How long would it take 12 workers to do the same job?
Feb 19­6:32 AM
1. The height that a ball bounces varies directly with the height from which it is dropped. A certain ball bounces 30 cm when dropped from a height of 50cm. How high will the ball bounce if dropped from a height of 120cm?
Feb 19­6:33 AM
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2.1­2.2 Notes.notebook
February 19, 2013
2. The number of chairs on a ski lift is inversely proportional to the distance between them. A lift has 70 chairs when they are spaced 24 meters apart. If 80 evenly spaced chairs are used on the lift, how much space will be left between them?
Feb 19­6:33 AM
3. The amount that a spring stretches varies directly with the weight of the object attached to it. If a spring is stretched 10 cm by a weight of 8kg, how much will it be stretched by a weight of 3kg?
Feb 19­6:34 AM
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2.1­2.2 Notes.notebook
February 19, 2013
4. For piano wires under the same tension, the number of vibrations per second (frequency) of each wire is inversely proportional to the length of the wire. A wire 0.75 meters long vibrates 480 times per second. How long is a wire that vibrates 300 times per second?
Feb 19­6:34 AM
5. The time it takes to fly from Los Angeles to New York is inversely proportional to the speed of the plane. If the trip takes 6 hours at 900km/hour, how long would it take at 800km/hour?
Feb 19­6:33 AM
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2.1­2.2 Notes.notebook
February 19, 2013
6. The number of calories in a container of milk is directly proportional to the amount of milk in the container. If there are 160 calories in an 8­ounce glass of milk, find the number of calories in a 15­ounce glass of milk.
Feb 19­6:35 AM
7. The amount of fertilizer needed for a lawn varies directly with the area of the lawn. If 4 points of fertilizer are needed for 500 square feet of lawn, how much is needed for Dr. Quagmire’s lawn, which is rectangular in shape and measures 25 feet by 50 feet? Feb 19­6:35 AM
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