Inverse and Direct Variation.notebook
December 04, 2015
Direct and Inverse Variation
Objective:
Write and use inverse variation models
Write and use direct variation models
WHY??
Connection to Physics: Newton's Law of Universal Gravitation is a combined variation
Title Slide
1
Inverse and Direct Variation.notebook
December 04, 2015
Direct Variation: Definition: If y varies directly with x, then as the value of x
increases, the value of y also increases. Or vice versa.
x and y vary directly if for a constant k, _____________________. The ratio, k, is a constant. Example of Direct Variation:
The circumference (C) of a circle varies directly as the diameter.
Direct Variation
2
Inverse and Direct Variation.notebook
December 04, 2015
Inverse Variation:
Definition: An inverse variation is a variation where as one increases
the other decreases in proportion.
x and y vary inversely if for a constant k, _________________.
The product, k, is the constant of variation.
Example of Inverse Variation:
The length (l) varies inversely as the width (w) for a rectangle of a
constant area (A).
Inverse Variation
3
Inverse and Direct Variation.notebook
December 04, 2015
Dec 3­1:54 PM
4
Inverse and Direct Variation.notebook
December 04, 2015
Determine whether x and y vary directly or inversely.
What Type?
5
Inverse and Direct Variation.notebook
December 04, 2015
How to find k and write an equation that relates the variables.
The distance traveled at a constant speed varies directly as the time traveled. Denny traveled 312 miles in 6 hours. First, find the constant of variation, k. Second, write an equation that relates the variables. Last, find how far he will travel in 4.5 hours.
Direct 1
6
Inverse and Direct Variation.notebook
December 04, 2015
The weight of a steel cable varies directly with its length. The weight of a 3­
meter section is 1.2 kilograms. First, find the constant of variation, k. Second, write an equation that relates the variables. Last, determine how heavy a 175­meter roll of cable is.
Direct 2
7
Inverse and Direct Variation.notebook
December 04, 2015
The amount that a spring stretches is directly proportional to 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?
Direct 3
8
Inverse and Direct Variation.notebook
December 04, 2015
The variables x and y vary inversely. Write and equation that relates the variables.
x = 2, y = 4
x = 1/2, y = 6
x = 3, y = .01
Inverse 1
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Inverse and Direct Variation.notebook
December 04, 2015
Boyle’s Law states that for a constant temperature, the pressure, P, of a gas varies inversely with its volume, V. A sample of hydrogen gas has a volume of 8.56 liters at a pressure of 1.5 atmospheres.
First, find the constant of variation, k. Second, write an equation that relates P and V. Last, find the volume of the hydrogen gas if the temperature remains constant and the pressure changes to 1.2 atmospheres.
Inverse 2
10
Inverse and Direct Variation.notebook
December 04, 2015
The amount of time necessary to make a trip varies inversely as the rate of travel. At 40 miles per hour it takes Valerie 5 hours to reach her destination. First, find the constant of variation, k. Second, write an equation that relates the variables. Last, find how long it would take if she drove at 50 miles per hour.
Inverse 3
11
Inverse and Direct Variation.notebook
December 04, 2015
The current in an electrical circuit varies inversely as the amount of resistance in the circuit. The current is 10 amps when the resistance is 24 ohms. Find the current when the resistance is 30 ohms.
Inverse 4
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Inverse and Direct Variation.notebook
December 04, 2015
Determining the type of Variation given a table
Type:
Direct
Inverse
Remember:
Find k for
each pair
of x and y.
They must
all be the
same to
be
variation.
X
Y
X
Y
5
55
2
35
6
66
7
10
7
77
10
7
Using Tables
13
Inverse and Direct Variation.notebook
December 04, 2015
Practice with tables:
X
Y
X
Y
X
Y
3
16
2
9
2
5
6
8
8
36
4
9
24
2
16
72
6
13
tables practice
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