Inverse variation

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Inverse variation
With inverse variation the independent variable,
x, appears in the denominator of the equation. An
example is where k is the constant of
variation. Types of inverse variation
include Linear Quadratic Cubic Square
root With all types of inverse variation as x
increases, y decreases and when x decreases, y
increases.
y varies
y ? 1/x
inversely as x
y varies inversely as the
y ? 1/x2
square of x
y varies inversely as the
y ? 1/x3
cube of x
y varies inversely as the
y ? 1/?x
square root of x
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Example 1
The speed at which a web page downloads is
inversely proportional to the number of people
connected to the net. A page downloads at 30 kb/s
when 6 people are connected. a) What speed would
it download the page if 5 people are online? b)
How many people were online if the page
downloaded at 20 kb/s?
? write a proportion statement
a) s ? 1/p
b) s 180/p 20 180/p 20p 180 p 180
? 20 p 9 people
? form an equation, add the constant of
variation k
s k/p
? sub in the initial values
30 k/6
? solve for k
k 30 6 180
? rewrite the equation
s 180/p
? answer the question
s 180/5 36 kb/s
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Example 2
The intensity of the signal sent out by a data
projector is inversely proportional to the square
of the distance of the projector to the screen.
At a distance of 32m the intensity is 450
candela (C). a) What is the intensity of light 4m
from the projector? b) How far from the screen is
the projector if the intensity is 128 C ?
? write a proportion statement
a) I ? 1/d2
b) I 4608/d2 128 4608/d2 128d2 4608
d2 4608 ? 128 d2 36 d 6m
? form an equation, add the constant of
variation k
I k/d2
? sub in the initial values
450 k/322
? solve for k
k 450 1024 4608
? rewrite the equation
I 4608/d2
? answer the question
I 4608/42 288 C
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Todays work
Exercise 12G page 386 Q1, 2, 8, 9, 11 to 15