Math 1310 Class Notes – Section 3.3, Page 1 of 4
Math 1310
Section 3.3
Variation
You’ll be asked to solve some problems involving functions using
variation.
We’ll
consider three types of variation.
•
Variation formulas
Direct variation
:
We say
y
varies directly as
x
, or
y
is directly proportional to
x
, if
,
kx
y
=
where
k
is a constant
( 29
.
0
≠
k
Inverse variation
:
We say
y
varies inversely as
x
, or
y
is inversely proportional to
x
, if
,
x
k
y
=
where
k
is a constant
( 29
.
0
≠
k
Joint variation
:
We way
y
varies jointly as
x
and
z
, or
y
is jointly proportional to
x
and
z
,
if
,
kxz
y
=
where
k
is a constant
( 29
.
0
≠
k
In each instance above,
k
is called the constant of proportionality.
You’ll be asked to find one (or more) of three things:
•
a formula that corresponds to a given statement
•
the constant of proportionality,
k
•
a value for one variable, given other values
Example 1:
Suppose
y
is directly proportional to
x
and
4
=
x
when
6
=
y
.
Write a
formula to express the given statement and find the constant of proportionality.
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 Summer '08
 MARKS
 Direct Variation, Inverse Variation, Formulas, Mass, Mathematical constant

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