Section 6.5.1

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Section 6.5.1 Ratio, Proportion, Variation The
Vocabulary
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y varies directly as x
y varies inversely as x
y varies jointly as x and z
y is (directly) proportional to x
y is inversely proportional to x
y is jointly proportional to x and z
k constant of variation/proportionality
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Using the constant k and the given information,
create a mathematical model for
The total (t) varies inversely as the square of
its parts (p)
Using the constant k and the given information,
create a mathematical model for
The simple interest (I) on an investment is
proportional to the amount of the investment (P).

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Using the constant k and the given information,
create a mathematical model for
The distance (d) a spring is stretched (or
compressed) varies directly as the force (F) on
the spring.
Using the constant k and the given information,
create a mathematical model for
The volume (v) varies directly as the cube of an
edge (e).
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Using the constant k and the given information,
create a mathematical model for
The height (h) of an object varies inversely as
the square root of its width (w).
Using the constant k and the given information,
create a mathematical model for
The length (L) of an object is jointly
proportional to the square of its width (w) and
the cube of its height (h).
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Using the constant k and the given information,
create a mathematical model for
The stopping distance (d) of an automobile is
directly proportional to the square of its speed
(s).
Using the constant k and the given information,
create a mathematical model for
The intensity (I) of a sound wave varies jointly
as the square of its frequency (f) and the speed
of sound (v) and inversely as the square of its
amplitude (r).