Sullivan Algebra and Trigonometry: Section 2.5 Variation

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Sullivan Algebra and Trigonometry Section
2.5Variation

• Objectives
• Construct a Model Using Direct Variation
• Construct a Model Using Inverse Variation
• Construct a Model Using Joint or Combined
  Variation

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Variation refers to how one quantity varies in
relation to another quantity. Quantities may vary
directly, inversely, or jointly.
Let x and y denote two quantities. Then y varies
directly with x, or y is directly proportional to
x, if there is a nonzero number k such that y
kx.
The number k is called the constant of
proportionality.
3
For regular unleaded gasoline, the revenue R (in
dollars) varies directly with the number of
gallons of gasoline sold g. If revenue is 15.00
when the number of gallons of gasoline sold is
12.5, find a formula that relates revenue R to
the number of gallons of gasoline g.
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Let x and y denote two quantities. Then y varies
inversely with x, or y is inversely proportional
to x, if there is a nonzero number k such that
y k/x
The number k is called the constant of
proportionality.
5
The weight of a body varies inversely with the
square of its distance from the center of Earth.
Assuming the radius of Earth is 3960 miles, how
much would a woman weigh at an altitude of 0.5
miles above the Earths surface if she weighs
120 pounds on Earths surface?
So,
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When a variable quantity Q is proportional to the
product of two or more other variables, we say
that Q varies jointly with these quantities.
Combined variation is a combination of direct
and/or inverse variation.
7
The maximum safe load for a horizontal
rectangular beam varies jointly with the width of
the beam and the square of the thickness of the
beam and inversely with its length. If a 10-foot
beam will support up to 600 pounds when the beam
is 3 inches wide and 4 inches thick, what is the
maximum safe load of a similar beam 12 feet long,
4 inches wide and 6 inches thick?