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Unformatted text preview: 8.4 Variation and Problem Solving Ejo<>< (E y varies directly as x, or y is directly proportional to
x, if there is a nonzero constant k such that y = kx. The family of equations of the form y = kx are referred to as
direct variation equations. The number k is called the constant of variation or the
constant of proportionality. Example: If y varies directly as x, ﬁnd the constant of variation k and the[d1rect var' ' e uatio given that y = 5 when x K(ﬂ:—Lx é If y varies directly as x, and y = 48 when x = 6, then ﬁnd y
when x = 15. Ejr—KX
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At sea, the distance to the horizon is directly proportional
to the square root of the elevation of the observer. If a
person who is ﬁg above water can see miles, ﬁnd how far a person 64 feet above the water can see. Round
your answer to tvvo decimal places. ' LJ : EDQZ/rlot'm \ “If
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D} f_ 1 13—53 LN : I 2%: (g) R y varies inversely as x, or y is inversely proportional to x,
if there is a nonzero constant k such that y = k/x. The family of equations of the form y = k/x are referred to
as inverse variation equations. The number k is still called the constant of variation or
the constant of proportionality. I; it} — Vi; Kth I : . 2 X1
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V “Z CLL’ZHL \ncJ’US NEE CLLLiQ‘R’W'htB \ If y varies inversely as x, ﬁnd the constant of variation k and the inverse variation equation, given that y = 63 when
x = 3. 7T, Gfe : 7?
[$12K y can vary directly or inversely as powers of x, as welly
varies directly as a power of x if there is a nonzero constant k and a natural number n such that y = kx”. y
varies inversely as a power of x if there is a nonzero
constant k and a natural number n such that y=;; W The maximum weight that a circular column can hold is
inversely proportional to the square of its height.
W : < h
h 7,
If an 8foot column can hold 2 tons, ﬁnd how much
weight a 10foot column can hold. \ﬂ:% W112 ‘5 x
Kathy spends 1.5 hours watchingitelevision and 8 hours
studying each week. If the amoufit of time spent
watching TV varies inversely with the amount of time spent studying, ﬁnd the amount of time Kathy will spend
watching TV if she studies 14 hours a week. ...
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 Fall '11
 JimCotter

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