# 8.4(one) - 8.4 Variation and Problem Solving Ejo<><(E...

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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 9%:H(é) Ll 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 :pir: Mfg? gal/Lima : . “l trail : klé) X ﬂ: K 22 [1253“: K r/":—r—~\ {rj :1.131\‘)U Win! “‘4’ ‘l X K's 6” 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 32317 -: K 9 ﬁt. ; K 2 Tr : _ a L i 7— _ at [014} 3 f a I: h l"?— D a , 2\ V~ glellg) V “Z CLL’ZHL \ncJ’U-S NEE CLLLiQ‘R’W'h-tB \ 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 8-foot column can hold 2 tons, ﬁnd how much weight a 10-foot 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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8.4(one) - 8.4 Variation and Problem Solving Ejo<><(E...

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