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Unformatted text preview: 2.8 Modeling Using Variation ﬂanking Variatinn i’rohlems 1.. Write as; equalities that éeserihes the: given English statmiter. 2. S'ﬁlflﬁiéiﬂiif Liar: given pair {themes inns the at; marina in slap % and strive far
A“. the swarm]; of venetian. 3. fittinst'étate the value {if ft. “min the equatinn in step .1.
4; Line {tie equating} 15mm step: 3 to answer the problem‘s rguearimn
[Ernest VarSalinas
if sitaamn is rieserilrert by as age Mine in the fern:
gr ‘ his
‘le l; is a Miriam: assistant, We say that y varies direftifgy as r U3' 3: is ﬂimﬁlﬁy
grtipurtienal tux» The Minibar l: is callers the constant of mainline iﬂ‘ liar:
constant sf m'opartinnnltiig,
Inverse Variation
Ef a situatina is described. by an squatter; in the term
‘ M J:
Jr ” where I: is a mmaem ermﬁzta‘ltn we say Haas. y varies inversely mm m' y is have rsel'}
pmpnrﬁrmai in 41"i’l'iie n umber S: is relied the ennsmm nil” variation.
Fiﬁreel Etariatinn with. wisers 3 varies ciireetlg as the HE] power of; if there exists same immerse ennsiam 31:
met; that v fear”.
we salsa an}; lift at y is tinearly mammalian! in the at?! power nix Solve direct variation problems. Solve inverse variation problems. Solve combined variation problems.
Solve problems involving joint variation. OL 33 PFC/OOVl'OnaLLl/i 1. Write an equation that expresses the relationship; then solve for y. Useﬂr as the constant of variation. x varies directly with y and inversely with the fourth
power of z 2:5:3
on“; 2. y varies jointly as x and the squ re root of z and inversely with r cubed.
[y=20,when x=2, 2:4, and i=1.TWhat isy,_ when x=3, 2:9, and r:2? derjz ta ,_ <fa‘xrlr';
3: k Xxl% 3“ t3 a
m : k a Li vi: Sﬁjﬁi )% 33
$10 : it All) j 19, :l< / r % 3. The volume of a sphere varies directly with the cube of the radius. llf the
volume of a sphere with a radius of 2 inches is 32 ' cubic inchesl what would be the volume of a sphere with. a radius of 6 inche’?
' ,_ 2
V: [<13 Vin
3 ,. I , A r
$9517" R l?) 3 f:
@117“
3(3)
91:: k 4. The force that it requires to stretch a spring varies directly with the distance that it is stretched. If a 10 pound force can stretch a spring 8 inches, how
much force would it take to stretch the spring 12 inches? F; 4$3>E) ...
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 Fall '11
 BlisinHestiyas

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