X is directly proportional to Y^1/2 and Z is inversely proportional to Y^2 When X = 12, Y = 4 . When Z = 5, Y = 8 . Express Z in terms of X . can anyone help ?

1 Answer
Jim G.
Jun 23, 2018

#z=414720/x^4#

Explanation:

#xpropy^(1/2)#

#"to convert to an equation multiply by k the constant"#
#"of variation"#

#x=ky^(1/2)=ksqrty#

#"to find k use the given condition"#

#y=4" when "x=12#

#x=ksqrtyrArrk=x/sqrty=12/sqrt4=12/2=6#

#•" equation is "x=6sqrtyto(color(red)(1))#

#"we also have"#

#zprop1/y^2#

#"multiply by k the constant of variation"#

#z=k/y^2#

#"using "y=8" when "z=5#

#k=zy^2=5xx8^2=5xx64=320#

#• " equation is "z=320/y^2to(color(red)(2))#

#"from "(color(red)(1))color(white)(x)sqrty=x/6rArry=(x/6)^2=x^2/36#

#"substitute "y=x^2/36" in equation "(color(red)(2))#

#z=(320)/(x^2/36)^2=320xx36^2/x^4=414720/x^4#

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