If z varies directly as x and inversely as y, and z = 8 when x = 12 and y = 3, the value of the constant of proportionality is what number?

2 Answers
Nov 13, 2017

Answer:

#k=2#

Explanation:

when z varies directly proportional to x means a division

#c=z/x# where c is a constant of proportionality

when z varies inversely proportional to x it means a product

#zy=c#

now with both

#k=(zy)/x#

#z=8; x=12 and y=3#

#k=(8.3)/12#

#k=2#

Nov 13, 2017

Answer:

#k=2#

Explanation:

#"the initial statement is "zpropx/y#

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

#rArrz=kxx x/y=(kx)/y#

#"to find k use the given condition"#

#z=8" when "x=12" and "y=3#

#z=(kx)/yrArrk=(yz)/x=(3xx8)/12=24/12=2#