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#z# is directly proportional to #x# and #y#. If when #x=6# and #y=8#, then #z=48#, then what is #z#, when #x=10# and #y=12#?

Answer 1

Ethan Adkins

#z=120#

#"the initial statement is " zpropxy#

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

#rArrz=kxy#

#"to find k use the condition given for x, y and z"#

#x=6,y=8" when " z=48#

#z=kxyrArrk=z/(xy)=48/(6xx8)=1#

#rArr" equation is " color(red)(bar(ul(|color(white)(2/2)color(black)(z=xy)color(white)(2/2)|)))#

#"when " x=10" and " y=12#

#z=10xx12=120#

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Answer 2

Nathan Axel

#z=120#

#z# varies jointly as #x# and #y# means #zpropx# and #zpropy# i.e.

#zpropx xxy#

In other words #z=kxx xy# where #k# is a constant

Since when #x=6# and #y=8#, w have #z=48#, we have

#48=kx6xx8# and #k=48/(6xx8)=48/48=1#

and hence #z=xy#

and when #x=10# and #y=12#

#z=10xx12=120#

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.