Question 1124147


1.{{{X}}},{{{Y}}} and {{{Z}}} are such that {{{X}}} varies directly as {{{Z}}} and inversely as the cube root of {{{Y}}}.

If {{{X=8}}},{{{Y=27}}} and {{{Z=4}}}, find,

i.an expression of {{{X}}} in terms of {{{Y}}} and {{{Z}}}.

{{{X=kZ/root(3,Y)}}}

{{{8=k*4/root(3,27)}}}

{{{8root(3,3^3)=4k}}}

{{{(8*3)/4=k}}}

{{{k=4*3}}}

{{{k=12}}}




ii.the value of {{{Y}}} when {{{X=12}}} and {{{Z=10}}}.


{{{X=kZ/root(3,Y)}}}

{{{12=(12*10)/root(3,Y)}}}

{{{12root(3,Y)=(12*10)}}}

{{{root(3,Y)=(cross(12)*10)/cross(12)}}}

{{{root(3,Y)=10}}}...cube both sides

{{{(root(3,Y))^3=10^3}}}

{{{Y=1000}}}