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Sagot :
SOLUTION
write out the giving parameters
[tex]y=-27,x=-18,z=-36[/tex]Then write out the expression for the variation
y varies directly as x and inversely as z can be writing as
[tex]y\propto x\propto\frac{1}{x}[/tex]which can be simplified as
[tex]y\propto\frac{x}{z}[/tex]Then we change the variation sign to equal sign and include the constant of proportionality k
[tex]y=\frac{kx}{z}[/tex]Then substitute the giving parameters into the equation in the last line above
[tex]\begin{gathered} y=\frac{kx}{z} \\ -27=\frac{k(-18)}{-36} \\ \\ -27=-\frac{18k}{-36} \\ \end{gathered}[/tex]
We simplify the expression to obtain the value of k
[tex]\begin{gathered} -27=\frac{k}{2} \\ \text{ multiply both sides by 2} \\ -54=k \\ \text{hence k=-54} \end{gathered}[/tex]The substitute the value of k into the expression to obtain the relationship between the three variables
[tex]\begin{gathered} y=\frac{kx}{z} \\ \sin ce\text{ k=-54} \\ y=-\frac{54x}{z}\text{ is the relationship betw}een\text{ the thr}ee\text{ variables } \end{gathered}[/tex]From the relationship, substitute the given value of x and z to find y
[tex]\begin{gathered} y=-\frac{54x}{z} \\ y=\text{?,x}=7,z=-2 \\ y=\frac{-54(7)}{-2} \\ \end{gathered}[/tex]Then we have
[tex]y=\frac{-54\times7}{-2}=27\times7=189[/tex]Therefore, the value of y is 189
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