Answer:
a
Step-by-step explanation:
given y varies directly as x² and inversely as z³ then the equation relating them is
y = [tex]\frac{kx^2}{z^3}[/tex] ← k is the constant of variation
to find k use the condition y = 12 when x = 4 and z = 2 , then
12 = [tex]\frac{k(4)^2}{2^3}[/tex] = [tex]\frac{16k}{8}[/tex] ( multiply both sides by 8 )
96 = 16k ( divide both sides by 16 )
6 = k
y = [tex]\frac{6x^2}{z^3}[/tex] ← equation of variation
when y = 1.728 and z = 5 , then
1.728 = [tex]\frac{6x^2}{5^3}[/tex] = [tex]\frac{6x^2}{125}[/tex] ( multiply both sides by 125 )
216 = 6x² ( divide both sides by 6 )
36 = x² ( take square root of both sides )
[tex]\sqrt{36}[/tex] = x , that is
x = 6
