Answer:
[tex]z = \frac{2}{7} [/tex] when x= [tex] \frac{6}{7} [/tex],
z= 179.2 when y= [tex] \frac{5}{28} [/tex]
Step-by-step explanation:
Let's start by writing out the two general equations for z.
Since z varies directly with x,
z= kx, where k is a constant.
Since z varies inversely with y,
[tex]z = \frac{k}{y} [/tex], where k is a constant.
When x= 12, z= 4,
4= k(12)
12k= 4
k= 4 ÷12
k= ⅓
∴ z= ⅓x
When x=[tex] \frac{6}{7} [/tex],
[tex]z = \frac{1}{3} ( \frac{6}{7} )[/tex]
[tex]z = \frac{2}{7} [/tex]
When y= 8, z= 4,
[tex]4 = \frac{k}{8} [/tex]
k= 4(8)
k= 32
[tex]∴z = \frac{32}{y} [/tex]
When y= [tex] \frac{5}{28} [/tex],
[tex]z = 32 \div \frac{5}{28} [/tex]
[tex]z = 32 \times \frac{28}{5} [/tex]
z= 179.2
