Answer:
13/9
Step-by-step explanation:
Directly proportional means it will be multiply to our constant k.
Inversely proportional means it will divide our k.
So we are given z is directly proportional to x and inversely proportional to y.
This means:
[tex]z=k \cdot \frac{x}{y}[/tex].
We are given (x=4,y=10,z=0.8). We can use this to find k. The k we will find using the point will work for any point (x,y,z) since k is a constant. A constant means it is to remain the same no matter what.
[tex]0.8=k \cdot \frac{4}{10}[/tex]
[tex]0.8=k(.4)[/tex]
Divide both sides by .4:
[tex]\frac{0.8}{0.4}=k[/tex]
[tex]k=2[/tex]
The equation for any point (x,y,z) is therefore:
[tex]z=2 \cdot \frac{x}{y}[/tex].
We want to find z given x=13 and y=18.
[tex]z=2 \cdot \frac{13}{18}[/tex]
[tex]z=\frac{2 \cdot 13}{18}[/tex]
[tex]z=\frac{13}{9}[/tex]
