Question

The variable z is directly proportional to x, and inversely proportional to y. When x is 4 and y is 10, z has the value 0.8. What is the value of z when x= 13, and y= 18

Answer 1

13/9

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:

`z=k \cdot (x)/(y)`.

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.

`0.8=k \cdot (4)/(10)`

`0.8=k(.4)`

Divide both sides by .4:

`(0.8)/(0.4)=k`

`k=2`

The equation for any point (x,y,z) is therefore:

`z=2 \cdot (x)/(y)`.

We want to find z given x=13 and y=18.

`z=2 \cdot (13)/(18)`

`z=(2 \cdot 13)/(18)`

`z=(13)/(9)`