# The relation of the quantity z to the quantities x and y if the quantities x , y and z are related by z = 3 x y .

### Precalculus: Mathematics for Calcu...

6th Edition
Stewart + 5 others
Publisher: Cengage Learning
ISBN: 9780840068071

### Precalculus: Mathematics for Calcu...

6th Edition
Stewart + 5 others
Publisher: Cengage Learning
ISBN: 9780840068071

#### Solutions

Chapter 1.11, Problem 3E
To determine

## To fill: The relation of the quantity z to the quantities x and y if the quantities x,y and z are related by z=3xy .

Expert Solution

The quantity z is directly proportional to the quantity x and inversely proportional to the quantity y .

### Explanation of Solution

If the quantities x,y and z are related by an equation,

z=kxy (1)

For some constant k0 , we say that z varies directly as x , or z is inversely proportional to y . The constant k is called the constant of proportionality.

The given equation is,

z=3xy (2)

Compare the equation (2) with equation (1) to infer that z is directly proportional to x and z is inversely proportional to y.

Therefore, the quantity z is directly proportional to the quantity x and inversely proportional to the quantity y .

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