# The equation relating x , y to z for the given conditions. ### 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 4E
To determine

## To fill: The equation relating x,y to z for the given conditions.

Expert Solution

The quantities x,y and z are related by equation z=12xy .

### Explanation of Solution

Given:

z is proportional to the product of x and y and z is 10 when x is 4 and y is 5.

Definition:

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

z=kxy (1)

For some constant k0 , we say that z is proportional to the product of x and y. The constant k is called the constant of proportionality.

Calculation:

It is given that z is proportional to the product of x and y.

Compare the above equation with the definition of proportionality in equation(1).

z=kxy (2)

Substitute 10 for z, 4 for x and 5 for y in equation (2).

10=k×4×510=20k

Simplify the above equation to find the value of k.

10=20kk=1020k=12

Substitute the value of k in equation (2)

z=12xy

Therefore, the quantities x,y and z are related by equation z=12xy .

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