Chapter 8, Problem 9E

Solution

To state: The function that models the relationship also find the value of $z\text{when}x=4,y=8$ . t z varies jointly with x and y . When $x=2,\text{and}y=2,z=7$ .

The resultant value of z is 56 and the function that models the relationship is $z=\frac{7}{4}xy$ .

Given information:

It is given that z varies jointly with x and y , when $x=2,\text{and}y=2,z=7$ .

Explanation:

Find the variation model if $x=2,\text{and}y=2,z=7$ and z varies jointly with x , y .

Let’s take k as the constant of variation then $z=kxy$ because z varies jointly with x and y .

  $z=kxy$

Substitute $x=2,y=2,z=7$ .

  $\begin{array}{l}7=k\left(2\right)\left(2\right)\\ 7=4k\\ k=\frac{7}{4}\end{array}$

Then the function that models the joint variation will become: $z=\frac{7}{4}xy$

Now use the function to find the value of $z\text{when}x=4,y=8$ ,

  $\begin{array}{c}z=\frac{7}{4}xy\\ z=\frac{7}{4}\left(4\right)\left(8\right)\\ z=56\end{array}$

Therefore, the value of z is 56.