Chapter 3.8, Problem 33E

To determine

To find: the statement of variation relating to the variables of the equation and name the constant of variation.

Answer to Problem 33E

y varies directly as square of $x$and inversely as cube of z.

Constant of variation $\left(k\right)$ is $7$ .

Explanation of Solution

Given information:

  $\frac{1}{7}y=\frac{x^2}{z^3}$

Calculation:

Rearrange the given equation as follows:

  $\begin{array}{l}\frac{1}{7}y=\frac{x^2}{z^3}\\ y=7\left(\frac{x^2}{z^3}\right)\\ y{z}^3=7x^2\end{array}$

The value of 7 is constant, whereas $x,y$ and $z$ are variables. The equation shows that y varies directly as $x^2$and inversely as $z^3$ . Thus, the constant of variation $\left(k\right)$ is 7.