Chapter 8.1, Problem 9PPSE

Solution

To find the relationship between the variables in given case is direct variation, an inverse variation, or nether. Also to determine the equation.

The equation is $y=\frac{0.3}{x}$ .

Given information:

The table is:

$x$	$y$
0.1	3
3	0.1
6	0.05
24	0.0125

Concept:

Inverse variation: When one of the given variables increases with decrease in other variable, then it is inverse variation or vice versa.

It can be represented as:

  $xy=k$ (Product of variables remains constant)

Direct variation: When one variable increases with increase in other variable, or decreases with decrease in other variable then it is direct variation.

It can be represented as:

  $k=\frac{x}{y}$ (Ratio of variable remains constant)

Calculation:

From the given table:

  $\begin{array}{l}0.1\times 3=0.3\\ 3\times 0.1=0.3\\ 6\times 0.05=0.3\\ 24\times 0.0125=0.3\end{array}$

As product is constant, it is indirect variation.

Equation shall be given by,

  $k=xy$

As the value of constant is 0.3, hence the equation is:

  $\begin{array}{l}0.3=xy\\ y=\frac{0.3}{x}\end{array}$

Conclusion:

Hence, the equation is $y=\frac{0.3}{x}$