Chapter 8.1, Problem 48PPS

(a)

To determine

To fill: The given empty table.

Answer to Problem 48PPS

The following table is been filled.

  $\begin{array}{ccc}x& y& \sqrt{xy}\\ 1& 64& 8\\ 2& 32& 8\\ 4& 16& 8\\ 8& 8& 8\\ 16& 4& 8\\ 32& 2& 8\\ 64& 1& 8\end{array}$

Explanation of Solution

Given information: Five ordered pairs $\left(x,y\right)$ such that $\sqrt{xy}=8$ .

Calculation: It is given that the five ordered pairs of $\left(x,y\right)$ is such that $\sqrt{xy}=8$ .

Hence, according to the given condition the following table is been filled.

  $\begin{array}{ccc}x& y& \sqrt{xy}\\ 1& 64& 8\\ 2& 32& 8\\ 4& 16& 8\\ 8& 8& 8\\ 16& 4& 8\\ 32& 2& 8\\ 64& 1& 8\end{array}$

(b)

To determine

To graph: The given ordered pairs.

Explanation of Solution

Given information: Table of five ordered pairs,

  $\begin{array}{ccc}x& y& \sqrt{xy}\\ 1& 64& 8\\ 2& 32& 8\\ 4& 16& 8\\ 8& 8& 8\\ 16& 4& 8\\ 32& 2& 8\\ 64& 1& 8\end{array}$

Graph: Graph of required ordered pairs has been plotted below,

(c)

To determine

To conjecture: About the graph that would be formed if you connected the points over graph.

Answer to Problem 48PPS

The line would have the form $y=\frac{64}{x}$ .

Explanation of Solution

Given information: Table of five ordered pairs,

  $\begin{array}{ccc}x& y& \sqrt{xy}\\ 1& 64& 8\\ 2& 32& 8\\ 4& 16& 8\\ 8& 8& 8\\ 16& 4& 8\\ 32& 2& 8\\ 64& 1& 8\end{array}$

Calculation: Any set of ordered pairs from the table would have the same general shape because they would also be a solution of $y=\frac{64}{x}$ .