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Chapter 5: Problem 114

Write a system of inequalities whose solution set includes every point in the rectangular coordinate system.

Short Answer

Expert verified
The system of inequalities that includes every point in the rectangular coordinate system is \(x \leq 鈭瀄), \(x \geq -鈭瀄), \(y \leq 鈭瀄), and \(y \geq -鈭瀄).

Step by step solution

01

Understand the Rectangular Coordinate System

The rectangular coordinate system includes all points with x and y coordinates that range from -鈭� to +鈭�. This means that any point in the rectangular coordinate system can be represented as (x, y), where x and y can be any real numbers.
02

Formulate the Inequalities

Based on the definition of the rectangular coordinate system, the applicable inequalities can be \(x \leq 鈭瀄), \(x \geq -鈭瀄), \(y \leq 鈭瀄), and \(y \geq -鈭瀄). Any point in the rectangular coordinate system will satisfy these conditions.
03

Combine the Inequalities

Combining these inequalities together would generate the system of inequalities: \(x \leq 鈭瀄), \(x \geq -鈭瀄), \(y \leq 鈭瀄), \(y \geq -鈭瀄). These inequalities cover every point in the rectangular coordinate system. Moreover, due to the unbounded nature of values, the graph depicting this will incorporate both positive and negative infinites for x and y.

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Most popular questions from this chapter

write the partial fraction decomposition of each rational expression. $$ \frac{2 x^{2}-18 x-12}{x^{3}-4 x} $$

write the partial fraction decomposition of each rational expression. $$ \frac{4 x^{2}-7 x-3}{x^{3}-x} $$

How can you verify your result for the partial fraction decomposition for a given rational expression without using a graphing utility?

determine whether each statement makes sense or does not make sense, and explain your reasoning. Because \((x+3)^{2}\) consists of two factors of \(x+3,1\) set up the following partial fraction decomposition: $$ \frac{5 x+2}{(x+3)^{2}}=\frac{A}{x+3}+\frac{B}{x+3} $$

write the partial fraction decomposition of each rational expression. $$ \frac{x^{3}-4 x^{2}+9 x-5}{\left(x^{2}-2 x+3\right)^{2}} $$
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