Chapter 11: Q. 50 (page 794)

In Problems 49 and 50, graph each system of inequalities by hand.
$\{\begin{cases} x^{2} + y^{2} \leq 25 \\ x y \leq 4 \end{cases}$

Short Answer

Expert verified

The graph of $\{\begin{cases} x^{2} + y^{2} \leq 25 \\ x y \leq 4 \end{cases}$ is

Step by step solution

Step 1. Given data

The given system of inequality is

$\{\begin{cases} x^{2} + y^{2} \leq 25 \\ x y \leq 4 \end{cases}$

Step 2. Properties of the graph of the inequality

Graph of $x^{2} + y^{2} \leq 25$ will be a circle of center $(0, 0)$

now test the origin point $(0, 0)$ for inequality $x^{2} + y^{2} \leq 25$

$x^{2} + y^{2} \leq 25 0^{2} + 0^{2} \leq 25 0 < 25$

inequality satisfied so the origin will lie in the region of inequality

So the region inside the circle will be shaded

Step 3. Properties of the graph of the inequality

Test the point $(0, 0)$ for inequality $x y \leq 4$

$x y \leq 4 0 \times 0 \leq 4 0 < 4$

inequality satisfied so the origin will lie in the region of inequality $x y \leq 4$

So the region toward origin from the graph ofrole="math" localid="1646962893657" $x y = 4$ will be shaded

Step 4. graph of the system of inequality

Graph of the system of inequality is

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In Problems 49 and 50, graph each system of inequalities by hand.
$\{\begin{cases} x^{2} + y^{2} \leq 25 \\ x y \leq 4 \end{cases}$

Short Answer

Step by step solution

Step 1. Given data

Step 2. Properties of the graph of the inequality

Step 3. Properties of the graph of the inequality

Step 4. graph of the system of inequality

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In Problems 49 and 50, graph each system of inequalities by hand.x2+y2≤25xy≤4

Short Answer

Step by step solution

Step 1. Given data

Step 2. Properties of the graph of the inequality

Step 3. Properties of the graph of the inequality

Step 4. graph of the system of inequality

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Decision Maths

Logic and Functions

Theoretical and Mathematical Physics

Discrete Mathematics

Pure Maths

Statistics

Study anywhere. Anytime. Across all devices.

In Problems 49 and 50, graph each system of inequalities by hand.
$\{\begin{cases} x^{2} + y^{2} \leq 25 \\ x y \leq 4 \end{cases}$