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Chapter 1: Problem 78

List the quadrant or quadrants satisfying each condition. $$x^{3}<0 \text { and } y^{3}>0$$

Short Answer

Expert verified
The conditions \(x^3<0\) and \(y^3>0\) are satisfied in the second quadrant

Step by step solution

01

Understanding the conditions

Let's first analyze each conditions separately. The condition \(x^3<0\) implies that x is negative since the cube of any negative number is negative, while the condition \(y^3>0\) implies that y is positive since the cube of any positive number remains positive.
02

Map the conditions to quadrants

Next move to the Cartesian coordinate system. In the 2D Cartesian plane, it is divided into 4 quadrants. The first quadrant (top right) is where both x and y are positive. The second quadrant (top left) is where x is negative and y is positive. The third quadrant (bottom left) is where both x and y are negative. And the last, the fourth quadrant (bottom right) is where x is positive and y is negative. Now, according to our conditions - x is negative and y is positive, these conditions are met in the second quadrant.
03

Identify the quadrant

Therefore, the only quadrant satisfying both conditions (\(x^3<0\) and \(y^3>0\)) is the second quadrant.

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Most popular questions from this chapter

Complete the square and write the equation in standard form. Then give the center and radius of each circle and graph the equation. $$x^{2}+y^{2}-6 y-7=0$$

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$$\text { Solve for } y: \quad x=y^{2}-1, y \geq 0$$
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