Problem 77 - College Algebra

Question

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

Step-by-Step Solution

Answer

The conditions are satisfied in the 4th quadrant.

Step 1: Identify the signs of x and y

We know that for \(x^{3} > 0\), x must be positive because the cube of a positive number is positive. Similarly, from \(y^{3} < 0\), y must be negative because the cube of a negative number is negative.

Step 2: Determine the quadrant

In a coordinate system with x-y axes, the quadrant where x is positive and y is negative is the 4th quadrant.