Question

Determine what signs on values of x and y would make each statement true. Assume that x and y are not 0. {x^3}/{y} > 0 .

a)x > 0, y > 0
b)x < 0, y < 0
c)x > 0, y < 0
d)x < 0, y > 0

Answer 1

To make the inequality x^3/y > 0 true, both x and y must be greater than zero.

Step-by-step explanation:

To determine what signs on values of x and y would make the inequality {x^3}/{y} > 0, we need to consider the properties of the inequality. A product is positive when both factors have the same sign, either both positive or both negative.

Since the numerator, x^3, is always non-negative (as any real number raised to the power of 3 is non-negative), we need the denominator, y, to be positive for the entire expression to be positive. This means that both x and y must be greater than zero, which corresponds to option a) x > 0, y > 0.