Question

A number n is increased by 8. If the cube root of that results equals -0.5, what is the value of n?

Answer 1

To find the value of n, we need to solve the cubic equation (n + 8)³ = (-0.5)³. After solving, the value of n is approximately -0.383.

Step-by-step explanation:

To find the value of n, we need to solve the equation that represents the given information. The equation states that the cube root of n + 8 equals -0.5. To isolate n, we cube both sides of the equation:

(n + 8)³ = (-0.5)³

Expanding the left side of the equation and simplifying, we get:

n³ + 24n² + 192n + 512 = -0.125

Simplifying further, we have:

n³ + 24n² + 192n + 512 + 0.125 = 0

After solving this cubic equation, we find that the value of n is approximately -0.383.

Answer 2

The cube root of (n increased by 8), or ∛(n+8), is -0.5, or -1/2.

∛(n+8) = -1/2. To solve this for n, cube both sides, obtaining n+8 = -1/8.

Eliminate the fraction by mult. all three terms by 8: 8n + 64 = -1

Solving for n: 8n = -65, so that n = -65/8.