Question

Consider the curve given by the equation (2y - 1)^3 − 24x = −3. What is the constant of proportionality for this curve?

A) 8
B) 12
C) 6
D) 3

Answer 1

The constant of proportionality for the curve given by the equation (2y - 1)^3 − 24x = −3 is 2.

Step-by-step explanation:

The given equation is:

(2y - 1)^3 - 24x = -3

To find the constant of proportionality for this curve, we need to isolate the variable y. Let's solve the equation for y:

(2y - 1)^3 = 24x - 3

Now, take the cube root of both sides:

2y - 1 = ∛(24x - 3)

Next, isolate y:

2y = 1 + ∛(24x - 3)

y = (1 + ∛(24x - 3))/2

Therefore, the constant of proportionality for this curve is 2.