Final answer:
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.