Question

Which of the following equations represents the relationship between N and the cube root of p, after evaluating the constant of proportionality?

A) N = k/(∛p)
B) N = k∛p
C) N = k/(p^(1/3))
D) N = k(p^(1/3))

Answer 1

The correct equation that represents the relationship between N and the cube root of p, with a constant of proportionality k, is D) N = k(p^(1/3)).

Step-by-step explanation:

The question involves establishing the relationship between N and the cube root of p (√p), given a constant of proportionality, k. When we say that N is directly proportional to the cube root of p, we mean that N increases or decreases as √p does, by a constant multiple. Since the cube root of p can be written as p1/3, we then say that N is equal to k times the cube root of p.

Looking at the options provided, the equation that correctly represents this relationship is:

N = k(p1/3)

This corresponds to option D in the question. Options A and C present N as being inversely proportional to the cube root of p, which is not the direct proportionality we are looking for. Hence, the correct answer is:

D) N = k(p1/3)