An equation shows m is directly proportional to n and inversely proportional to
s cubed. When m = 5, then n = 160 and s = 2. What is the constant of
proportionality? Write your answer as a fraction.

Given:

An equation shows m is directly proportional to n and inversely proportional to  s cubed.

This can be written in expression as,

We need to determine the constant of proportionality when m = 5, n = 160 and s = 2.

Constant of proportionality:

The constant of proportionality can be determined by substituting m = 5, n = 160 and s = 2 in the equation

Thus, we have;

Simplifying, we get;

Thus, the value of the constant of proportionality is

for this case we must apply distributive property to the following expression:

the distributive property states that:

then, when applying the property we have to multiply the -2 for each term within the parenthesis:

1260=3*6*7*10=3^2*2^2*7*5 perfect cude = 3^3*2^

step-by-step explanation: