Given:
An equation shows m is directly proportional to n and inversely proportional to s cubed.
This can be written in expression as,
[tex]m=k(n)(\frac{1}{s^3})[/tex]
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 [tex]m=k(n)(\frac{1}{s^3})[/tex]
Thus, we have;
[tex]5=k(160)(\frac{1}{2^3})[/tex]
Simplifying, we get;
[tex]5=k(160)(\frac{1}{8})[/tex]
[tex]5=20k[/tex]
[tex]\frac{5}{20}=k[/tex]
[tex]\frac{1}{4}=k[/tex]
Thus, the value of the constant of proportionality is [tex]\frac{1}{4}[/tex]
