If g (n) varies inversely with n and g (n) = 8 when n = 3, find the value of n when g (n) = 6.

n = 4 when g (n) = 6

Step-by-step explanation:

If g (n) varies inversely with n

g (n) α 1/n

g (n) = k/n where k is the constant of proportionality

if g (n) = 8 when n = 3, then

8 = k/3

k = 24

g (n) = 24/n

when g (n) = 6

6 = 24/n

6n = 24

n = 24/6

n = 4

4

Step-by-step explanation:

g (n) varies inversely with n.

This can be expressed alternatively as / [g (n) = / frac{k}{n}/] where k is a constant value.

Given that when n = 3, g (n) = 8.

This implies, / [8 = / frac{k}{3}/]

Simplifying the equation to solve for k, k = 8 * 3 = 24

Now when g (n) = 6, / [g (n) = / frac{k}{n}/]

/[6 = / frac{24}{n}/]

Calculating the value of n, / [n = / frac{24}{6}/] = 4

So the required value of n is 4.