The number of hours needed to paint a house, h, varies inversely with the number of painters, n. Four painters need 6 hours to paint a house. How many hours would it take 3 painters to paint the house?

It would take 3 painters, a total number of 8 hours, to paint the house

Step-by-step explanation:

Let the number of hours be denoted by N, and the number of painters be denoted by P. The inverse relationship can be expressed as:

N α

Removing the proportionality symbol (α), introduces a constant of proportionality, which can be assumed to be C, in this example.

So, N =

When N = 6, P = 4

6 =

C = 24

So that, N = . This is the formula to use for determination of the other variable when one of them is known.

Now, given 3 painters, the number of hours needed can be obtained as follows:

N = = 8 hours

for this pair of functions g(x)=x-2 and f(x)=|x| is (g o f)(a)= |a| -2

step-by-step explanation:

g(x)=x-2

f(x)=|x|

(g o f)(a)=?

(g o f)(x)=g(f(x))

(g o f)(x)=g(|x|)

(g o f)(x)=|x|-2

(g o f)(a)=|a|-2