Question

Write a specific formula to describe the variation: Q varies jointly with the square of the inverse of the sum of b and R; Q = 4 when b = 2, R = 8.

Answer 1

Given the following variation

`Q\propto(1)/((b+R)^2)`

Introducing the constant of proportionality c as shown below

`\begin{gathered} Q=c*(1)/((b+R)^2) \\ Q=(c)/((b+R)^2) \end{gathered}`

Q=4, when b=2, R= 8

Let use the above values of Q, b, and R to find the value of c as shown below:

`\begin{gathered} 4=(c)/((2+8)^2) \\ 4=(c)/(10^2) \\ 4=(c)/(100) \\ c=4*100 \\ c=400 \end{gathered}`

Let us substitute c in the formula as shown below

`Q=(400)/((b+R)^2)`

Hence, the specific formula to describe the variation is

Q= 400/(b+R)²