Answer:
The constant of proportionality is 54.
k = 54
c as a function of d:
[tex]c(d) = \dfrac{54}{d^2}[/tex]
[tex]c(7) = \dfrac{54}{49}[/tex]
Step-by-step explanation:
We are given the following in the question:
c is inversely proportional to the square of d.
[tex]\Rightarrow c\propto \dfrac{1}{d^2}\\\\\Rightarrow c = \dfrac{k}{d^2}\\\\\text{where k is constant of proportionality}[/tex]
When c = 6, d = 3.
Plugging the values, we get,
[tex]6 = \dfrac{k}{3^2}\\\\\Rightarrow k = 6\times 3^2 = 54[/tex]
Thus, the constant of proportionality is 54.
c as a function of d can be written as:
[tex]c(d) = \dfrac{54}{d^2}[/tex]
We have to find value of c when d = 7.
Putting values, we get,
[tex]c(7) = \dfrac{54}{(7)^2}=\dfrac{54}{49}[/tex]
is the required value of c.
