Answer:
52
Step-by-step explanation:
Here it's given that p is inversely proportional to the square of q. We can write this mathematically as ,
[tex]\longrightarrow p \propto \dfrac{1}{q^2} [/tex]
Let k be the constant of proportionalality .
[tex]\longrightarrow p = \dfrac{k}{q^2}[/tex]
Again it's given that when p is 13 , q is 4 . On substituting this in the above equation we can find out the value of k , as ;
[tex]\longrightarrow 13 =\dfrac{k}{4^2}[/tex]
Solve out for k ,
[tex]\longrightarrow k = 13 (16)[/tex]
Multiply ,
[tex]\longrightarrow k = 208 [/tex]
Again when the value of q is 2 , we need to find out the value of p . So ,
[tex]\longrightarrow p =\dfrac{k}{q^2}[/tex]
Substitute ,
[tex]\longrightarrow p =\dfrac{208}{2^2}\\ [/tex]
[tex]\longrightarrow p = \dfrac{208}{4}[/tex]
Simplify,
[tex]\longrightarrow p = 52 [/tex]
This is the required answer.
