If a varies directly as the square of b, then, you can write the following equation:
[tex]a=kb^2[/tex]where k is the constant of proportionality.
a = 6 when b = 5. Use this information to find the value of k, as follow:
[tex]\begin{gathered} 6=k(5)^2 \\ k=\frac{6}{(5)^2}=\frac{6}{25} \end{gathered}[/tex]Then, the equation that relates a and b becomes:
[tex]a=\frac{6}{25}b^2[/tex]Now, if b=2, you obtain for a:
[tex]\begin{gathered} a=\frac{6}{25}(2)^2 \\ a=\frac{6}{25}\cdot4 \\ a=\frac{24}{25} \end{gathered}[/tex]Hence, a = 24/25 when b = 2
