Answer: [tex]m=\dfrac{81}{32}[/tex]
Step-by-step explanation:
Given: m is directly proportional to the square of b.
[tex]m=kb^2[/tex], where k= constant of proportionality
when m= 2 and b=8 , we get
[tex]2=k(8)^2\\\\\Rightarrow\ 2=k(64)\\\\\Rightarrow\ k=\dfrac{2}{64}\\\\\Rightarrow\ k=\dfrac{1}{32}[/tex]
so the equation becomes [tex]m=\dfrac{1}{32}b^2[/tex]
When b= 9
[tex]m=\dfrac{1}{32}(9)^2=\dfrac{1}{32}\times81=\dfrac{81}{32}[/tex]
Hence, [tex]m=\dfrac{81}{32}[/tex]
