Mathematics: Set up an equation by finding the constant of proportionality, k, then answer the question. If m is directly proportional to the square of b, and m=2 when b=8, find m when b=9

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Set up an equation by finding the constant of proportionality,

emilyy47

07.02.2022

$m=\dfrac{81}{32}$

Step-by-step explanation:

Given: m is directly proportional to the square of b.

m=kb^2 , where k= constant of proportionality

when m= 2 and b=8 , we get

$2=k(8)^2\\\\\Rightarrow\ 2=k(64)\\\\\Rightarrow\ k=\dfrac{2}{64}\\\\\Rightarrow\ k=\dfrac{1}{32}$

so the equation becomes $m=\dfrac{1}{32}b^2$

When b= 9

$m=\dfrac{1}{32}(9)^2=\dfrac{1}{32}\times81=\dfrac{81}{32}$

Hence, $m=\dfrac{81}{32}$

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