Question

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

Answer 1

Answer:
`m=(81)/(32)`

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=(2)/(64)\\\\\Rightarrow\ k=(1)/(32)`

so the equation becomes
`m=(1)/(32)b^2`

When b= 9

`m=(1)/(32)(9)^2=(1)/(32)*81=(81)/(32)`

Hence,
`m=(81)/(32)`