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

Question

asked Jul 26, 2021 55.1k views

1 Answer

Somejkuser · Answer 1 · 2021-07-30T12:03:24+0000

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)