Question

Suppose g(m) varies inversely with m and g(m)=3.5 when m=10. What is the value of m when g(m)=10?

Answer 1

Give that g(m) varies inversely with m

So that means we can write equation:

$g\left(m\right)=\frac{k}{m}$

where is k is constant of variation.

Given that g(m)=3.5 when m=10.

so plug these values into above formula:

$g\left(10\right)=\frac{k}{10}$

$3.5=\frac{k}{10}$

$3.5*10=\frac{k}{10}*10$

$35=k$

To find the value of m when g(m)=10, we just need to plug g(m)=10 and k=35 into above formula then solve for m

$g\left(m\right)=\frac{k}{m}$

$10=\frac{35}{m}$

$10m=35$

$m=\frac{35}{10}$

m=3.5

Hence final answer is m=3.5