m is inversely proportional to g. when m=90, g=40 find the value of m when g=m

Have a look at the definition of a inversely propotional relationship.

Hence

$$m = \frac{k}{g} \Leftrightarrow k = mg \Leftrightarrow k = 90 \times 40 = 3600$$

Now if

$$m = g$$

we can write

$$m^2 = k = 3600 \Leftrightarrow m = \sqrt{3600} = 60$$

Therefore

$$m = g = 60$$

(11-11-2014 edit)

or

$$m = g = -60$$

$$\\m=\frac{k}{g}\\
90=\frac{k}{40}\\
90*40=k\\
k=3600\\
so\\
m=\frac{3600}{g}\\
$When g=m$\\
m=\frac{3600}{m}\\
m^2=3600\\
m=\pm 60$$

Reinout, can the constant be negative.

I know it is not here but it can be can't it?

Also why can't m=g=-60 ?

I should have said Reinout, it is really good to see you on the forum.  :))

Alan or Chris, could you please comment on my question here.

two things are directly proportional if as one gets bigger the other also gets proportionally bigger but the constant can be negative, cant it? So how does that work?

Thanks you

y is inversely proportional to x just means: y = k/x where k can be positive or negative.

"Proportional to" just refers to the magnitude unless otherwise specified.

.

Thank you Alan.  I know that what you are saying is correct 

BUT 

i  find it confusing (misleading) because when teachers talk about directly proportional to they tend to say that as one gets bigger the other gets bigger but if the contant is negative this is not true.

Imagine a mass on a spring subject to Hooke's law.  

Restoring force = - k*displacement (k is positive constant)

As the displacement gets bigger the restoring force gets bigger.

.

You mean the absolute value - or non directional value of it gets bigger ?