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)=5?

Answer 1

Answer:

M = 7

Step-by-step explanation:

As g(m) varies inversely with M, that is represented by the expression:

$g(m)=\frac{1}{M}$

Now we have to introduce a constant of proportionality (k), that is multiplying the function:

$g(m)=\frac{1}{M}*k$

Then we can replace the given values to find the value of k:

When m=10, g(m)=3.5

$g(m)=\frac{1}{M}*k\\k=g(m)*M$

k=3.5*10

k=35

Now, we can replace the given value of g(m)=5 to find M:

$M=\frac{1}{g(m)}*k\\M=\frac{1}{5}*35\\M=7$

Answer 2

In an inverse variation, the function takes the form xy=k
where k is a constant.
Given g(10)=3.5, we find k=xy=3.5*10=35.  
This means the function is
m*g(m)=35
When g(m)=5, then m=35/5=7.