Mathematically, if T is directly proportional to r squared, we write that as:

T∝r^2

To get from a proportional expression (∝) to an equation (=), we have to add a multiplication factor to r^2 to account for the how fast T changes with respect to r^2, so:

T=k*(r)^2 (1)

From...

## See

This Answer NowStart your **48-hour free trial** to unlock this answer and thousands more. Enjoy eNotes ad-free and cancel anytime.

Already a member? Log in here.

Mathematically, if T is directly proportional to r squared, we write that as:

T∝r^2

To get from a proportional expression (∝) to an equation (=), we have to add a multiplication factor to r^2 to account for the how fast T changes with respect to r^2, so:

T=k*(r)^2 (1)

From here, we can plug in the numbers we know, which leads to:

9=k*(r)^2 (2)

And understanding that r doubling is the same as 2*r,

T=k*(2*r)^2 (3)

Using the distributive property we get:

T=k*(2)^2*(r)^2 (4)

Which simplifies to:

T=4*k*(r)^2 (5)

Now, if we look to work we did up above in equation (2), we see that:

k*(r)^2=9 (6)

So, now we substitute 9 into equation (5) and get:

T=4*9=28,

So, T=28 when r is doubled.