Can You Find the Constant Value K for a Slowly Inflating Balloon?

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The discussion focuses on determining the constant value K in the equation dr/dt = k/r² for a spherical balloon's inflation. The user has provided specific values: the radius (r) is 6 cm and the rate of change of the radius (dr/dt) is 5/36π cm per second. By substituting these values into the equation, K can be calculated as K = (dr/dt) * r², resulting in K = (5/36π) * (6²) = 5/6π.

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Hi,
I'm working on a problem about a spherical balloon as its inflated slowly the radius of the balloon is in cm and the time is in seconds

dr/dt = k/r2

Now I know how to rearrange this equation using separable differentiation

r=3√3kt+c

However I would like to find the value of the constant K

For example the radius is 6cm and the radius is increasing at the rate of 5/36pi cm per second and I would like to rearrange the dr/dt=k/r2 to find the value of K

Any help would be appreciated
 
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You are given dr/dt (5/36pi cm per second) at a given r (6cm). Plug these into your first equation and solve for k.
 

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