When an spherical balloon volume is increasing at the rate of
then the diameter of the balloon is increasing ![\frac{3}{2\pi }ft /min](https://tex.z-dn.net/?f=%5Cfrac%7B3%7D%7B2%5Cpi%20%7Dft%20%2Fmin)
How can we find the rate of change of balloon's diameter ?
The volume of a spherical balloon is ![v=\frac{4}{3} \pi r^3](https://tex.z-dn.net/?f=v%3D%5Cfrac%7B4%7D%7B3%7D%20%5Cpi%20r%5E3)
In form of diameter we can write as
![v=\frac{4}{3} \pi (\frac{D}{2} )^3\\=\frac{1}{6} \pi D^3](https://tex.z-dn.net/?f=v%3D%5Cfrac%7B4%7D%7B3%7D%20%5Cpi%20%28%5Cfrac%7BD%7D%7B2%7D%20%29%5E3%5C%5C%3D%5Cfrac%7B1%7D%7B6%7D%20%5Cpi%20D%5E3)
Now we will differentiate both sides wrt to
we get
![\frac{dv}{dt} =\frac{1}{6} \pi 3D^2 \frac{dD}{dt} \\\frac{dD}{dt} =\frac{2}{\pi D^2} \frac{dv}{dt} \\\\when r=1\\D=2ft](https://tex.z-dn.net/?f=%5Cfrac%7Bdv%7D%7Bdt%7D%20%3D%5Cfrac%7B1%7D%7B6%7D%20%5Cpi%203D%5E2%20%5Cfrac%7BdD%7D%7Bdt%7D%20%5C%5C%5Cfrac%7BdD%7D%7Bdt%7D%20%3D%5Cfrac%7B2%7D%7B%5Cpi%20D%5E2%7D%20%5Cfrac%7Bdv%7D%7Bdt%7D%20%5C%5C%5C%5Cwhen%20r%3D1%5C%5CD%3D2ft)
Given in the question ![\frac{dv}{dt} =3ft^3/min](https://tex.z-dn.net/?f=%5Cfrac%7Bdv%7D%7Bdt%7D%20%3D3ft%5E3%2Fmin)
thus when we substitute the values we get
![\frac{dD}{dt} =\frac{2}{\pi *2^2} (3)\\\frac{dD}{dt}=\frac{3}{2\pi } ft/min](https://tex.z-dn.net/?f=%5Cfrac%7BdD%7D%7Bdt%7D%20%3D%5Cfrac%7B2%7D%7B%5Cpi%20%2A2%5E2%7D%20%283%29%5C%5C%5Cfrac%7BdD%7D%7Bdt%7D%3D%5Cfrac%7B3%7D%7B2%5Cpi%20%7D%20%20ft%2Fmin)
Learn more about the differentiation here:
brainly.com/question/28046488
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It is 9 because 11 minus 2 is equal to 9.
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X=82
Step-by-step explanation:
Answer:
y-6
Step-by-step explanation: