Answer:
hey what is the question man
Answer:
line
Step-by-step explanation:
you can obviously see lines in the shape
Answer:
This is the rate at which the radius of the balloon is changing when the volume is 300

Step-by-step explanation:
Let
be the radius and
the volume.
We know that the gas is escaping from a spherical balloon at the rate of
because the volume is decreasing, and we want to find 
The two variables are related by the equation

taking the derivative of the equation, we get

With the help of the formula for the volume of a sphere and the information given, we find
![V=\frac{4}{3}\pi r^3\\\\300=\frac{4}{3}\pi r^3\\\\r^3=\frac{225}{\pi }\\\\r=\sqrt[3]{\frac{225}{\pi }}](https://tex.z-dn.net/?f=V%3D%5Cfrac%7B4%7D%7B3%7D%5Cpi%20r%5E3%5C%5C%5C%5C300%3D%5Cfrac%7B4%7D%7B3%7D%5Cpi%20r%5E3%5C%5C%5C%5Cr%5E3%3D%5Cfrac%7B225%7D%7B%5Cpi%20%7D%5C%5C%5C%5Cr%3D%5Csqrt%5B3%5D%7B%5Cfrac%7B225%7D%7B%5Cpi%20%7D%7D)
Substitute the values we know and solve for 
![\frac{dV}{dt}=4\pi r^2 \frac{dr}{dt}\\\\\frac{dr}{dt}=\frac{\frac{dV}{dt}}{4\pi r^2} \\\\\frac{dr}{dt}=-\frac{12}{4\pi (\sqrt[3]{\frac{225}{\pi }})^2} \\\\\frac{dr}{dt}=-\frac{3}{\pi \left(\sqrt[3]{\frac{225}{\pi }}\right)^2}\\\\\frac{dr}{dt}=-\frac{3}{\pi \frac{225^{\frac{2}{3}}}{\pi ^{\frac{2}{3}}}}\\\\\frac{dr}{dt}=-\frac{3}{225^{\frac{2}{3}}\pi ^{\frac{1}{3}}} \approx -0.05537 \:\frac{ft}{h}](https://tex.z-dn.net/?f=%5Cfrac%7BdV%7D%7Bdt%7D%3D4%5Cpi%20r%5E2%20%5Cfrac%7Bdr%7D%7Bdt%7D%5C%5C%5C%5C%5Cfrac%7Bdr%7D%7Bdt%7D%3D%5Cfrac%7B%5Cfrac%7BdV%7D%7Bdt%7D%7D%7B4%5Cpi%20r%5E2%7D%20%5C%5C%5C%5C%5Cfrac%7Bdr%7D%7Bdt%7D%3D-%5Cfrac%7B12%7D%7B4%5Cpi%20%28%5Csqrt%5B3%5D%7B%5Cfrac%7B225%7D%7B%5Cpi%20%7D%7D%29%5E2%7D%20%5C%5C%5C%5C%5Cfrac%7Bdr%7D%7Bdt%7D%3D-%5Cfrac%7B3%7D%7B%5Cpi%20%5Cleft%28%5Csqrt%5B3%5D%7B%5Cfrac%7B225%7D%7B%5Cpi%20%7D%7D%5Cright%29%5E2%7D%5C%5C%5C%5C%5Cfrac%7Bdr%7D%7Bdt%7D%3D-%5Cfrac%7B3%7D%7B%5Cpi%20%5Cfrac%7B225%5E%7B%5Cfrac%7B2%7D%7B3%7D%7D%7D%7B%5Cpi%20%5E%7B%5Cfrac%7B2%7D%7B3%7D%7D%7D%7D%5C%5C%5C%5C%5Cfrac%7Bdr%7D%7Bdt%7D%3D-%5Cfrac%7B3%7D%7B225%5E%7B%5Cfrac%7B2%7D%7B3%7D%7D%5Cpi%20%5E%7B%5Cfrac%7B1%7D%7B3%7D%7D%7D%20%5Capprox%20-0.05537%20%5C%3A%5Cfrac%7Bft%7D%7Bh%7D)