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)
Answer:
1
Step-by-step explanation:
take the -2 and divide it by 2
that gives you -1
then square it
now its positive 1
formula is 
where b is the term next to the x
Answer:
Step-by-step explanation:
Variability (also called spread or dispersion) refers to how spread out a set of data is. Variability gives you a way to describe how much data sets vary and allows you to use statistics to compare your data to other sets of data.
