jdjdus8sisiiwisjw eusheu2ikwa
Step-by-step explanation:
udusbwha8doeny1iwjdhs79osbxyaim2
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)
So you need to put both the equation in the y equals if you have a graphing calculator
Then you compare the two equation
f(x) is an decay and g(x) is growth
For choice one and three, the answer choice doesn't make sense leaving you with two and four as the only ones.
Since f(x) is a decay, it cant be choice four either leaving choice 2 as the final answer
This makes sense because g(x) is a growth
I hope this helps!
Answer:
please answer only neeed solve questions
Step-by-step explanation:
I think hlp
