Answer:
![\frac{dr}{dt} = 0.0535 ft/hr](https://tex.z-dn.net/?f=%5Cfrac%7Bdr%7D%7Bdt%7D%20%3D%200.0535%20ft%2Fhr)
Step-by-step explanation:
Rate at which gas is escaping, dV/dt = 14 ft³/hr
Volume, V = 400 ft³
Volume of a sphere,
................(1)
Differentiate both sides with respect to t
![\frac{dV}{dt} = \frac{4}{3} \pi * 3r^{2}\frac{dr}{dt}](https://tex.z-dn.net/?f=%5Cfrac%7BdV%7D%7Bdt%7D%20%20%3D%20%5Cfrac%7B4%7D%7B3%7D%20%5Cpi%20%2A%203r%5E%7B2%7D%5Cfrac%7Bdr%7D%7Bdt%7D)
........................................(2)
From equation (1)
![400 = \frac{4}{3} \pi r^{3}\\\\ r = (\frac{1200}{4\pi } )^{1/3} \\\\r = 4.564 ft](https://tex.z-dn.net/?f=400%20%3D%20%5Cfrac%7B4%7D%7B3%7D%20%5Cpi%20r%5E%7B3%7D%5C%5C%5C%5C%20r%20%3D%20%20%28%5Cfrac%7B1200%7D%7B4%5Cpi%20%7D%20%29%5E%7B1%2F3%7D%20%5C%5C%5C%5Cr%20%3D%204.564%20ft)
Substitute the value of r and dV/dt into equation (2)
![14 =4\pi * 4.564^{2} \frac{dr}{dt}\\\\\frac{14}{261.79} = \frac{dr}{dt}\\\\\frac{dr}{dt} = 0.0535 ft/hr](https://tex.z-dn.net/?f=14%20%3D4%5Cpi%20%2A%204.564%5E%7B2%7D%20%20%20%5Cfrac%7Bdr%7D%7Bdt%7D%5C%5C%5C%5C%5Cfrac%7B14%7D%7B261.79%7D%20%3D%20%5Cfrac%7Bdr%7D%7Bdt%7D%5C%5C%5C%5C%5Cfrac%7Bdr%7D%7Bdt%7D%20%3D%200.0535%20ft%2Fhr)
Answer:
74.64
Step-by-step explanation:
hope this helps :)
Answer:
hi
Step-by-step explanation:
Answer:
12.6
Step-by-step explanation:
We can start by finding the area of the rectangle
13x4=52
Now the semicircles, the diameter of the circle is 4, so the radius is 2 to find the area we do
pi x 2=6.3
6.28^2=39.4
since there are two circles we can just add them together instead of dividing the answer above by 2, now we can subtract this from 52
52-39.4=12.6