Answer:
0.13 ft/min
Step-by-step explanation:
We are given that
![\frac{dV}{dt}=15ft^3/min](https://tex.z-dn.net/?f=%5Cfrac%7BdV%7D%7Bdt%7D%3D15ft%5E3%2Fmin)
We have to find the increasing rate of change of height of pile when the pile is 12 ft high.
Let d be the diameter of pile
Height of pile=h
d=h
Radius of pile,r=![\frac{d}{2}=\frac{h}{2}](https://tex.z-dn.net/?f=%5Cfrac%7Bd%7D%7B2%7D%3D%5Cfrac%7Bh%7D%7B2%7D)
Volume of pile=![\frac{1}{3}\pi r^2 h=\frac{1}{12}\pi h^3](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B3%7D%5Cpi%20r%5E2%20h%3D%5Cfrac%7B1%7D%7B12%7D%5Cpi%20h%5E3)
![\frac{dV}{dt}=\frac{1}{4}\pi h^2\frac{dh}{dt}](https://tex.z-dn.net/?f=%5Cfrac%7BdV%7D%7Bdt%7D%3D%5Cfrac%7B1%7D%7B4%7D%5Cpi%20h%5E2%5Cfrac%7Bdh%7D%7Bdt%7D)
h=12 ft
Substitute the values
![15=\frac{1}{4}\pi(12)^2\frac{dh}{dt}](https://tex.z-dn.net/?f=15%3D%5Cfrac%7B1%7D%7B4%7D%5Cpi%2812%29%5E2%5Cfrac%7Bdh%7D%7Bdt%7D)
![\frac{dh}{dt}=\frac{15\times 4}{\pi(12)^2}](https://tex.z-dn.net/?f=%5Cfrac%7Bdh%7D%7Bdt%7D%3D%5Cfrac%7B15%5Ctimes%204%7D%7B%5Cpi%2812%29%5E2%7D)
![\frac{dh}{dt}=0.13ft/min](https://tex.z-dn.net/?f=%5Cfrac%7Bdh%7D%7Bdt%7D%3D0.13ft%2Fmin)
Answer:
Here are pictures of the graph and corresponding table. Hope this helps!
Step-by-step explanation:
Answer:
Step-by-step explanation:
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Answer:
Step-by-step explanation:
Least common denominator is 10
there are 10/10 portions in the whole circle
1/2 = 5/10
2/5 = 4/10
10/10 - 5/10 - 4/10 = 1/10