Answer:
The water level changing by the rate of -0.0088 feet per hour ( approx )
Step-by-step explanation:
Given,
The volume of a segment of height h in a hemisphere of radius r is,
![V=\pi h^2(r-\frac{h}{3})](https://tex.z-dn.net/?f=V%3D%5Cpi%20h%5E2%28r-%5Cfrac%7Bh%7D%7B3%7D%29)
Where, r is the radius of the hemispherical tank,
h is the water level, ( in feet )
Here, r = 9 feet,
![\implies V=\pi h^2(9-\frac{h}{3})](https://tex.z-dn.net/?f=%5Cimplies%20V%3D%5Cpi%20h%5E2%289-%5Cfrac%7Bh%7D%7B3%7D%29)
![V=9\pi h^2-\frac{\pi h^3}{3}](https://tex.z-dn.net/?f=V%3D9%5Cpi%20h%5E2-%5Cfrac%7B%5Cpi%20h%5E3%7D%7B3%7D)
Differentiating with respect to t ( time ),
![\frac{dV}{dt}=18\pi h\frac{dh}{dt}-\frac{3\pi h^2}{3}\frac{dh}{dt}](https://tex.z-dn.net/?f=%5Cfrac%7BdV%7D%7Bdt%7D%3D18%5Cpi%20h%5Cfrac%7Bdh%7D%7Bdt%7D-%5Cfrac%7B3%5Cpi%20h%5E2%7D%7B3%7D%5Cfrac%7Bdh%7D%7Bdt%7D)
![\frac{dV}{dt}=\pi h(18-h)\frac{dh}{dT}](https://tex.z-dn.net/?f=%5Cfrac%7BdV%7D%7Bdt%7D%3D%5Cpi%20h%2818-h%29%5Cfrac%7Bdh%7D%7BdT%7D)
Here, ![\frac{dV}{dt}=-2\text{ cubic feet per hour}](https://tex.z-dn.net/?f=%5Cfrac%7BdV%7D%7Bdt%7D%3D-2%5Ctext%7B%20cubic%20feet%20per%20hour%7D)
And, h = 6 feet,
Thus,
![-2=\pi 6(18-6)\frac{dh}{dt}](https://tex.z-dn.net/?f=-2%3D%5Cpi%206%2818-6%29%5Cfrac%7Bdh%7D%7Bdt%7D)
![\implies \frac{dh}{dt}=\frac{-2}{72\pi}=-0.00884194128288\approx -0.0088](https://tex.z-dn.net/?f=%5Cimplies%20%5Cfrac%7Bdh%7D%7Bdt%7D%3D%5Cfrac%7B-2%7D%7B72%5Cpi%7D%3D-0.00884194128288%5Capprox%20-0.0088)
Answer:
y = 3x + 1 I think........
Answer:
m = -4/5 or m = -0.8
Step-by-step explanation:
Hope it helps:)
Answer:
5
Step-by-step explanation:
2x + 4 = 14 ( - 4 )
2x + 10 ( /2)
x= 5