Answer:0.210 ft/min
Explanation:
Given
Length of trough ![L=16 ft](https://tex.z-dn.net/?f=L%3D16%20ft)
width of base ![b=2 ft](https://tex.z-dn.net/?f=b%3D2%20ft)
height of triangle![h=1 ft](https://tex.z-dn.net/?f=h%3D1%20ft)
From Similar triangles property
![\frac{4}{2x}=\frac{1}{y}](https://tex.z-dn.net/?f=%5Cfrac%7B4%7D%7B2x%7D%3D%5Cfrac%7B1%7D%7By%7D)
![2y=x](https://tex.z-dn.net/?f=2y%3Dx)
volume of water in time t
![V=\frac{1}{2}\times (2x\cdot y)\cdot](https://tex.z-dn.net/?f=V%3D%5Cfrac%7B1%7D%7B2%7D%5Ctimes%20%282x%5Ccdot%20y%29%5Ccdot%20)
![V=16xy](https://tex.z-dn.net/?f=V%3D16xy)
![V=32y^2](https://tex.z-dn.net/?f=V%3D32y%5E2)
differentiating
![\frac{\mathrm{d} V}{\mathrm{d} t}=32\times 2\times y\times \frac{\mathrm{d} y}{\mathrm{d} t}](https://tex.z-dn.net/?f=%5Cfrac%7B%5Cmathrm%7Bd%7D%20V%7D%7B%5Cmathrm%7Bd%7D%20t%7D%3D32%5Ctimes%202%5Ctimes%20y%5Ctimes%20%5Cfrac%7B%5Cmathrm%7Bd%7D%20y%7D%7B%5Cmathrm%7Bd%7D%20t%7D)
at ![y=8 in.\approx 0.667 ft](https://tex.z-dn.net/?f=y%3D8%20in.%5Capprox%200.667%20ft)
![9=64\times 0.667\times \frac{\mathrm{d} y}{\mathrm{d} t}](https://tex.z-dn.net/?f=9%3D64%5Ctimes%200.667%5Ctimes%20%5Cfrac%7B%5Cmathrm%7Bd%7D%20y%7D%7B%5Cmathrm%7Bd%7D%20t%7D)
![\frac{\mathrm{d} y}{\mathrm{d} t}=\frac{9}{64\times 0.667}](https://tex.z-dn.net/?f=%5Cfrac%7B%5Cmathrm%7Bd%7D%20y%7D%7B%5Cmathrm%7Bd%7D%20t%7D%3D%5Cfrac%7B9%7D%7B64%5Ctimes%200.667%7D)
![\frac{\mathrm{d} y}{\mathrm{d} t}=0.210 ft/min](https://tex.z-dn.net/?f=%5Cfrac%7B%5Cmathrm%7Bd%7D%20y%7D%7B%5Cmathrm%7Bd%7D%20t%7D%3D0.210%20ft%2Fmin)
Answer:
30 m³
Explanation:
Parameters given:
Initial volume of helium, V1 = 5 m³
Initial pressure in balloon, P1 = 30 kPa
Final pressure, P2 = 5 kPa
To find the volume of the balloon at that volume, we apply Boyle's law.
It states that at constant temperature, the pressure of a gas is inversely proportional to the volume of the gas.
Mathematically:
P = k / V
Where k = constant of proportionality
This implies that:
P * V = k
This means that if the pressure or volume of the gas changes at the same temperature, the product of the pressure and volume would be the same:
Hence:
P1 * V1 = P2 * V2
Hence, to find the final volume:
30 * 5 = 5 * V2
=> V2 = (30 * 5) / 5
V2 = 30 m³
The volume of the gas when the pressure is 5 kPa is 30 m³.
C a sliding Door ig idk tell me the right answer
Answer:
I think is B. sound, nuclear, electrical
but if I wrong then I am so sorry