Answer:
The answer is below
Step-by-step explanation:
a) The maximum capacity of he tank is 6 L and initially it contains 11 mg of salt dissolved in 3 L of water. Solution enters the tank at a rate of 3 L/hr, therefore in x hours, the amount of water that have entered the tank = 3x.
Solution also leaves the tank at a rate of 2L/hr, therefore in x hours, the amount of water that have left the tank = 2x
Hence the amount of water present in the tank at x hours is given as:
3 + 3x - 2x = 3 + x
The time taken to full the tank can be gotten from:
3 + x = 6
x = 6 - 3
x = 3 hr
b)
![\frac{dQ}{dx}=3-\frac{2Q}{3+x}\\ \\\frac{dQ}{dx}+\frac{2Q}{3+x}=3\\\\let\ u'=\frac{2u}{3+x}\\\\\frac{u'}{u}=\frac{2Q}{3+x}\\\\ln(u)=2ln(3+x)\\\\u=(3+x)^2\\\\(3+x)^2Q]'=3(3+x)^2\\\\(3+x)^2Q=(3+x)^3+c\\\\Q(0)=11\\\\(3+0)^2(11)=(3+0)^3+c\\\\x=72\\\\Q=x+3+\frac{72}{(x+3)^2}\\ \\Q(3)=3+3+\frac{72}{(3+3)^2}=8\ mg](https://tex.z-dn.net/?f=%5Cfrac%7BdQ%7D%7Bdx%7D%3D3-%5Cfrac%7B2Q%7D%7B3%2Bx%7D%5C%5C%20%20%5C%5C%5Cfrac%7BdQ%7D%7Bdx%7D%2B%5Cfrac%7B2Q%7D%7B3%2Bx%7D%3D3%5C%5C%5C%5Clet%5C%20u%27%3D%5Cfrac%7B2u%7D%7B3%2Bx%7D%5C%5C%5C%5C%5Cfrac%7Bu%27%7D%7Bu%7D%3D%5Cfrac%7B2Q%7D%7B3%2Bx%7D%5C%5C%5C%5Cln%28u%29%3D2ln%283%2Bx%29%5C%5C%5C%5Cu%3D%283%2Bx%29%5E2%5C%5C%5C%5C%283%2Bx%29%5E2Q%5D%27%3D3%283%2Bx%29%5E2%5C%5C%5C%5C%283%2Bx%29%5E2Q%3D%283%2Bx%29%5E3%2Bc%5C%5C%5C%5CQ%280%29%3D11%5C%5C%5C%5C%283%2B0%29%5E2%2811%29%3D%283%2B0%29%5E3%2Bc%5C%5C%5C%5Cx%3D72%5C%5C%5C%5CQ%3Dx%2B3%2B%5Cfrac%7B72%7D%7B%28x%2B3%29%5E2%7D%5C%5C%20%5C%5CQ%283%29%3D3%2B3%2B%5Cfrac%7B72%7D%7B%283%2B3%29%5E2%7D%3D8%5C%20mg)
8 mg/ 6 L = 4/3 mg/L
Answer:
31
Step-by-step explanation:
y=kx
The answer is 3.16 ft
The surface area (SA) of the rectangular prism is:
SA = 2lw + 2ld + 2wd
However, the pool is without the top side, so the area of the top side should be excluded from the surface area of the pool. The surface area of the rectangular pool is:
SA = lw + 2ld + 2wd
We know:
SA = 210 ft²
l = 9 ft
w = 10 ft
d = ?
210 = 9 * 10 + 2 * 9 * d + 2 * 10 * d
210 = 90 + 18d + 20d
210 - 90 = 38d
120 = 38d
d = 120/38
d = 3.16 ft
Without replacement 26*25*24*23*22
with replacement 26^5