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umka21 [38]
3 years ago
9

5x^2 - 9 - 7x^2 - x + 1

Mathematics
1 answer:
algol133 years ago
6 0

Answer:

−2x^2−x−8

Step-by-step explanation:

5x^2 - 9 - 7x^2 - x + 1 = −2x^2−x−8

5*x^2-9-7*x^2-x+1 = (-2*x^2)-x-8

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A tank has capacity 6 L and initially contains 11 mg of salt dissolved in 3 L of water. A solution containing 1 mg/L of salt ent
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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

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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

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