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3 years ago

Help me plz? Plllzzzz?

Mathematics

1 answer:

Tamiku [17]3 years ago

6 0

Answer: a). 11449 b). 39996 e). 996004

Explanation:

107^2
= (100+7)^2
= (100+7)(100+7)
= 10000 + 700 + 700+ 49
= 10000 + 1400 + 49
= 11449

198 x 202
= (200-2)(200+2)
= 40000 - 4
= 39996

998^2
= (1000-2)(1000-2)
= 1000000 - 2000 - 2000 + 4
= 1000000 - 4000 + 4
= 996000 + 4
= 996004

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A tank is filled with 1000 liters of pure water. Brine containing 0.04 kg of salt per liter enters the tank at 9 liters per minu

klemol [59]

Answer:

The differential equation which describes the mixing process is $\frac{dc_{salt,out}}{dt} + \frac{2}{125}\cdot c_{salt,out} = \frac{71}{100000}$ .

Step-by-step explanation:

The mixing process within the tank is modelled after the Principle of Mass Conservation, which states that:

$\dot m_{salt,in} - \dot m_{salt,out} = \frac{dm_{tank}}{dt}$

Physically speaking, mass flow of salt is equal to the product of volume flow of water and salt concentration. Then:

$\dot V_{water, in, 1}\cdot c_{salt, in,1} + \dot V_{water, in, 2} \cdot c_{salt,in, 2} - \dot V_{water, out}\cdot c_{salt, out} = V_{tank}\cdot \frac{dc_{salt,out}}{dt}$

Given that $\dot V_{water, in, 1} = 9\,\frac{L}{min}$ , $\dot V_{water, in, 2} = 7\,\frac{L}{min}$ , $c_{salt,in,1} = 0.04\,\frac{kg}{L}$ , $c_{salt, in, 2} = 0.05\,\frac{kg}{L}$ , $\dot V_{water, out} = 16\,\frac{L}{min}$ and $V_{tank} = 1000\,L$ , the differential equation that describes the system is:

$0.71 - 16\cdot c_{salt,out} = 1000\cdot \frac{dc_{salt,out}}{dt}$

$1000\cdot \frac{dc_{salt, out}}{dt} + 16\cdot c_{salt, out} = 0.71$

$\frac{dc_{salt,out}}{dt} + \frac{2}{125}\cdot c_{salt,out} = \frac{71}{100000}$

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riadik2000 [5.3K]

Answer:

Yes

Step-by-step explanation:

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