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A tank contains 200 liters of fluid in which 30 grams
A tank contains 200 liters of fluid in which 30 grams
A tank contains 200 liters of fluid in which 30 grams
Q21E A tank contains 200 litres of f… [FREE SOLUTION] [1]
A tank contains 200 litres of fluid in which 30 grams of salt is dissolved. Brine containing 1 gram of salt per litre is then pumped into the tank at a rate of ; the well-mixed solution is pumped out at the same rate
The number of grams of salt in the tank at time is .. The mixing of two fluids sometimes gives rise to a linear first-order differential equation.
As the equation (2) is linear and separable, so integrate the equation and separate the variables.. To find the values of constants, apply the point in the equation (3), then
Answer in Differential Equations for JSE #122451 [2]
“R_{in} = \\frac{1g}{1L} \\frac{5L}{1 min} = 5 g\/min”. “R_{out} = \\frac{A}{200}*{5} = \\frac{A}{40} g\/min”
(2) For this part, since we are pumping pure water so “R_{in} = 0”. “R_{out} = \\frac{A}{420}*6 = \\frac{A}{70} g\/min”
Differential equations: Modeling with first order DE [3]
We assume that each day, the amount of newly produced goods is the same (constant). The result product from the factory is being accumulated, but the change of goods made at any day is zero.
Transmutation of radioactive particles depends on number of such particles. The number of observed transmutations is not constant in time, but (at given time) is e.g
Carbon dating is used to determine approximate ages of fossilized matters. All living organism contain two isotopes of carbon: C12 and C14
Mixture DE [4]
A tank contains 200 liters of fluid which 30 grams of salt is dissolved. Brine containing 1 gram of salt per liter is then pumped into the tank at a rate of 4 L/min; the well-mixed solution is pumped out at the same rate
[tex]\frac{dA}{dt} = (1g/L)(4L/min) – \frac{(4L/min)(A(t))g}{(200L) + (4L/min – 4L/min)t}[/tex]. [tex]f(t) = \frac{1}{e^{\frac{At}{50}}}[\int (e^{\frac{At}{50}})(4) dt + c][/tex]
[tex]f(t) = \frac{200e^{\frac{At}{50}}}{Ae^{\frac{At}{50}}} + \frac{c}{e^{\frac{At}{50}}}][/tex]
Answered: A tank contains 200 liters of fluid in… [5]
A tank contains 200 liters of fluid in wich 30 grams of salt in dissolved. Brine containing 1 gram of per liter is then pumped into the tank at a rate of 4 liter/minutes the well mixed solution is pumped out at the same rate
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Brine containing 1 g of salt/L is then poured into the tank at the rate of 4L / m * i * n and the solution is mixed well and is pumped out of the same rateFind the amount of salt in the container after 5 minutes ?. APPLICATIONS OF DIFFERENTIAL EQUATION: A tank is initially filled with 100 liters of pure water
SOLVED: A tank contains 200 liters of fluid in which 30 grams of salt is dissolved. Brine containing 1 gram of salt per liter is then pumped into the tank at a rate of 4 L/min. The well-mixed solution [6]
Get 5 free video unlocks on our app with code GOMOBILE. A tank contains 200 liters of fluid in which 30 grams of salt is dissolved
The well-mixed solution is pumped out at the same rate. Find the number of grams of salt in the tank at time t.
Brine containing 1 gram of salt per liter is then pumped into the tank at a rate of $4 \mathrm{L} / \mathrm{min} ;$ the well-mixed solution is pumped out at the same rate. Find the number $A(t)$ of grams of salt in the tank at time $t$
A tank contains 200 liters of fluid in which 30 grams of salt is dissolved. brine containing 1 gram of salt per liter is then pumped into the tank at a rate of 5 l/min; the well-mixed solution is pump [7]
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brine containing 1 gram of salt per liter is then pumped into the tank at a rate of 5 l/min; the well-mixed solution is pump. A tank contains 200 liters of fluid in which 30 grams of salt is dissolved
find the number a(t) of grams of salt in the tank at time t.
(Get Answer) – A tank contains 200 liters of fluid in which 30 grams of salt is… [8]
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Find the number A(t) of grams of salt in the tank at time t.. Given problem:- A tank contains 200 liters of fluid in which 30 grams of salt is dissolved
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[Solved] A tank contains 200 liters of fluid in wh [9]
A tank contains 200 liters of fluid in which 30 grams of salt is dissolved. Brine containing 1 gram of salt per liter is then pumped into the tank at a rate of 4 L/min; the well-mixed solution is pumped
Brine containing 1 gram of salt per liter is then pumped into the tank at a rate of 4 L/min; the well-mixed solution is pumped out at the same rate. Find the number A(t) of grams of salt in the tank at time t.
A First Course in Differential Equations with Modeling Applications. Solve Problem 21 assuming that pure water is pumped into the tank
How do I solve for number of grams of salt in a tank at time ‘t’ with a changing volume correctly (mixing problem) [10]
I went through this problem by adapting my work from a problem that had a constant volume, but my final answer is not realistic, so I know I messed up somewhere along the road. -Tank contains 200 liters of fluid in which 30 grams of salt is dissolved
-The well-mixed solution is then pumped out at a rate of 5L/min. From this, found the volume equation $V(t) = 200 – t$.
$$\frac{dx}{dt} = (1 g/L)(4L/min) – (5 L/min)\frac{x(t)}{200-t}.$$. So my integrating factor $\mu = e^{-5\ln(200-t)}$, which simplified was $\mu = (200-t)^{-5}$
[Tamil] A tank contains 5000 litres of pure water. Brine (very salty w [11]
Brine (very salty water) that contains 30 of salt per litre of water is pumped into grams the tank at a rate of 25 litres per minute. The concentration of salt water after t minutes (in grams per litre) is C(t)=30t200+t.What happens to the concentration as t→∞?Solution in Tamil
Brine (very salty water) that contains 30 of salt per litre of water is pumped into grams the tank at a rate of 25 litres per minute. The concentration of salt water after t minutes (in grams per litre) is C(t)=(30t)/(200+t).What happens to the concentration as trarrinfty? by Maths experts to help you in doubts & scoring excellent marks in Class 11 exams.
Sources
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- https://www.numerade.com/ask/question/11-a-tank-contains-200-liters-of-fluid-in-which-30-grams-of-salt-is-dissolved-brine-containing-1-gram-of-salt-per-liter-is-then-pumped-into-the-tank-at-a-rate-of-4-llmin-the-well-mixed-solut-18562/
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- https://math.stackexchange.com/questions/2657922/how-do-i-solve-for-number-of-grams-of-salt-in-a-tank-at-time-t-with-a-changing
- https://www.doubtnut.com/question-answer/a-tank-contains-5000-litres-of-pure-water-brine-very-salty-water-that-contains-30-of-salt-per-litre–320197005
