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2 years ago

I need help please with this equation:

Mathematics

1 answer:

swat322 years ago

8 0

Answer:

y=-3x+2

Step-by-step explanation:

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A tank contains 240 liters of fluid in which 20 grams of salt is dissolved. Brine containing 1 gram of salt per liter is then pu

Novosadov [1.4K]

Answer:

$A(t)=240-220e^{-\frac{t}{40}}$

Step-by-step explanation:

A tank contains 240 liters of fluid in which 20 grams of salt is dissolved.

Volume of the tank = 240 liters
Initial Amount of Salt in the tank, A(0)=20 grams

Brine containing 1 gram of salt per liter is then pumped into the tank at a rate of 6 L/min

$R_{in}=$ (concentration of salt in inflow)(input rate of fluid)

$R_{in}=(1\frac{gram}{liter})( 6\frac{Liter}{min})=6\frac{gram}{min}$

$R_{out}=$ (concentration of salt in outflow)(output rate of fluid)

$R_{out}=(\frac{A(t)}{240})( 6\frac{Liter}{min})\\R_{out}=\frac{A}{40}$

Rate of change of the amount of salt in the tank:

$\dfrac{dA}{dt}=R_{in}-R_{out}$

$\dfrac{dA}{dt}=6-\dfrac{A}{40}$

We then solve the resulting differential equation by separation of variables.

$\dfrac{dA}{dt}+\dfrac{A}{40}=6\\$The integrating factor: e^{\int \frac{1}{40}dt} =e^{\frac{t}{40}}\\$Multiplying by the integrating factor all through\\\dfrac{dA}{dt}e^{\frac{t}{40}}+\dfrac{A}{40}e^{\frac{t}{40}}=6e^{\frac{t}{40}}\\(Ae^{\frac{t}{40}})'=6e^{\frac{t}{40}}$

Taking the integral of both sides

$\int(Ae^{\frac{t}{40}})'=\int 6e^{\frac{t}{40}} dt\\Ae^{\frac{t}{40}}=6*40e^{\frac{t}{40}}+C, $(C a constant of integration)\\Ae^{\frac{t}{40}}=240e^{\frac{t}{40}}+C\\$Divide all through by e^{\frac{t}{40}}\\A(t)=240+Ce^{-\frac{t}{40}}$

Recall that when t=0, A(t)=20 (our initial condition)

$20=240+Ce^{-\frac{0}{40}}\\20-240=C\\C=-220\\$Therefore, the number A(t) of grams of salt in the tank at time t\\A(t)=240-220e^{-\frac{t}{40}}$

3 0

2 years ago

Write a rule to represent the sequence of numbers: 2, 8, 14, 20, 26

Yuki888 [10]

Answer:

Start at 2 and add 6 each time.

Example:

2+6= 8

8+6= 14

14+6= 20

20+6= 26

and you can keep on going if you want

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2 years ago

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Nicole works 50 hours a week and earns $25 per hour. Her company pays overtime of one and half times for all hours worked over 4

ankoles [38]

Her gross weekly pay would be $1375.

25 * 40 = $1000

time and a half means she would make $37.50 for the 10 hours overtime she works. 10 * 37.5 = 375

375 + 1000 = $1375

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3 years ago

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2 years ago

What shape has 4 sides that are different lengths

denis-greek [22]

Theres no real name for a shape with uneven sides. I just realized that. A four sided figure is a quadrilateral. Or irregular polygon/quadrilateral. A four sided shape with no even sides.

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3 years ago

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