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hram777 [196]
3 years ago
5

PLEASE HELP! LINE DILATIONS DUE TOMORROW! ILL MARK BRAINLIEST IF YOU EXPLAIN! TYSMMMMM

Mathematics
2 answers:
Ilya [14]3 years ago
8 0
It is b
gn hope it helps
kirill115 [55]3 years ago
6 0
The answer is B. The +2 is the slope
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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
3 years ago
9 yd<br> 12 yd<br> What is the length of the hypotenuse?
alexandr402 [8]
A^2 + b^2 = c^2
9^2 + 12^2= c^2
81 + 144 = 225
C= 15
The answer is 15 yards.
7 0
3 years ago
Read 2 more answers
Plzzz i need an actual answer plz
natta225 [31]

Answer:

185.60944

Step-by-step explanation:

Using the formulas

A=πrl+πr2

l=r2+h2

Solving forA

A=πr(r+h2+r2)=π·4·(4+102+42)≈185.60944

5 0
2 years ago
Reason for 4 pleaseeee
Marina CMI [18]

The reason for statement 4 is CPCTC.

6 0
3 years ago
Elsa earns 5140 for working 20 hours
lys-0071 [83]

Answer:

$2.57

Step-by-step explanation:

divide 5,140 by 20,

5,140/20=257=2.57

7 0
2 years ago
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