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2 years ago

I'm too lazy to do the work by myself anyway, someone please help me thank you <3 !!

Mathematics

1 answer:

In-s [12.5K]2 years ago

7 0

Answer:

Step-by-step explanation:

10-3=7

7x7=49

49 x2 = 98

Have a good day! uwu

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A 1000-liter (L) tank contains 500 L of water with a salt concentration of 10 g/L. Water with a salt concentration of 50 g/L flo

djverab [1.8K]

Answer:

a) $y(t)=50000-49990e^{\frac{-2t}{25}}$

b) $31690.7 g/L$

Step-by-step explanation:

By definition, we have that the change rate of salt in the tank is $\frac{dy}{dt}=R_{i}-R_{o}$ , where $R_{i}$ is the rate of salt entering and $R_{o}$ is the rate of salt going outside.

Then we have, $R_{i}=80\frac{L}{min}*50\frac{g}{L}=4000\frac{g}{min}$ , and

$R_{o}=40\frac{L}{min}*\frac{y}{500} \frac{g}{L}=\frac{2y}{25}\frac{g}{min}$

So we obtain. $\frac{dy}{dt}=4000-\frac{2y}{25}$ , then

$\frac{dy}{dt}+\frac{2y}{25}=4000$ , and using the integrating factor $e^{\int {\frac{2}{25}} \, dt=e^{\frac{2t}{25}$ , therefore $(\frac{dy }{dt}+\frac{2y}{25}}=4000)e^{\frac{2t}{25}$ , we get $\frac{d}{dt}(y*e^{\frac{2t}{25}})= 4000 e^{\frac{2t}{25}$ , after integrating both sides $y*e^{\frac{2t}{25}}= 50000 e^{\frac{2t}{25}}+C$ , therefore $y(t)= 50000 +Ce^{\frac{-2t}{25}}$ , to find $C$ we know that the tank initially contains a salt concentration of 10 g/L, that means the initial conditions $y(0)=10$ , so $10= 50000+Ce^{\frac{-0*2}{25}}$

$10=50000+C\\C=10-50000=-49990$

Finally we can write an expression for the amount of salt in the tank at any time t, it is $y(t)=50000-49990e^{\frac{-2t}{25}}$

b) The tank will overflow due Rin>Rout, at a rate of $80 L/min-40L/min=40L/min$ , due we have 500 L to overflow $\frac{500L}{40L/min} =\frac{25}{2} min=t$ , so we can evualuate the expression of a) $y(25/2)=50000-49990e^{\frac{-2}{25}\frac{25}{2}}=50000-49990e^{-1}=31690.7$ , is the salt concentration when the tank overflows

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3 years ago

H + 7 = −7<br> h = Plz help im having truouble.

Natalija [7]

-14 because -14 + 7= -7

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2 years ago

If an ecosystem can only hold about 12-15 animals what is this called?

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It is called Ecological Succesion hope that helped:)

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2 years ago

The Coffee Shop around the Corner (CS) is famous for its fresh-made muffins. Hank, the owner of CS, knows that the demand for mu

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Answer:

The responses to the given question can be defined as follows:

Step-by-step explanation:

Please find the complete question in the attached file.

$Day \ \ \ \ \ \ \ \ \ \ Period \ \ \ \ \ \ \ \ \ \ Demand \ \ \ \ \ \ \ \ \ \ 5-period moving average$

$1 \ \ \ \ \ \ \ \ \ \ \ Morning \ \ \ \ \ \ \ \ \ \ \ 37 \\\\$

$Afternoon \ \ \ \ \ \ \ \ \ \ \ 25 \\\\ Evening \ \ \ \ \ \ \ \ \ \ \ 9$

$2 \ \ \ \ \ \ \ \ \ \ \ Morning \ \ \ \ \ \ \ \ \ \ \48 \\\\$

$Afternoon\ \ \ \ \ \ \ \ \ \ \ 28 \\\\$

$Evening \ \ \ \ \ \ \ \ \ \ \ 14 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 29.4 \\\\$

$3 \ \ \ \ \ \ \ \ \ \ \ Morning \ \ \ \ \ \ \ \ \ \ \ 53 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 24.8\\\\$

$Afternoon \ \ \ \ \ \ \ \ \ \ \ 33 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 30.4\\\\Evening \ \ \ \ \ \ \ \ \ \ \ 17 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 35.2\\\\$

$4\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ Morning \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 29\\\\$

$Afternoon\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 29.25\\\\Evening \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 34.33333\\\\$

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3 years ago

If x=-4 what is the value of the following expression?

Gre4nikov [31]

Answer:

2x^2 +3x -2

-22

-46

Step-by-step explanation:

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2 years ago