What is the missing value to the equation -3x + 7y = 5x + 2y

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

4 0

3 years ago

The number of eggs in the refrigerator e decreased by 5 equals 18

AnnZ [28]

Answer:

e=23

Step-by-step explanation:

The equation representing this scenario is e-5=18.

Add 5 to both sides and you get e=23 (eggs)

7 0

3 years ago

9.50 One way to evaluate the effectiveness of a teaching assistant is to examine the scores achieved by his or her students on a

EleoNora [17]

Answer:

Step-by-step explanation:

Given that a professor sets a standard examination at the end of each semester for all sections of a course. The variance of the scores on this test is typically very close to 300.

$H_0: s^2 = 300\\H_a: s^2 \neq 300$

(Two tailed test for variance )

Sample variance =480

We can use chi square test for testing of hypothesis

Test statistic = $\frac{(n-1)s^2}{\sigma^2} \\=62.4$

p value = 0.0100

Since p <0.05 our significance level, we reject H0.

The sample variance cannot be claimed as equal to 300.

5 0

3 years ago

13. Distributive Property<br> 3(x - 1) = 3x - ?

goblinko [34]

Answer:

$\huge\boxed{3x-3}$

Step-by-step explanation:

$3(x-1)=\\\\\text{Distribute: }\left \{ {{3*x=3x} \atop {3*-1=-3}} \right.\\\\3(x-1)=\boxed{3x-3}$

8 0

3 years ago

Read 2 more answers

What is science ? or what is math

german

Answer:

Science is a set of tools people used to build robust predictions. The tools are called The Scientific Method. (Some people prefer to say that Science creates explanations. That's fine. They are explanations in the form of predictions.)

The first step is to come up with a falsifiable hypothesis. That's a claim which can, in theory, be proven wrong. The next step is to try to prove it wrong via careful observation and experimentation.

If you manage to falsify the hypothesis or are unable to falsify it, you will be able to use it to make predictions.

I would define mathematics as the study of structure divorced from context.

In mathematics, we study various structures: numbers, groups, geometric objects, etc. We study their patterns and figure out how they work and interconnect. I would make the argument that anything existing in the universe and anything that can be cooked up by the human mind that has some sort of structure to it can be studied mathematically.

Of course, what one might argue is that disciplines like physics, chemistry, and biology do the same thing: they search for the physical patterns and structures that exist out in the world.

Step-by-step explanation:

please give me brainliest

7 0

3 years ago