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3 years ago

What is a statement of cell theory

Mathematics

1 answer:

tatyana61 [14]3 years ago

6 0

Answer:

Its B.

Step-by-step explanation:

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A brine solution of salt flows at a constant rate of 8L/min into a large tank that initially held 100L of brine solution in whic

GaryK [48]

Answer:

The mass of salt in the tank after t minutes is

$y(t) = 5-4.5e^{-\frac{2t}{25}}$

The concentration of salt in the tank reach 0.02 kg/L when $t=-\frac{25\ln \left(\frac{83}{75}\right)}{2} \approx -1.2669$

Step-by-step explanation:

Let y(t) be the mass of salt (in kg) that is in the tank at any time, t (in minutes).

The main equation that we will be using to model this mixing process is:

Rate of change of $\frac{dy}{dt}$ = Rate of salt in - Rate of salt out

We need to determine the rate at which salts enters the tank. From the information given we know:

The brine flows into the tank at a rate of $8\:\frac{L}{min}$
The concentration of salt in the brine entering the tank is $0.05\:\frac{kg}{L}$

The Rate of salt in = (flow rate of liquid entering) x (concentration of salt in liquid entering)

$(8\:\frac{L}{min}) \cdot (0.05\:\frac{kg}{L})=0.4 \:\frac{kg}{min}$

Next, we need to determine the output rate of salt from the tank.

The Rate of salt out = (flow rate of liquid exiting) x (concentration of salt in liquid exiting)

The concentration of salt in any part of the tank at time t is just y(t) divided by the volume. From the information given we know:

The tank initially contains 100 L and the rate of flow into the tank is the same as the rate of flow out.

$(8\:\frac{L}{min}) \cdot (\frac{y(t)}{100} \:\frac{kg}{L})= \frac{2y(t)}{25} \:\frac{kg}{min}$

At time t = 0, there is 0.5 kg of salt, so the initial condition is y(0) = 0.5. And the mathematical model for the mixing process is

$\frac{dy}{dt}=0.4-\frac{2y(t)}{25}, \quad{y(0)=0.5}$

$\frac{dy}{dt}=0.4-\frac{2y(t)}{25}\\\\\mathrm{Rewrite\:in\:the\:form\:of\:a\:first\:order\:separable\:ODE}\\\\ \frac{1}{2}\frac{dy}{5-y}=\frac{1}{25}dt \\\\\frac{1}{2}\int \frac{dy}{5-y}=\int \frac{1}{25}dt\\\\\frac{1}{2}\left(-\ln \left|5-y\right|+C\right)=\frac{1}{25}t+C\\\\-\frac{1}{2}\ln \left|5-y\right|+C_1\right)=\frac{1}{25}t+C\\\\-\frac{1}{2}\ln \left|5-y\right|=\frac{1}{25}t+C_2\\\\5-y=C_3e^{-\frac{2t}{25} }\\\\y(t) =5-C_3e^{-\frac{2t}{25} }$

Using the initial condition y(0)=0.5

$y(t) =5-C_3e^{-\frac{2t}{25} }\\y(0)=0.5=5-C_3e^{-\frac{2(0)}{25}} \\C_3=4.5$

The mass of salt in the tank after t minutes is

$y(t) = 5-4.5e^{-\frac{2t}{25}}$

To determine when the concentration of salt is 0.02 kg/L, we solve for t

$y(t) = 5-4.5e^{-\frac{2t}{25}}\\\\0.02=5-4.5e^{-\frac{2t}{25}}\\\\5\cdot \:100-4.5e^{-\frac{2t}{25}}\cdot \:100=0.02\cdot \:100\\\\500-450e^{-\frac{2t}{25}}=2\\\\500-450e^{-\frac{2t}{25}}-500=2-500\\\\-450e^{-\frac{2t}{25}}=-498\\\\e^{-\frac{2t}{25}}=\frac{83}{75}\\\\\ln \left(e^{-\frac{2t}{25}}\right)=\ln \left(\frac{83}{75}\right)\\\\\frac{2t}{25}=\ln \left(\frac{83}{75}\right)\\\\t=-\frac{25\ln \left(\frac{83}{75}\right)}{2} \approx -1.2669$

5 0

3 years ago

Jack works at a party supply store. He sold 846 balloons in the last 18 days. What was his selling rate in balloons per day?

ser-zykov [4K]

Answer:

Step-by-step explanation:

Make a proportion.

x is the number of balloons sold each day.

$x=\frac{846}{18} \\ \\ x=47$

4 0

3 years ago

Read 2 more answers

5x - y = 6 -2x +y = 8 What’s the answer

nevsk [136]

Answer:

x= $4\frac{2}{3}$

y= $17\frac{1}{3}$

Step-by-step explanation:

$5x-y=6\\-2x+y=8\\$

Simplify, find the x-value first:

$3x=14\\x=4\frac{2}{3}$

Substitute x-value into any equation (i did the second equation) and simplify:

$-2(4\frac{2}{3})+y=8\\ -9\frac{1}{3} +y=8\\$

$y=17\frac{1}{3}$

4 0

4 years ago

What is the circumference?

Tanya [424]

Answer: the circumference is the perimeter of a circle or ellipse. That is, the circumference would be the arc length of the circle, as if it were opened up and straightened out to a line segment. More generally, the perimeter is the curve length around any closed figure.

8 0

3 years ago

Read 2 more answers

If log subscript 2 left parenthesis 3 x minus 2 right parenthesis equals 4, then what is the value of x?

elena-14-01-66 [18.8K]

Answer:

x = 6

See image.

Step-by-step explanation:

Logarithms are just another way to write exponents. The base on the logarithm that is the small font subscript IS the base (normal font/on the line) of an exponential equation. The "answer" in the logarithmic equation is the exponent (small font/superscript) .It is just a triple shuffle. When the logarithmic equation cant be worked on to solve it, CHANGE IT to exponential form. See image.

6 0

2 years ago