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3 years ago

15

The bacteria took 1 hour and 40 minutes to fill the initial bottle. Explain how it only took 10 minutes to fill 3 additional emp

ty bottles.

2 answers:

nadezda [96]3 years ago

6 0

Answer: The bacteria took 1 hour and 40 minutes to fill the initial bottle.

Step-by-step explanation: The bacteria took more time to double from 1 cell to a bottle full of cells. Once the bottle was full, each cell in the full bottle doubled, causing an additional bottle to be filled in 5 minutes. Then the 2 full bottles doubled in the next 5 minutes, causing all 3 bottles to be full.

Dovator [93]3 years ago

5 0

The growth rate is exponential, it doubles every time interval. So by the time you have one bottle, after the next interval you have 2, 4 and so forth.

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eimsori [14]

Answer:laaa vidas so las vi vi ras ony laa viras so las vi vi ras

Step-by-step explanation:laaaa vidas so las vi vi ras boty hastice hastice sola vi vi rasss*birb falling*

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3 years ago

The Department of Agriculture is monitoring the spread of mice by placing 100 mice at the start of the project. The population,

uranmaximum [27]

Answer:

Step-by-step explanation:

Assuming that the differential equation is

$\frac{dP}{dt} = 0.04P\left(1-\frac{P}{500}\right)$ .

We need to solve it and obtain an expression for $P(t)$ in order to complete the exercise.

First of all, this is an example of the logistic equation, which has the general form

$\frac{dP}{dt} = kP\left(1-\frac{P}{K}\right)$ .

In order to make the calculation easier we are going to solve the general equation, and later substitute the values of the constants, notice that $k=0.04$ and $K=500$ and the initial condition $P(0)=100$ .

Notice that this equation is separable, then

$\frac{dP}{P(1-P/K)} = kdt$ .

Now, intagrating in both sides of the equation

$\int\frac{dP}{P(1-P/K)} = \int kdt = kt +C$ .

In order to calculate the integral in the left hand side we make a partial fraction decomposition:

$\frac{1}{P(1-P/K)} = \frac{1}{P} - \frac{1}{K-P}$ .

So,

$\int\frac{dP}{P(1-P/K)} = \ln|P| - \ln|K-P| = \ln\left| \frac{P}{K-P} \right| = -\ln\left| \frac{K-P}{P} \right|$ .

We have obtained that:

$-\ln\left| \frac{K-P}{P}\right| = kt +C$

which is equivalent to

$\ln\left| \frac{K-P}{P}\right|= -kt -C$

Taking exponentials in both hands:

$\left| \frac{K-P}{P}\right| = e^{-kt -C}$

Hence,

$\frac{K-P(t)}{P(t)} = Ae^{-kt}$ .

The next step is to substitute the given values in the statement of the problem:

$\frac{500-P(t)}{P(t)} = Ae^{-0.04t}$ .

We calculate the value of $A$ using the initial condition $P(0)=100$ , substituting $t=0$ :

$\frac{500-100}{100} = A}$ and $A=4$ .

So,

$\frac{500-P(t)}{P(t)} = 4e^{-0.04t}$ .

Finally, as we want the value of $t$ such that $P(t)=200$ , we substitute this last value into the above equation. Thus,

$\frac{500-200}{200} = 4e^{-0.04t}$ .

This is equivalent to $\frac{3}{8} = e^{-0.04t}$ . Taking logarithms we get $\ln\frac{3}{8} = -0.04t$ . Then,

$t = \frac{\ln\frac{3}{8}}{-0.04} \approx 24.520731325$ .

So, the population of rats will be 200 after 25 months.

6 0

3 years ago

Anyone know how to work this out?

dsp73

The first and crucial thing we want to take notice is that the lines DF and EG intersect at point H which creates 4 different triangles in the rhombus. The innermost angles of DGH and EFH are vertical angles and vertical angles are congruent. So if the angles of the triangles are congruent than the triangles themselves are congruent. This is supported by the vertical angles theorem.

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3 years ago

Read 2 more answers

Name the postulate or theorem you can use to prove TKS=TLR

OlgaM077 [116]

Answer:

ASA postulate

Step-by-step explanation:

To prove two triangles are congruent, you need 3 congruent parts in one of the patterns ASA, AAS, SSS, or SAS. Place your pencil on one vertex of the triangle then trace the figure. As you come to each congruent part, write either A for angle or S for side depending on what the part is. After doing so, you will see the pattern A - S - A since a side is congruent between two angles.

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3 years ago

Need help with number 4 and number 6

Ann [662]

Answer:

4. x=14.1 mi 6.x=8r3 km

Step-by-step explanation:

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3 years ago