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storchak [24]
2 years ago
13

Find the inverse of f(x)=7.50x

Mathematics
1 answer:
m_a_m_a [10]2 years ago
8 0
there is no inverse though
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g100num [7]

Answer:

2 miles is your answer hope this helps!!!!!!

Step-by-step explanation:


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3 years ago
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The slope of the line is -3/4
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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
Jennifer was baking cupcakes for her class. She needed to bake 35 cupcakes in all. Each cupcake needed .13 cups of sugar. How ma
Paraphin [41]
Answer and working out attached below. Hope it helps

3 0
2 years ago
Using =2L+2W, Find L when P is 50 and W is 10
mestny [16]

Answer:

L = 15

Step-by-step explanation:

P = 2L + 2W

you know that P = 50, W=10

So you have to replace those values on the equation

50 = 2L + 2*(10)  --> Replace P and W

50 = 2L + 20  --> Multiply and now you are going to separate the unknown and the constants.

Remember that if you send a constant to the other side of the equal the sign will change to its opposite

50 - 20 = 2L  --> Solve the constants

30 = 2L    --> Now for the L, you have to leave it alone, so the 2 that is multiplying you have to send it to the other side of the equal but with the opposite operation,  the opposite operation of multiplying is dividing, so you have:

30/2 = L

L= 15

5 0
3 years ago
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