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lianna [129]
3 years ago
9

work out the circumference of this circle take (pie) to be 3.142 and give ur answer in 1 decimal place radius=9m

Mathematics
1 answer:
Whitepunk [10]3 years ago
4 0

Answer:

56.6m to 1.d.p

Step-by-step explanation:

circumference=2πr

=2×3.142×9

=56.556m

=56.6m to 1.d.p

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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
Is -8 = 8
madam [21]
No solution

The answer is D
5 0
2 years ago
Pls look at this picture and answer
Pepsi [2]

Answer:

625

Step-by-step explanation:

7 0
3 years ago
Which represents a side length of a square that has an area of 450 square inches?
amm1812

The formula of an area of a square:


A=a^2


a - a side


We have A=450\ in^2


substitute:


a^2=450\to a=\sqrt{450}\\\\a=\sqrt{225\cdot2}\\\\a=\sqrt{225}\cdot\sqrt2\\\\\boxed{a=15\sqrt2\ in}


Used:

\sqrt{a\cdot b}=\sqrt{a}\cdot\sqrt{b}

5 0
3 years ago
Do –2(3x – 1) = –6x – 1 have one solution
PolarNik [594]

Answer:

No solutions

Step-by-step explanation:

–2(3x – 1) = –6x – 1

First distribute the left side

-6x + 2 = -6x - 1

Add 1 to both sides

-6x + 3 = -6x

Add 6x to both sides

3 = 0

This equation is not true because 3 does NOT equal 0. Therefor, this equation has no solutions.

4 0
3 years ago
Read 2 more answers
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