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3 years ago

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