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3 years ago

What is the value of the expression 3p (4p +5) + 3 for p= -1 isplzzzzzzzz i want it fast

Mathematics

1 answer:

AleksAgata [21]3 years ago

7 0

Answer:

Step-by-step explanation

well at least thats my guess!

we have to go by bidmas. so you substitute first!

so its going to be: 3(-1)(4(-1)+5)+3

all I did is that I replaced all p's by -1 and then you multiply it!

so its gonna be: -3(-4+5)+3

you first solve what's in the brackets which is -4+5 so the answer is 1 like this: -3(1)+3 now its much simpler. all we have to do is to expand the bracket so its going to be -3+3 so the answer is 0!

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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.

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3 years ago

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olganol [36]

Hopefully this helps!!!

8 0

2 years ago

What is the quotient of 5 1/2 and 1/8

Stels [109]

Answer:

Step-by-step explanation:

5 1/2 / 1/8

turn into improper fraction

11/2 then change to multiplication

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3 years ago

Which expression is equal to 5^4 ⋅ 5^8?

alex41 [277]

It should be A. You would keep the 5, and the exponent should be 4+8, which is 12.

3 0

3 years ago

Read 2 more answers

Aregular polygon is drawn in a circle so that each vertex is on the circle and is connected to the center by a radius. Each of

katrin [286]

Answer:

The number of sides the polygon have 9

Step-by-step explanation:

Given in question as :

For The circle , the central angles measure be 40 °

Let the number of sides of polygon = n

Now . as we know

External angle = $\frac{360^{\circ} }{n}$

Or , 40° = $\frac{360^{\circ} }{n}$

Or, $\frac{360^{\circ} }{n}$ = 40°

So, n = $\frac{360^{\circ} }{40^{\circ}}$ = 9

Hence The number of sides the polygon have 9 Answer

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3 years ago