Someone pls help me :((

Answer:

[tex]\mathbf{P =\bigg (P_o +\dfrac{ I}{k} \bigg)e^{kt}- \dfrac{I}{k}}[/tex]

Step-by-step explanation:

Given that:

A country population at any given time (t) is:

[tex]\dfrac{dP}{dt}= kP+I[/tex]

where;

P = population at any time t

k = positive constant

I = constant rate of immigration into the country.

Using the method of separation of the variable;

[tex]\dfrac{dP}{kP+1}= dt[/tex]

Taking integration on both sides:

[tex]\int \dfrac{dP}{kP+I}= \int \ dt[/tex]

[tex]\dfrac{1}{k} log (kP + I) = t+c_1 \ \ \ here: c_1 = constant \ of \ integration[/tex]

[tex]log (kP + I) =k t+kc_1[/tex]

By applying the exponential on both sides;

[tex]e^{log (kP + I) }=e^{k t+kc_1 }[/tex]

[tex]KP+I = e^{kt} *e^{kc_1}[/tex]

Assume [tex]e^{kc_1 }= C[/tex]

Then:

[tex]kP + I = Ce^{kt}[/tex]

[tex]kP = Ce^{kt}-I[/tex]

[tex]P =\dfrac{ Ce^{kt}-I}{k} \ \ \---- Let \ that \ be \ equation \ (1)[/tex]

When time t = 0, The Total population of the country is also [tex]P_o[/tex]

[tex]P_o = \dfrac{Ce^{0(t)} -I}{k}[/tex]

[tex]P_o = \dfrac{Ce^{0} -I}{k}[/tex]

[tex]P_o = \dfrac{C-I}{k}[/tex]

C - I = kP₀

C =  kP₀ + I

Substituting the value of C back into equation(1), we have:

[tex]P =\dfrac{ (kP_o+1)e^{kt}-I}{k}[/tex]

[tex]P =\dfrac{ (kP_o+1)e^{kt}}{k} - \dfrac{I}{k}[/tex]

[tex]\mathbf{P =\bigg (P_o +\dfrac{ I}{k} \bigg)e^{kt}- \dfrac{I}{k}}[/tex]

Answer:

Mean is 6, median 5.5, mode 2

Step-by-step

Answer:

mean=8+2+7+2+6+5

=30

30÷6=5

note: divide the total with it's sum.

median=7+2

=9

9÷2= 4.5

note: median is the middle no. since there is no middle no. so just add those two no. and divide it by 2.

mode= 2

since it occurs twice

Answer:

29

Step-by-step explanation:

Answer: 80 miles

Step-by-step explanation:

320miles/8hours= 40mph

40mph=xmiles/2hrs

40*2= 80 miles

Answer:

Let `f` be a function defined on [0,2]. Then find the domain of function `g(x)=f(9x^2-1)

Step-by-step explanation:

I'm not sure if that's right

Answer:

1/2 yard is equal to 18 inches

Step-by-step explanation:

Answer:

it would take 22 gallons of gas

Step-by-step explanation:

3 divided by 60

that’s the amount of gas per single mile

then that number times 440 (number of miles you wish to go).

Answer: The price is now 14.40

Step-by-step explanation: The difference is 9.60

Answer:

Already simplified

Step-by-step explanation:

Answer:

Step-by-step explanation:

its preety simple you just have to divide 3/10 and 1/8 and you will get your two answers

Answer:

It would be a I think

Step-by-step explanation:

Answer:

The answer is A

Step-by-step explanation:

Answer:

C) $54.00

Step-by-step explanation:

300*6%*3

300*0.06*3

which is $54.

Hope this helps plz hit the crown :D

Answer:

28258933-1

Step-by-step explanation:

hope it helps you

The relation between the dollars and forints will be directly proportional. Then the number of dollars will be $ 85.

A ratio is an ordered set of integers a and b expressed as a/b, with b never equaling 0. A proportional is a mathematical expression in which two things are equal.

Levante changes 24 650 Hungarian forints to dollars.

Then the relation between the dollars and forints will be directly proportional. Then we have

Let x be the number of the dollars. Then we have

x / 1 = 24650 / 290

    x = $ 85

More about the ratio and the proportion link is given below.

https://brainly.com/question/14335762

#SPJ2

Given:

Vertices of a parallelogram ABCD are A(7,-4), B(-1,-4), C(-1,-12), D(7, -12).

To find:

Whether the parallelogram ABCD is a rhombus, rectangle or square.

Solution:

Distance formula:

[tex]D=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

Using distance formula, we get

[tex]AB=\sqrt{(-4-(-4))^2+(-1-7)^2}[/tex]

[tex]AB=\sqrt{(-4+4)^2+(-8)^2}[/tex]

[tex]AB=\sqrt{0+64}[/tex]

[tex]AB=8[/tex]

Similarly,

[tex]BC=\sqrt{(-1-(-1))^2+(12-(-4))^2}=8[/tex]

[tex]CD=\sqrt{(7-(-1))^2+(-12-(-12))^2}=8[/tex]

[tex]AD=\sqrt{(7-7)^2+(-12-(-4))^2}=8[/tex]

All sides of parallelogram are equal.

[tex]AC=\sqrt{(-1-7)^2+(-12-(-4))^2}=8\sqrt{2}[/tex]

[tex]BD=\sqrt{(7-(-1))^2+(-12-(-4))^2}=8\sqrt{2}[/tex]

Both diagonals are equal.

Since, all sides are equal and both diagonals are equal, therefore, the parallelogram ABCD is a square.

We know that, a square is special case of rectangles and rhombus.

So, parallelogram ABCD is a rhombus, rectangle or square. Therefore, the correct option is c.

Answer:

$14

Step-by-step explanation:

56 × 0.25 = 14

to check this, you can divide 14 ÷ 56 = 0.25

to turn a percentage into a decimal, just divide it by 100

Answer:

pretty sure it's

2

−

3

=

9

\frac{X}{2}-3=9

2X−3=9

2

−

3

+

3

=

9

+

3

Answer :

R = 6.25%

Solution,

Let P is the principal. It means interest will be :

I=3/8 P

The formula for the interest is given by :

[tex]I=\dfrac{PRT}{100}\\\\\dfrac{3}{8}P=\dfrac{PR\times 6}{100}\\\\\dfrac{3}{8}=\dfrac{6R}{100}\\\\R=\dfrac{300}{8\times 6}\\\\=6.25\%[/tex]

Hence, the rate of interest is 6.25%.

Answer:

8571 letters per day

Step-by-step explanation:

60,000/1 week is the same as 60,000/7 days so

60,000/7 = 8571.428571

is aproximately 8571 letters per day

Answer:

its c i believe <3

Answer:

rates of change, positive or negative

Step-by-step explanation:

Answer:

one number= x = 44

the other number= (x-4)= 40

Step-by-step explanation:

one number= x

the other number= (x-4)

x + (x-4) = 84

2x= 84+4

2x= 88

x= 88/2= 44

one number= x = 44

the other number= (x-4)= 40

9514 1404 393

Answer:

  rotated vertices are (1, 1), (-2, -1), (-4, 0)

Step-by-step explanation:

When the rotation direction is not specified, it is usually taken to be counterclockwise. Rotation 270° CCW is the same as rotation 90° CW. The transformation of coordinates is ...

  (x, y) ⇒ (y, -x)

Then your rotated points become ...

  A(-1, 1) ⇒ A'(1, 1)

  B(1, -2) ⇒ B'(-2, -1)

  C(0, -4) ⇒ C'(-4, 0)

_____

In the attached, the rotated triangle is shown in red. As an example, the arc through which point C is rotated is shown.

Answer:

For the first one =5.29150262

Step-by-step explanation:

8 squared - 6 squared =64-36=28

square root of 28=5.29150262

Answer:

It is TRUE.

Other:

Brainliest? Thanks!

Answer:

Step-by-step explanation:

False,true,true

Answer:

5 times

Step-by-step explanation:

Because he enters through the front door.

Answer:

-7

Step-by-step explanation:

Answer:

7i

Step-by-step explanation:

the square root of 49 is 7

i equals -1

7 squared times -1 equals -49