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PolarNik [594]
3 years ago
10

Question is below....

Mathematics
1 answer:
Kamila [148]3 years ago
4 0

Answer:

Step-by-step explanation:

For window, area 3×2

=6

For wall, area=20×16

=320

Area of wall withot window=320-6

=316

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Let P(t) be a population at time t. A simple population model supposes the rate of growth of the population is proportional to t
jeka94

Answer:

(a) \dfrac{dP}{dt} =k P(t)\\(b)P(t)=Ce^{kt}

(c)P(10)\approx 272

(ii)P(1000)\approx 26.88 \times 10^{44}\\

Step-by-step explanation:

(a)The rate of growth of the population is proportional to the population, this is written as:

\dfrac{dP}{dt} \propto P(t)\\$Introducing our proportionality constant, k\\ \dfrac{dP}{dt} =k P(t)

(b)

\dfrac{dP(t)}{P(t)} =k dt\\$Take the integral of both sides\\\int \dfrac{dP(t)}{P(t)} =\int k dt\\\ln P(t)=kt+C, $C a constant of integration\\Take the exponential of both sides\\e^{\ln P(t)}=e^{kt+C}\\P(t)=e^{kt}\cdot e^C  $, (Since e^C$ is a constant, we then have:)\\P(t)=Ce^{kt}

(c)

Suppose the net birthrate of the population is .1, and the initial population is 100.

k=0.1

P(0)=100

Substitution into P(t) gives:

100=Ce^{kX0}

C=100

Therefore:

P(t)=100e^{0.1t}

(i)When t=10

P(10)=100e^{0.1 \times 10}\\=271.8\\\approx 272

(ii)When t=1000

P(1000)=100e^{0.1 \times 1000}\\=26.88 \times 10^{44}\\

8 0
4 years ago
The polynomial is a difference of perfect squares. Use the formula a2 – b2 = (a + b)(a – b) to factor completely.
mash [69]

Answer:

81x^{2} -49\\(9x)^2-7^2\\(9x-7)(9x+7)

6 0
3 years ago
PLEASE HELP, ASAP! PLEASE AND THANK YOU!
Gala2k [10]

Answer:

The answer to your question is 6.- B    7.- D

Step-by-step explanation:

Data

Parallelogram ACFG

6.-

m∠GAC = 112°

m∠ACF = ?

Process

These angles are supplementary, they measure the same.

                  ∠GAC + ∠ACF = 180

-Substitution

                      112 + ∠ACF = 180°

-Solve for ∠ACF

                      ∠ACF = 180° - 112°

-Result

                      ∠ACF = 68°

7.-

m∠AGF = 2a + 10

m∠ACF = a + 20

The angles ∠GAC and ACF are equal, they measure the same.

                   ∠GAC = ∠ACF

-Substitution

                   a + 20 = 2a + 10

-Solve for a

                   a - 2a = 10 - 20

-Result

                   -a = -10

                    a = 10

-Find ∠AGF

      ∠AGF = 2(10) + 10

                 20 + 10

                = 30°

3 0
3 years ago
At first Davian has $120 less than Jeremy.
Crazy boy [7]

Answer: YOU SHOULD DIVIDE ALL OF THEM TO GET YOUR ANSWER

8 0
3 years ago
Find the height of the flagpole to the nearest meter. <br> 40<br> 33<br> 20<br> 27
alex41 [277]

Answer:

<h2>40</h2>

Step-by-step explanation:

<h3>I think 40 because it's to long line</h3>

3 0
3 years ago
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