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defon
3 years ago
15

Which best describes the capture of Constantinople in 1453?

Advanced Placement (AP)
1 answer:
katrin2010 [14]3 years ago
5 0

<span>The correct answer is the second statement. The Fall of Constantinople, capital of the Byzantine Empire, is important historical event that marked the end of the Middle Age period. Constantinople was successfully invaded in 1453. by them army of the Ottoman Empire, led by Sultan Mehmed the Conqueror. His forces penetrated Constantinople’s walls through direct infantry assaults and use of gunpowder.</span>

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2. Find the solution of each differential equation. (a) y/2y-8y = 0 (b) 25y/- 20y + 4y = 0 (c) y + 2y + 2y = 0 2. Find the solut
jek_recluse [69]

Each of these ODEs is linear and homogeneous with constant coefficients, so we only need to find the roots to their respective characteristic equations.

(a) The characteristic equation for

y'' - 2y' - 8y = 0

is

r^2 - 2r - 8 = (r - 4) (r + 2) = 0

which arises from the ansatz y = e^{rx}.

The characteristic roots are r=4 and r=-2. Then the general solution is

\boxed{y = C_1 e^{4x} + C_2 e^{-2x}}

where C_1,C_2 are arbitrary constants.

(b) The characteristic equation here is

25r^2 - 20r + 4 = (5r - 2)^2 = 0

with a root at r=\frac25 of multiplicity 2. Then the general solution is

\boxed{y = C_1 e^{2/5\,x} + C_2 x e^{2/5\,x}}

(c) The characteristic equation is

r^2 + 2r + 2 = (r + 1)^2 + 1 = 0

with roots at r = -1 \pm i, where i=\sqrt{-1}. Then the general solution is

y = C_1 e^{(-1+i)x} + C_2 e^{(-1-i)x}

Recall Euler's identity,

e^{ix} = \cos(x) + i \sin(x)

Then we can rewrite the solution as

y = C_1 e^{-x} (\cos(x) + i \sin(x)) + C_2 e^{-x} (\cos(x) - i \sin(x))

or even more simply as

\boxed{y = C_1 e^{-x} \cos(x) + C_2 e^{-x} \sin(x)}

3 0
1 year ago
Is good communication just common sense? (Interpersonal Communication)
REY [17]

Answer:

So, good communication in an impersonal communication is yes common sense.

Explanation:

Rationally for this is bc it can allow us to work more efficiently in our communities.  This is my reasoning on why it's common sense.

8 0
3 years ago
Read 2 more answers
Please help me solve with steps
trasher [3.6K]

The capital on 31 January 2020 was approx $ 50000 as the owner has not make any drawing this year. Hence option B is correct

<h3>What is capital?</h3>

Capital is defined as the total amount of financial resources needed to manufacture goods or services. These cash may be employed to start up operations, cover ongoing costs, or develop and extend the company.

As given profit made this year = $ 10000

So the capital on 31 January 2020 = approx $ 50000

Thus, the capital on 31 January 2020 was approx $ 50000 as the owner has not make any drawing this year. Hence option B is correct

To learn more about capital, refer to the link below:

brainly.com/question/29052534

#SPJ1

5 0
1 year ago
Unemployment characterized by large numbers of workers who have recently been replaced by machines or laid-off due to technologi
lana [24]
The answer is C. Structural
7 0
3 years ago
Several United States Presidents committed military troops to serve in Vietnam in an effort to
blagie [28]
The purpose of sending troops to Vietnam was to prevent Vietnam from becoming a communist state- much like the neighbouring China did. The US feared the domino effect in which more and more neighbouring states become communist.

This policy was called the containment policy (the answer is B) - communism were to be contained.
3 0
3 years ago
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