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Ede4ka [16]
2 years ago
12

Help ASAP. In the 1800s, the United States was still a very young nation, trying to solidify its identity. The Industrial Revolu

tion began in Great Britain, a fast development of society following
the introduction of machines. The United States was slower than Great Britain to fully embrace the changes. Yet key technological developments caused a rapid growth in
American urban areas
Better farming methods and tools in the 1800s increased food production Americans were able to grow enough food for their families as well as to sell. The abundance caused food
prices to fall
The expansion of cotton and the growth of textile factones in northern states helped produce the first wave of American industry. More people turned to work in northern factories as
a way to support their families. Thousands of immigrants to the United States also settled in or near port cities, looking for work. Even today, the need for work is a common reason
people move to urban areas
As a result, cities grew in numbers of people and physical space As more people and businesses moved in, they needed buildings for living and working. They needed ways to
move around the city. We call this process urbanization
In 1820, the United States had only a few cities of 10,000 residents or more About seven percent of U.S. residents lived in urban areas. The number of cities with more than
10,000 people grew quickly over the next 40 years, especially in the Northeast and Midwest. By 1860, about 20 percent lived in cities Philadelphia and New York City were the
most populated cities in 1860 and would soon reach one million residents
The urbanization of the United States quickened due to technology improvements Without innovations in food production, the factories could not have grown so quickly. The trend
quickened after 1860 and continued throughout the 21st century as well. By 2007, more Americans lived in or near cities than they did in rural areas,
Select a sentence from the body of this article that can be removed without affecting the author's explanation. Place the sentence in quotes and explain why it is an unnecessary
detail.
Mathematics
1 answer:
lions [1.4K]2 years ago
3 0

Answer:

ok

Step-by-step explanation:

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Complete the identity.<br> 1) sec^4 x + sec^2 x tan^2 x - 2 tan^4 x = ?
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Answer:

See Explanation

Step-by-step explanation:

<em>Question like this are better answered if there are list of options; However, I'll simplify as far as the expression can be simplified</em>

Given

sec^4 x + sec^2 x tan^2 x - 2 tan^4 x

Required

Simplify

(sec^2 x)^2 + sec^2 x tan^2 x - 2 (tan^2 x)^2

Represent sec^2x with a

Represent tan^2x with b

The expression becomes

a^2 + ab- 2 b^2

Factorize

a^2 + 2ab -ab- 2 b^2

a(a + 2b) -b(a+ 2 b)

(a -b) (a+ 2 b)

Recall that

a = sec^2x

b = tan^2x

The expression (a -b) (a+ 2 b) becomes

(sec^2x -tan^2x) (sec^2x+ 2 tan^2x)

..............................................................................................................................

In trigonometry

sec^2x =1  +tan^2x

Subtract tan^2x from both sides

sec^2x - tan^2x =1  +tan^2x - tan^2x

sec^2x - tan^2x =1

..............................................................................................................................

Substitute 1 for sec^2x - tan^2x in (sec^2x -tan^2x) (sec^2x+ 2 tan^2x)

(1) (sec^2x+ 2 tan^2x)

Open Bracket

sec^2x+ 2 tan^2x ------------------This is an equivalence

(secx)^2+ 2 (tanx)^2

Solving further;

................................................................................................................................

In trigonometry

secx = \frac{1}{cosx}

tanx = \frac{sinx}{cosx}

Substitute the expressions for secx and tanx

................................................................................................................................

(secx)^2+ 2 (tanx)^2 becomes

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Open bracket

\frac{1}{cos^2x}+ 2 (\frac{sin^2x}{cos^2x})

\frac{1}{cos^2x}+ \frac{2sin^2x}{cos^2x}

Add Fraction

\frac{1 + 2sin^2x}{cos^2x} ------------------------ This is another equivalence

................................................................................................................................

In trigonometry

sin^2x + cos^2x= 1

Make sin^2x the subject of formula

sin^2x= 1  - cos^2x

................................................................................................................................

Substitute the expressions for 1  - cos^2x for sin^2x

\frac{1 + 2(1  - cos^2x)}{cos^2x}

Open bracket

\frac{1 + 2  - 2cos^2x}{cos^2x}

\frac{3  - 2cos^2x}{cos^2x} ---------------------- This is another equivalence

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Answer:

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Step-by-step explanation:

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Answer:

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Step-by-step explanation:

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