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4 years ago

A "Gallop Poll" is a national

Mathematics

1 answer:

Triss [41]4 years ago

8 0

Answer:

How polls are conducted Gallup?

Gallup World Poll methodology

Gallup asks each respondent the survey questions in his or her own language to produce statistically comparable results. Gallup uses telephone surveys in countries where telephone coverage represents at least 80% of the population

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 = ?

Alecsey [184]

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

$(\frac{1}{cosx})^2+ 2 (\frac{sinx}{cosx})^2$

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

8 0

3 years ago

Perform the indicated operation. Be sure the answer is reduced.

ANTONII [103]

$\frac{m}{n} . \frac{n}{p} \div \frac{p}{q} \\ = \frac{m}{p} \div \frac{p}{q} \\ = \frac{m}{p} . \frac{q}{p} \\ = \frac{mq}{ {p}^{2} }$

Hope it helps...

Regards;

Leukonov/Olegion.

8 0

3 years ago

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A car rental company charges $0.10 per mile plus $30 per day for a midsize sedan. If

Ket [755]

Answer:8 days and 12 hours

Step-by-step explanation:30$ is each day

4 0

4 years ago

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Write the equation and state the domain/range

aliya0001 [1]

Answer:

Step-by-step explanation:

6 0

3 years ago

A model plane is 1/48 the size of the actual plane. If the model plane is 28 inches long, how long is the actual plane?

Hoochie [10]

I am not so sure because i have not studied this yet i am very sorry

3 0

4 years ago

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