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2 years ago

David is writing an explicit function for the arithmetic sequence:

Mathematics

2 answers:

mash [69]2 years ago

5 0

Answer:

C) $n\geq 1$

Step-by-step explanation:

pantera1 [17]2 years ago

4 0

Answer: C

n > 1 where n is an integer

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Simplify the expression. <br> -4 + 6 • (-1) <br> A. -10 <br> B. -2 <br> C. 2 <br> D. 10

viva [34]

Answer:

- 10

Step-by-step explanation:

Order of operations: PEMDAS

Multiply first then add

-4 + -6 = -10

8 0

3 years ago

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

Savatey [412]

Answer: b

Step-by-step explanation:

6 0

3 years ago

Read 2 more answers

Write down letters of the circled points and order them by least to greasiest. You will spell a word that describes y way to com

Kaylis [27]

One way to compare quantities is with fractional numbers that represent quantities using divided numbers.

<h3>What is a fraction?</h3>

Fractional number is a mathematical concept that refers to a quantity divided by another quantity. Common fractions are made up of: numerator, denominator and dividing line between them (horizontal or oblique bar).

The denominator "b" expresses the number of equal parts that represent the unit.
The numerator "a" indicates how many of them are taken.

Some examples of fractional numbers are:

$\frac{1}{2}$
$\frac{2}{4}$
$\frac{3}{4}$
$\frac{50}{100}$

Note: This question is incomplete because there is some information missing. However I can answer it based on my general prior knowledge.

Learn more about fractional numbers in: brainly.com/question/13398430

5 0

2 years ago

Assume the readings on thermometers are normally distributed with a mean of 0 degrees C and a standard deviation of 1.00 degrees

lozanna [386]

Answer: 0.0035

Step-by-step explanation:

Given : The readings on thermometers are normally distributed with a mean of 0 degrees C and a standard deviation of 1.00 degrees C.

i.e. $\mu=0$ and $\sigma= 1$

Let x denotes the readings on thermometers.

Then, the probability that a randomly selected thermometer reads greater than 2.17 will be :_

$P(X>2.7)=1-P(\xleq2.7)\\\\=1-P(\dfrac{x-\mu}{\sigma}\leq\dfrac{2.7-0}{1})\\\\=1-P(z\leq2.7)\ \ [\because\ z=\dfrac{x-\mu}{\sigma}]\\\\=1-0.9965\ \ [\text{By z-table}]\ \\\\=0.0035$

Hence, the probability that a randomly selected thermometer reads greater than 2.17 = 0.0035

The required region is attached below .

8 0

3 years ago