Evaluate the following indefinite integral

The result of expanding the trigonometry expression [tex]\sin^2(\theta) * (1 + \cos(\theta))[/tex] is [tex]cos^0(\theta) + \cos(\theta) - \cos^2(\theta) - \cos^3(\theta)[/tex]

The expression is given as:

[tex]\sin^2(\theta) * (1 + \cos(\theta))[/tex]

Express [tex]\sin^2(\theta)[/tex] as [tex]1 - \cos^2(\theta)[/tex].

So, we have:

[tex]\sin^2(\theta) * (1 + \cos(\theta)) = (1- \cos^2(\theta)) * (1 + \cos(\theta))[/tex]

Open the bracket

[tex]\sin^2(\theta) * (1 + \cos(\theta)) = 1 + \cos(\theta) - \cos^2(\theta) - \cos^3(\theta)[/tex]

Express 1 as cos°(Ф)

[tex]\sin^2(\theta) * (1 + \cos(\theta)) = cos^0(\theta) + \cos(\theta) - \cos^2(\theta) - \cos^3(\theta)[/tex]

Hence, the result of expanding the trigonometry expression [tex]\sin^2(\theta) * (1 + \cos(\theta))[/tex] is [tex]cos^0(\theta) + \cos(\theta) - \cos^2(\theta) - \cos^3(\theta)[/tex]

Read more about trigonometry expressions at:

https://brainly.com/question/8120556

#SPJ1

A graph that uses bars of various heights to represent the frequencies is a Histogram

A histogram is an approximate representation of the distribution of numerical data. The term was first introduced by Karl Pearson. To construct a histogram, the first step is to "bin" (or "bucket") the range of values—that is, divide the entire range of values into a series of intervals—and then count how many values fall into each interval.

Therefore, a graph that uses bars of various heights to represent the frequencies is a Histogram

================================

[tex] \large \sf \underline{Question:}[/tex]

A graph that uses bars of various heights to represent the frequencies.

================================

[tex] \large \sf \underline{Answer:}[/tex]

[tex] \qquad \qquad \huge \bold{Option \: A}[/tex]

================================

[tex] \large \sf \underline{Explanation:}[/tex]

A graph that uses bars of various heights to represent the frequencies is called Histogram

A Histogram is typically a statistical schematic diagram which bars are displayed at random with no space interval. The bars of a Histogram are side-by-side, there are no spaces between the bars.

================================

The probability of getting exactly two tail is 1/4.

Answer:

Hope it help

Step-by-step explanation:

1. B
2. A
3. C
4. C

5. D

Answer:

The graph I expect to have a negative correlation is the third graph.

Step-by-step explanation:

Positive correlation is when the the x-values increase with a corresponding increase in y-values.

Negative correlation is when the x-values increases with a corresponding decrease in y-values.

No correlation is when only x or y variable changes.

From the graphs given the only one that has a negative correlation is the third graph.

Answer:

0.06

Step-by-step explanation:

The product of 2 numbers means that we have to multiply them.

So, we do 0.2 x 0.3 = 0.06

To do this, we convert the decimal fractions into whole numbers by multiply both by 10.

ie. 0.2 x 10 = 2

and

0.3 x 10 = 3

Now multiply together

2 x 3 = 6.

However, we have to remember that we multiplied both numbers by 10 (ie. 10 x 10 = 100) so we must remember to divide the answer by 100

...0.06

Hope this helps!

- profparis

Answer:

=0.06

Step-by-step explanation:

0.2

× 0.3

= 0.06

therefore the answer is 0.06

Part A: The total length of the two sides, 1 and 2, of the triangle is 10x² + 14x - 8

Part B: The length of the third side of the triangle is 10x³ -2x²  - 16x + 2

From the given information,

The length of side 1 is

6x² - 4x - 2

and the length of side 2 is

18x + 4x² - 6

Part A

The total length of the two sides, 1 and 2, of the triangle will be

Length of side 1 + Length of side 2

That is,

6x² - 4x - 2 + 18x + 4x² - 6

This becomes,

6x² + 4x² + 18x - 4x - 2   - 6

10x² + 14x - 8  

Therefore, the total length of the two sides, 1 and 2, of the triangle is 10x² + 14x - 8

Part B

The length of the third side will be

Perimeter of the triangle - the total length of sides 1 and 2

From the given information,

The perimeter of the triangle is 10x³ + 8x² - 2x - 6

Then,

Length of third side = 10x³ + 8x² - 2x - 6 - (10x² + 14x - 8)

Length of third side = 10x³ + 8x² - 2x - 6 - 10x² - 14x + 8

Length of third side = 10x³ + 8x² - 10x²  - 2x - 14x - 6  + 8

Length of third side = 10x³ -2x²  - 16x + 2

Hence, the length of the third side of the triangle is 10x³ -2x²  - 16x + 2

Learn more on Calculating the sides of a triangle here: https://brainly.com/question/12183930

#SPJ1

Combine like terms

Answer:

8x

Step-by-step explanation:

Given expression:

As we know, any negative integer being added by itself is 0. [-2y + 2y = 0]

Collect like terms and simplify;

Therefore, 8x is the simplified term.

Learn more about this topic: https://brainly.com/question/12605426

Statement 8 (x = 10/5 or x = 2) is given by the division property of equality. Then the correct option is B.

Division means the separation of something into different parts, sharing of something among different people, places, etc.

Suppose that we're taking about

It means, we divide p into q equal parts.

And each part is of value p/q

Statement 7 is given below.

5x - 10 = 0

Then statement 8 is given by the division property of equality.

5x = 10

 x = 10/5

 x = 2

More about the division link is given below.

https://brainly.com/question/369266

#SPJ1

Answer:

I think that the answer is -81

Step-by-step explanation:

We have 3x+4x-81-14 x is given as 2.So we'll have 3*2+4*2-81-14= -81 per my calculations. TRY THIS

The correct answer is option D which is a = 5, b = 2, c = - 1.

It is a polynomial with a degree of 2 or the maximum power of the variable is 2 in quadratic equations. It has two solutions as its maximum power is 2.

Given that:-

The general form of the equation is given as:-

Y = ax² + bx + c

We have a quadratic equation:-

y = 5x² + 2x - 1

By comparing the equation with the general form the value of a, b and c is calculated:-

a  =  5

b  =  2

c  =  -1

Therefore the correct answer is option D which is a = 5, b = 2, c = - 1.

To know more about quadratic equations follow

https://brainly.com/question/1214333

#SPJ1

Answer:

The area is 9 units^2

Step-by-step explanation:

Answer:

[tex]D.\:\:\:\:\:\sec^4\theta[/tex]

Step-by-step explanation:

Hope it helps you in your learning process.

Answer:

D

Step-by-step explanation:

using the identities

1 + tan²Θ = sec²Θ and cosΘ = [tex]\frac{1}{sec0}[/tex] , then

[tex]\frac{1+tan^20}{cos^20}[/tex]

= [tex]\frac{sec^20}{\frac{1}{sec^20} }[/tex]

= sec²Θ × sec²Θ

= [tex]sec^{4}[/tex]Θ

Answer:

6 pelicans

Step-by-step explanation:

Let x = number of pelicans

Cody saw 4 times as many seagulls as pelicans:

⇒ number of seagulls = 4x

Total of 30 birds:

⇒ seagulls + pelicans = 30

⇒ 4x + x = 30

⇒ 5x = 30

⇒ x = 6

Therefore, there were 6 pelicans (and 24 seagulls).

ATQ

Pellicans are 6

Answer:

34.98

Simply add the 27.99 with 25%

= 34.98

Answer:

1887.97 (3853 * 0.49)

Step-by-step explanation:

3853 * 0.49

The period of time does the stock price rise is 0 ≤ t ≤ 10/3.

It would sell in 3.34 days.

It is the process of finding the derivative, or rate of change, of a function.

The price of a certain computer stock after t days is

p(t) = 100 + 20t - 3t²

Now, take the derivative of the given function and equate it to zero to find the critical points,

p'(t) = 20 - 6t = 0

t = 20/6

t = 10/3 days

Thus, there are two intervals in which the given function is defined

(0, 10/3) and (10/3, ∞)

For the interval (0,10/3 ),

p'(1) = 20 - 6(1) =14

For the interval (10/3, ∞),

p'(2) = 20 - 6(2) = 8

Since p'(t) in the interval (0, 10/3) indicates that the function is increasing.

0 < t <10/3

Since at the point t = 3.34 days it would sell.

Learn more about this concept here:

https://brainly.com/question/23857227

#SPJ1

Answer:

Top Image: 56°

Bottom Image: 134°

Step-by-step explanation:

I'm not sure which image you have a question on, so I'll just solve both.

Top Image:

 We know that the sum of the angles will add up to 180 and that the angles of the triangle are f, f, and 68°. Therefore, we can set up the following equation:

f + f + 68° = 180°

Solving this gets f = 56°

Bottom Image:

  We know that the sum of the angles will add up to 180 and that the angles of the triangle are 23°, 23°, and g. Therefore, we can set up the following equation:

 23° + 23° + g = 180°

Solving this gets g = 134°

The total amount of time spent by the student as shown by the line plot is: D. 5 ¼ hours.

Each dot or x-mark represents a value. To find the total, add each of the data points given in the line plot.

Total amount of time is:

2(1/4) + 5(1/2) + 3(3/4)

= 1/2 + 5/2 + 9/4

= (2 + 10 + 9)/4

= 21/4

= 5 ¼ hours.

Total time spent by students is: D. 5 ¼ hours.

Learn more about line plot on:

https://brainly.com/question/27246403

#SPJ1

Answer:

A lot

Step-by-step explanation:

So basically you learn a lot

Answer:

[tex]\huge\boxed{\sf x > -1.25}[/tex]

Step-by-step explanation:

0.2 (x + 20) - 3 > -7 - 6.2x

Distribute

0.2x + 4 - 3 > -7 - 6.2x

0.2x + 1 > -7 - 6.2x

Add 6.2x to both sides

0.2x + 6.2x + 1 > -7

6.4x + 1 > -7

Subtract 1 to both sides

6.4x > -7 - 1

6.4x > -8

Divide 6.4 to both sides

x > -8/6.4

x > -1.25

[tex]\rule[225]{225}{2}[/tex]

Answer:

x > -1.25

Step-by-step explanation:

Using the distributive property: a(b + c) → ab + ac

1. Distribute '0.2'

0.2(x) + 0.2(20) - 3 > -7 - 6.2x

0.2x + 4 - 3 > -7 - 6.2x

0.2x + 1  > -7 - 6.2x

2. Add '6.2x' to both sides

0.2x + 6.2x + 1  > -7 - 6.2x + 6.2x

6.4x + 1 > -7

3. Subtract '1' from both sides

6.4x + 1 - 1 > -7 - 1

6.4x > -8

4. Divide both sides by '6.4' to isolate the variable

6.4x ÷ 6.4 > -8 ÷ 6.4

x > -1.25

Final answer: x > -1.25

Learn more about solving inequalities here:

brainly.com/question/21857626

Answer:

30 books

Step-by-step explanation:

36 / 1.2 = 30

You can pack 30 books and it will not exceed 36 Kg.

- - -

Side Note:

We don't know how heavy the suitcase is...

4/12 chance of dying

Answer:

B. Multiply the top equation by-3 and the bottom equation by 2.

Step-by-step explanation:

-3(4x-2y=7)

2(3x-3y=15)

-12x + 6y= -21

6x  - 6y = 30                  

6y and -6y both cancel each other out which gives us 0 when -3 is multiplied by the top and the bottom is multiplied by 2, which gives us the answer B.

1.  The percent of cats between 24.16 and 35.84 is 95%

2. The percent of cats who are longer than 35.84 is 2.28 %

3. The percent of cats shorter than 24.16 inches is 2.28%

The empirical rule - formula

95% of data falls within 2 standard deviations from the mean - between μ – 2σ and μ + 2σ .

Mean, u = 30 inches

Standard Deviation, s = 2.92 inches

Formula for z-score = (x-u)/s

1. We have to find the percent of cats between 24.16 and 35.84 inches.

24.16, z-score = -2

35.84, z-score = 2

According to the empirical rule,

95% of the data values are within 2 standard deviations of the mean.

So, 95% of the cats are between 24.16 and 35.84 inches.

2. Here, x = 35.84

   z=(35.84-30)/2.92

   z= 2

According to the Empirical Rule,

95% of the values lie within 2 standard deviations of the mean.

So, the percent of cats who are longer than 35.84

100 - 97.72 = 2.28%

3. Now, x = 36.22

Using the formula mentioned above, we get:

z= 24.16-30/2.92

z=-2

According to empirical rule,

68% of the values lie within 1 standard deviation of the mean.

i.e., remaining 32% are outside the 1 standard deviation and  half of the values i.e. 16% are below 1 standard deviation.

The percent of cats shorter than 24.16 inches is 2.28%

Learn more about this concept here:

https://brainly.com/question/12449630

#SPJ1

Given

Find z-scores for x = 24.16 and x = 35.84

Use formula

Find the corresponding percentage from z-score table

The percent of cats between 24.16 and 35.84

The percent of cats who are longer than 35.84

The percent of cats shorter than 24.16 inches

Answer:

76 unit^2

Step-by-step explanation:

Total area: (0.5  * base * height) +( length * breadth ) + (0.5 * base * height)

= (0.5 * 8 * 2) + ( 7*8) +( 0.5 * 8 * 3) = 8 + 56 + 12 = 76