Add: 8 yd 1 ft + 11 yo 2 ft

Answer:

[tex] \displaystyle 2 \sin(x) + 2x \cos( \alpha ) + \rm C[/tex]

Step-by-step explanation:

we would like to integrate the following integration:

[tex] \displaystyle \int \frac{ \cos(2x) - \cos(2 \alpha ) }{ \cos(x) - \cos( \alpha ) } dx[/tex]

notice that you can simplify the integrand

recall that,

[tex] \displaystyle \cos(2 \theta) = 2 \cos(\theta) ^{2} - 1[/tex]

thus substitute:

[tex]\displaystyle \int \frac{ 2\cos^{2} (x)- 1 - \{2\cos ^{2} (\alpha ) - 1 \} }{ \cos(x) - \cos( \alpha ) } dx[/tex]

remove parentheses:

[tex]\displaystyle \int \frac{ 2\cos^{2} (x)- 1 - 2\cos ^{2} (\alpha ) + 1}{ \cos(x) - \cos( \alpha ) } dx[/tex]

[tex]\displaystyle \int \frac{ 2\cos^{2} (x) - 2\cos ^{2} (\alpha ) }{ \cos(x) - \cos( \alpha ) } dx[/tex]

factor out 2:

[tex]\displaystyle \int \frac{ 2(\cos^{2} (x) - \cos ^{2} (\alpha )) }{ \cos(x) - \cos( \alpha ) } dx[/tex]

we can use algebraic identity i.e

a²-b²=(a+b)(a-b) to factor the denominator

[tex]\displaystyle \int \frac{ 2(\cos^{} (x) + \cos ^{} (\alpha ))( \cos(x) - \cos( \alpha ) ) }{ \cos(x) - \cos( \alpha ) } dx[/tex]

reduce fraction:

[tex]\displaystyle \int \frac{ 2(\cos^{} (x) + \cos ^{} (\alpha ))( \cancel{\cos(x) - \cos( \alpha ) ) }}{ \cancel{\cos(x) - \cos( \alpha ) }} dx[/tex]

[tex] \displaystyle \int 2( \cos(x) + \cos( \alpha ) )dx[/tex]

distribute:

[tex] \displaystyle \int 2 \cos(x) + 2\cos( \alpha ) dx[/tex]

use sum integration formula:

[tex] \rm \displaystyle \int 2 \cos(x) dx+ \int2\cos( \alpha ) dx[/tex]

recall integration rules:

[tex] \displaystyle 2 \sin(x) + 2x \cos( \alpha ) [/tex]

and we of course have to add constant of integration

[tex] \displaystyle 2 \sin(x) + 2x \cos( \alpha ) + \rm C[/tex]

Answer:

1.4

Step-by-step explanation:

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

0 0

Answer:

Step-by-step explanation:

From the question we are told that:

Initial bearing [tex]\angle _1=21 \textdegree[/tex]

Initial distance [tex]d_1=99miles[/tex]

Final bearing [tex]\angle _2=227 \textdegree[/tex]

Let [tex]\triangle OAB[/tex] be the perimeter travailed

[tex]\angle OAB=90+21=111 \textdegree\\\angle ABO=270-227=43 \textdegree[/tex]

Generally the equation for OB using sine rule is mathematically given by

[tex]OB=99*\frac{sin111}{sin43}[/tex]

[tex]OB=135.52miles[/tex]

Therefore the helicopter flight on the final leg of its​ journey is

[tex]OB=135.52miles[/tex]

Answer:

$4895

Step-by-step explanation:

P(winning) = 1 / 1000000 = 0.000001

P(not winning) = 1 - 1/1000000 = 0.999999

Winning amount = 4,900,000,000 - 5 = 4899999995

Amount lost = - 5

__ X: - 5 _________ 4899999995

P(X) : 0.999999 ___ 0.000001

Expected value E(x) = Σx * p(x)

E(x) = - 5(0.999999) + 4899999995(0.000001)

E(x) = - 4.999995 + 4899.999995

E(x) = 4895

Hence, expected value is 4895

E⁣⁣⁣xplanation i⁣⁣⁣s i⁣⁣⁣n a f⁣⁣⁣ile

bit.[tex]^{}[/tex]ly/3a8Nt8n

Answer:

1385.4

Step-by-step explanation:

I just did the question

Answer:

x=22

Step-by-step explanation:

Answer:

x=22

Step-by-step explanation:

Answer: 3

Step-by-step explanation:

Answer:

Step-by-step explanation:

No, not quite. She's close.

The middle term (often called the linear term) is + which means that the absolute value of the factors must be plus.

(x + 5)(x - 3) is what should should think.

x + 5 = 0

x = - 5

x + 2 = 0

x = - 2

(x + 5)(x - 2)

x^2 - 2x + 5x - 10

x^2 + 3x - 10

Answer:

167.467mm^3

Step-by-step explanation:

Volume of cone:1/3hpir^2

1/3(10)(pi)(4)^2

=160/3(pi)

(Pi=3.14)

160/3pi=167.467mm^3

Answer:

6x^2^x^2+x^4

Step-by-step explanation:

Answer:

Yes your answer is correct

Step-by-step explanation:

First of all you multiply 3x with 2x which equals 6x power 2 because we sum the power. Then we multiply 6x power 2 with x power 4 which equals 6x power 6 because X is 1X so the answer is 6X power 6

Answer:

[tex] \boxed{A ≈ 58.1 \: cm^{2}} [/tex]

Step-by-step explanation:

When given a regular polygon.

s = a × 2 tan (π / n [radians]).

s = a × 2 tan (180 / n [degrees])

A = (n × s × a) / 2

Where s is the side length, n is the number of sides, a is the apothem length, and A is the area.

You may also see A = p × a.

Where p is the perimeter, the perimeter is the same as n × s.

The apothem is also known as the inradius.

______________________________________

Given a regular pentagon which has 5 sides, and an apothem of 4 cm.

s = 4 × 2 tan (180 / 5) = 4 × 2 × (0.726542528) = 8 × (0.726542528) = 5.81234022404.. ≈ 5.8 cm.

Now that we have sufficient information, we can now solve for the area.

A = (n × s × a) / 2

A = (5 × 5.81234022404.. cm × 4) / 2

A = (20 × 5.81234022404.. cm) / 2

A = (116.236804481.. cm²) / 2

A = 58.1234022404.. cm²

A ≈ 58.1 cm²

The area of the regular polygon is the amount of space it covers

The area of the regular polygon is 58.1 square centimeter

The given parameter is:

[tex]\mathbf{a=4}[/tex]

Start by calculating the side lengths using

[tex]\mathbf{s = 2a\ tan (\frac{180}{ n} )}[/tex]

Where n represents the number of sides.

In this case

[tex]\mathbf{n =5}[/tex]

So, we have:

[tex]\mathbf{s = 2a\ tan (\frac{180}{ 5} )}[/tex]

[tex]\mathbf{s = 2a\ tan (36)}[/tex]

Substitute 4 for (a)

[tex]\mathbf{s = 2 \times 4\ tan (36)}[/tex]

[tex]\mathbf{s = 8\ tan (36)}[/tex]

[tex]\mathbf{s = 5.8123}[/tex]

The surface area is then calculated as:

[tex]\mathbf{A = \frac{n \times s \times a}{ 2}}[/tex]

So, we have:

[tex]\mathbf{A = \frac{5 \times 5.8123 \times 4}{2}}[/tex]

[tex]\mathbf{A = 58.123}[/tex]

Approximate

[tex]\mathbf{A = 58.1}[/tex]

Hence, the area of the regular polygon is 58.1 square centimeter

Read more about areas at:

https://brainly.com/question/12000718

Answer:

103.62

Step-by-step explanation:

Formula: v = πr²[tex]\frac{h}{3}[/tex], v = πr²h

Given: π = 3.14, r = 3, h = 5

Sub: 3.14(3)²[tex]\frac{5}{3}[/tex]

Simplify: 3.14(9)[tex]\frac{5}{3}[/tex]

Simplify: (28.26)[tex]\frac{5}{3}[/tex]

Solve: 47.1

Given: π = 3.14, r = 3, h = 6

Sub: 3.14(3)6

Simplify: (9.42)6

Solve: 56.52

V = v1 + v2

V = 47.1 + 56.52

V = 103.62

The total volume of the figure is 103.62

Answer: 5/8

Step-by-step explanation:

Probability of getting a red jellybean = 1/8

Probability of getting an orange jellybean = 1/4

Probability of getting a yellow jellybean = 1 - (⅛ + ¼)

= 1 - (1/8 + 2/8)

= 1 - 3/8

= 5/8

Therefore, the probability of getting a yellow jellybean is 5/8

Answer:

426

Step-by-step explanation:

Answer:

x=4

Step-by-step explanation:

[tex] \frac{x}{6} = \frac{6}{9} = > 9x = 6 \times 6 = > x = \frac{36}{9} = > x = 4[/tex]

Answer:

-15

Step-by-step explanation:

in 1950 it was 45 and in 1980 it was 30 so it is -15

The average rate of change can be define as the value of something is changing with respect to another thing is tinging. The average rate of change of the population between 1950 and 1980 is 500 per year. It means the population is decreasing with 500 per year.

The given graph shows the population of a city between the year 1900 to 2000.

The average rate of change can be define as the value of something is changing with respect to another thing is tinging.

Form the given graph,

The year 1950 is between the year 1940 and year 1960. The value at the y axis where the population (in thousand) shown is 45,000 for the year 1950.

The year 1980 is shown in graph at the x axis and the value of the population in the y axis is 30,000.

Thus the population is decreasing from year 1950 to 1980. The difference in the population of the year 1950 and 1980 is,

[tex]d=45000-30000[/tex]

[tex]d=15000[/tex]

Thus the change in the population between 1950 and 1980 is 15,000.

Average rate of change of the population between 1950 and 1980 -

As the population and the year both are changing. The rate of change for the population with respect to the year can be calculating by dividing the difference of the population between two year to the total years between the 1950 to 1980.

There is total 30 year from 1950 to 1980, thus the average rate of change is,

[tex]A(x)=\dfrac{15000}{30} \\ A(x)=500[/tex]

Thus the average rate of change of the population between 1950 and 1980 is 500 per year. It means the population is decreasing with 500 per year.

Learn more about the average rate of change here;

https://brainly.com/question/2530409

Answer:

a,d,e

Step-by-step explanation: trust

Answer:

15 ; yes

Step-by-step explanation:

Base = 15 inches

Height = 10 inches

Area of triangle = 1/2* base * height

Area of triangle = 0.5 * 15 * 10

Area of triangle = 75 in²

Area of trapezium < 2(75)

Area of trapezium, A

A = 1/2*(x+b)h

x = top base ; b = bottom base ; h = 10

1/2*(x + 15)10 < 150

5x + 75 < 150

5x < 150 - 75

5x < 75

x < 15

Hence, Area of trapezoid :

A = 1/2 * (15 + 15)10

A = 1/2 * (30)10

A = 1/2 * 300

A = 150

Hence, Area of trapezium can be twice the area of triangle.

2(75) = 150

Answer:

Brother there's nothing there

Step-by-step explanation:

Answer:

no

Step-by-step explanation:

Using the converse of Pythagoras' identity.

If the square of the longest side is equal to the sum of the squares of the other 2 sides then the triangle is right.

longest side = 30 , then 30² = 900

20² + 23² = 400 + 529 = 929 ≠ 900

Then the triangle is not right.

Answer:

A. (125.6 in)

Step-by-step explanation:

R = d / 2 = 40 / 2 = 20 in

Circumference is:

S = 2*π*R=2*3.14*20=125.6 in

Answer:

I want to say it's 90,000J

Answer:

D. 735.25 cubic inches.

Step-by-step explanation:

Well hello there! My name is Lunako, and I'm here to help you out.

Firstly, do you remember the formula for finding the volume of the sphere? Yep, it's 4π(r³/3)! I'll substitute r for 5.6 -- which is 11.2 divided by 2, but you knew that already right? -- and π for 3.14 -- I'm doing that for relative ease.

4(3.14) * (5.6³/3) {Firstly we need to need find the cube of 5.6. That would be 175.616. Let me show the work for that: 5.6 * 5.6 = 25 + 3 + 3 + 0.36 = 31.36; 31.36 * 5.6 = 150 + 5 + 1.5 + 0.3 + 18 + 0.6 + 0.18  + 0.036 = 155 + 1.8 + 18.6 + 0.216 = 156.8 + 18.816 = 175.616}

4(3.14) * (175.616/3) {Now divide 175.616 by 3 to get 58.5387 (rounded to 54 places).}

4(3.14) * 58.5387 {Now onto the left sides. 3.14 quadrupled is 12.56.}

12.56 * 58.5387 {Now for the last step: Multiplying 12.56 by 58.5387. The work for that is shown in the picture. You should get 735.246072.}

735.246072 in³ {While this is the answer, we need to round it to two decimal places, like in the answer choices. 6 is greater then 5, so round up to 735.25.}

735.25 in³ {And with that this problem is solved.}

The volume of the sphere is 735.25 cubic inches, which is D.

Answer:

150

Step-by-step explanation:

Answer:

18

Step-by-step explanation:

Since this is a multiple choice question, I will employ the guess and check method - meaning I will check each answer one by one.

Variable x = dimes = $0.10

Variable y = quarters = $0.25

Set up a system of equations:

x + y = 38

x(0.10) + y(0.25) = 6.80

Plug in each choice into the second equation. You can find the number of quarters that correspond to each number of dimes by using the first equation.

20 dimes:

20 + y = 38

y = 18

20(0.10) + 18(0.25) = 6.80

2 + 4.5 = 6.80

6.5 does not equal 6.80

Because dimes (x) are worth less than quarters (y), this result tells us the answer will be less than 20 dimes as with 20 or more we have less than $6.80. Another example just to show this is true:

38 dimes:

38 + y = 38

y = 0

38(0.10) + 0(0.25) = 6.80

3.8 + 0 = 6.80

3.8 does not equal 6.80.

Since x is worth less than y, we need more of y rather than x. Adding more x will only mean we will get a lower price. Adding more y will mean we get a higher price which is what we need. So only solve for x that is less than 20.

6

6 + y = 38

y = 22

6(0.10) + 32(0.25) = 6.80

0.60 + 8 = 8.60

8.60 does not equal 6.80.

This result is higher than what we wanted (6.80) which means we need more x. Now we only have to solve for x numbers that are greater than 6 and less than 20.

18

18 + y = 38

y = 20

18(0.10) + 20(0.25) = 6.80

1.8 + 5 = 6.8

6.8 does equal 6.8.

Correct!

Answer:

600ft²

Step-by-step explanation:

Oh boy, this is gonna be a long one, so proceed with caution:

So we're gonna start with the one to the very left, we can split this into three different rectangles:

So we got the length of the bottom minus the length we don't want there because we're doing the big rectangle:

35 - 10 = 25

25 x 20 = 500

So we're just gonna keep that on a back burner, cause now we gotta do the two smaller ones:

So we got the measure from the one side, but we gotta subtract the 10 from the other side:

20 - 10 = 10

10 x 10 = 100

Now we gotta add that all up:

500 + 100 = 600

So the area of the first shape is 600ft²

I gotta go, but hope this helps a little bit

Answer:line

Step-by-step explanation: the section between any two points on a line is called a line segment a line segment can be very long or very short or somewhere in between the difference between a line and a line segment is that a line segment has two endpoints and a line goes on forever

Answer:

71

Step-by-step explanation:

64+3×5-8

64+15-8

79-8

71

Answer:

71

Step-by-step explanation:

4^3 = 64 + 15 = 79 - 8 = 71

Give me my brainllest

Answer:

9.7cm

Step-by-step explanation

According to the sine rule;

a/sinA = c/sinC

8/sin55 = c/sin82

Cross multiply

csin55 = 8sin82

c(0.8192) = 8(0.9903)

c = 8(0.9903)/0.8192

c = 7.9221/0.8192

c = 9.67

Hence the value of c to the nearest tenth is 9.7cm