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The spherical coordinate (4,6π,2π/3) is (5,2π3,0.927) in spherical coordinates.

I’m going to assume that your values are in the form of:

(r,θ,z)=(4,6π,2π/3)

where

(r,θ)are the polar coordinates of the point’s projection in the xy-plane

z is the usual z-coordinate in the Cartesian coordinate system

Now solving for Cartesian coordinates:

x=rcosθ=4cos(6π)=4(0.86)=3.44

y=rsinθ=4sin(6π)=2

Now for spherical transformation, note that:

(ρ,θ,ϕ)

ρ is the distance between P and the origin

θ is the same angle used to describe the location in cylindrical coordinates

ϕ is the angle formed by the positive z-axis and line segment from the origin and point in space, note that0≤ϕ≤π

OK, now that we have that out of the way, let’s compute:

ρ=r2+z2 = 5

θ=θ=6π

ϕ=arccos(zr2+z2−−−−−−√)=arccos(35)≈0.927rad

The spherical coordinate (4,6π,2π/3) is (5,2π3,0.927) in spherical coordinates.

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The given equation, x.cosec²x = cot x - d/dx x.cot x, is proved using the product rule of differentials.

In the question, we are asked to show that x.cosec²x = cot x - d/dx x.cot x.

To prove, we go by the right-hand side of the equation:

cot x - d/dx x.cot x.

We solve the differential d/dx using the product rule, according to which, d/dx uv = u. d/dx(v) + v. d/dx(u), where u and v are functions of x.

cot x - {x. d/dx(cot x) + cot x. d/dx(x)}

= cot x - {x. (-cosec²x) + cot x} {Since, d/dx(cot x) = -cosec²x, and d/dx(x) = 1}

= cot x + x. cosec²x - cot x

= x. cosec²x

= The left-hand side of the equation.

Thus, the given equation, x.cosec²x = cot x - d/dx x.cot x, is proved using the product rule of differentials.

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Answer:

The answer is A. V=pi r³

Step-by-step explanation:

:)

The expression for the volume of the pyramid in terms of the radius r of the cone is [tex]\pi r^3[/tex]. So, option A is correct.

The cone is a three-dimensional figure with a vertex and a flat base.

The volume of a pyramid is given by the formula:

[tex]V = \dfrac{1}{3} \times base\ area \times height.[/tex]

Given that:

The base area of the pyramid = B

The height is 3r

The base area of the pyramid is the same as that of the cone.

The base of the cone = [tex]\pi r^2[/tex]

The volume of the pyramid is calculated as:

[tex]V = \dfrac{1}{3} \times \pi r^2 \times 3r[/tex]

V =[tex]\pi r^3[/tex]

Therefore, the volume of the pyramid is [tex]\pi r^3[/tex]. So, option A is correct.

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Answer:

61.9°

Step-by-step explanation:

The angles of a triangle always add up to 180°. Using this information along with the values of two of the three angles, we can set up an equation to find the measure of the third angle.

Let the measure of the third angle be represented as "x". The first angle + the second angle + the third angle must equal 180 therefore...

[tex]35.5+82.6+x=180[/tex]

Start by adding the like terms on the left side of the equation:

[tex]118.1+x=180[/tex]

Then, subtract both sides by 118.1:

[tex]x=61.9[/tex]

Therefore the measure of the third angle of the triangle is 61.9°.

Jane lost 5 points in the game.

Given that, Jane gained 25 points in the first round of a game. In the second round, she lost 40 points and in the third round, she gained 10 points.

We need to write and evaluate an expression to find how many points Jane gained or lost.

An integer is a number with no decimal or fractional part and it includes negative and positive numbers, including zero.

Now, for the given situation we can write an expression as follows:

25 – 40 + 10

=25 + 10 + ( -40 )

=35 -40= -5

Therefore, Jane lost 5 points in the game.

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Answer:

Step-by-step explanation:

Congruent parts of congruent triangles are congruent, so we can easily demonstrate BD ≅ DF ≅ BF.

AB ≅ BC ≅ CD≅ DE≅ EF ≅ FA . . . . definition of regular hexagon

∠A ≅ ∠C ≅ ∠E . . . . definition of regular hexagon

ΔFAB ≅ ΔBCD ≅ ΔDEF . . . . SAS congruence

FB ≅ BD ≅ DF . . . . CPCTC

ΔBDF is equilateral . . . . definition of equilateral triangle

When calculating a nation’s digital power, the term that is used to refer to the demonstrated capabilities of a nation-state in cyber offense or defense is Cyberwarfare.

Cyberwarfare  can be regarded as the use of cyber attacks against a nation-state so as to produce significant harm.

It should be noted that Cyber Warfare is set of actions  which is been carried out by  nation or organization so as to be able to launch an attack on institutions' computer network systems.

The interests or reasons for cyberwarfares based on the Cybersecurity as well as Infrastructure Security Agency are;

In order to achieve the goals behind the cyberwarfare programs, it is usually designed to focus on spectrum of objectives which will bring harm to national interests.

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There are 8855 ways in which a 4-member committee be formed from 23 members

What is an equation?

An equation is an expression that shows the relationship between two or more numbers and variables.

An independent variable is a variable that does not depend on any other variable for its value while a dependent variable is a variable that depends on other variable.

The number of ways that a 4-member committee be formed from 23 members is:

Number of ways = 23! / [(23 - 4)!4!] = 8855 ways

There are 8855 ways in which a 4-member committee be formed from 23 members

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Answer:

The answer is 212,520.

Step-by-step explanation:

This is a permutation, not a combination. So, we need to follow the formula

[tex]nP_{r} =\frac{n!}{(n-r)!}[/tex]

Plug in the numbers and solve:

[tex]nP_{r}= \frac{23!}{(23-4)!}[/tex]

[tex]nP_{r}= \frac{23!}{19!}\\[/tex]

[tex]nP_{r}= \frac{25,852,016,738,884,976,640,000}{121,645,100,408,832,000}[/tex]

[tex]nP_{r}= 212,520[/tex]

Because 212,520 is an answer choice, this is the correct answer.

Answer:

A

Step-by-step explanation:

Answer:

heat map is the answer

The magnitude of the larger earthquake is about 1.3 greater than the magnitude of the smaller earthquake.

In physics, significance is defined actually as “distance or quantity.” It depicts the absolute or relative course or size wherein an object moves within the sense of motion. it's miles used to express the scale or scope of something. In physics, importance normally refers to distance or quantity.

Magnitude is described as big in size or very vital. An example of value is the depth of the Grand Canyon. An instance of importance is the dimensions of the trouble of world hunger. (geology) A measure of the amount of energy launched by using an earthquake, as indicated on the Richter scale.

The magnitude is more than a few that characterizes the relative size of an earthquake. value is primarily based on the measurement of the maximum movement recorded with the aid of a seismograph.

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Answer:

1/15 of the dishes on the menu are vegetarian pasta.

Step-by-step explanation:

1/10 of 2/3 of all dishes are vegetarian pasta.

1/10 of 2/3 of all = 1/10 * 2/3 * 1 = 2/30 = 1/15

Answer:

probability result of sample space would result in 12/144

Step-by-step explanation:

as result there is 12 numbers on each dice, blth have exact same numbers, resulting in 144 combinations ti be thrown as sample space event outcome wluld be;

1/1 1/2 1/3 1/4 1/5 1/6 1/7 1/8 1/9 1/10 1/11 1/12

2/1 2/2 2/3 2/4 2/5 2/6 2/7 2/8 2/9 2/10 2/11 2/12

3/1 3/2 3/3 3/4 3/5 3/6 3/7 3/8 3/9 3/10 3/11 3/12

4/1 4/2 4/3 4/4 4/5 4/6 4/7 4/8 3/9 4/10 4/11 4/12

5/1 5/2 5/3 5/4 5/5 5/6 5/7 5/8 5/9 5/10 5/11 5/12

6/1 6/2 6/3 6/4 6/5 6/6 6/7 6/8 6/9 6/10 6/11 6/12

7/1 7/2 7/3 7/4 7/5 7/6 7/7 7/8 7/9 7/10 7/11 7/12

8/1 8/2 8/3 8/4 8/5 8/6 8/7 8/8 8/9 8/10 8/11 8/12

9/1 9/2 9/3 9/4 9/5 9/6 9/7 9/8 9/9 9/10 9/11 9/12

10/1 10/2 10/3 10/4 10/5 10/6 10/7 10/8 10/9 10/10 10/11 10/12

11/1 11/2 11/3 11/4 11/5 11/6 11/7 11/8 11/9 11/10 11/11 11/12

12/1 12/2 12/3 12/4 12/5 12/6 12/7 12/8 12/9 12/10 12/11 12/12

giving 12 matching numbers in a 144 possible rolled outcome

mathematic formula would be P(A) = n(A)/n(S)

As P(A)= probabolity of event A

n(A)= number of favouravle outcome

n(S)= total number of outcome in sample space

giving

12=2/144=0,0138888889

Answer: 3.2

Step-by-step explanation: 3.2 is the answer because the number 7 is higher than 5. so the number 1 goes up by one, which that equals 3.2

Mya would have both lessons on the same day again on the 12th day.

In order to determine when they would have the both lessons on the same day, the common multiple of 6 and 4 has to be determined. A multiple of a number is the product of an integer and that number. A common multiple is the multiple that is common to two or more numbers.

Multiple of 6 = 6, 12, 28, 24, 30, 36,

Multiple of 4 = 4, 8, 12, 16, 20, 24, 28

Common multiple = 12

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Answer:

x^2-3/3x

Step-by-step explanation:

=x*x-1*3/3*x

=x^2-3/3x

Step-by-step explanation:

1: change 'sin²A' and 'cos²B' into (1-cos²A)and (1-sin²A) respectively.

2:open the brackets and put signs accordingly.

3: cancel (-1) and (+1).

4: remaining is your answer.

The value of given trigonometric value cos(22. 5°) is 0.387.

According to the statement

we have given that the trigonometric value and we have to find the exact value of that given value with the help of the half angle formula.

So, For this purpose, we know that the

The half angle formulas are used to find the exact values of the trigonometric ratios of the angles like 22.5°.

So,

The given value is :

cos(22. 5°)

Then the value of cos half angle formula is

[tex]cos (theta/2) = +- sqrt((1-cos theta) / 2)[/tex]

then

The value of θ/2 is 22.5 degree.

And θ is 22.5*2

θ = 45 degree

and cos 45 degree is 1/squareroot 2

And by this the value of given value become is

[tex]cos 22.5 = +\sqrt{((\sqrt{2} -1)/(2 \sqrt{2} )) } = + 0.3827[/tex]

So, The value of given trigonometric value cos(22. 5°) is 0.387.

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The area of the shaded region shown in the image is 14π unit²

An equation is an expression that shows the relationship between two or more numbers and variables.

Area of semicircle = π*diameter² / 4

The area of the shaded region is the sum of the area of the individual semi circles shown in the diagram.

Area of shaded region = area of SR + area of QR + area of PQ

Area of shaded region = (1/2) * π(4²/4) +  (1/2) * π(2*4²/4) + (1/2) * π(2 * 2 * 4²/4) = 14π

The area of the shaded region shown in the image is 14π unit²

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Angles are said to be produced whenever two or more straight lines intersect. Some types of angles are right angle, obtuse angle, acute angle, etc. Thus, the required proof is stated below:

Prove: <A > <C

           <B > <D

An obtuse angle is a given angle that is greater than [tex]90^{o}[/tex] but less than [tex]180^{o}[/tex]. While an acute angle is a given angle that is less than [tex]90^{o}[/tex].

Thus extend AB to F, such that BF = CD.

Draw a perpendicular from a to intersect CD at point E.

So that;

<BAD = <BAE + <DAE (addition property of an angle)

Such that;

<A is an obtuse angle, while <C is an acute angle. Thu,

<A > <C (different types of angles)

Also,

<ADC = <CDF - <ADF (subtraction property of angles)

But both angles B and D are acute angles.

So that;

<B > <C (comparison of measures of two angles)

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Answer:

5x^2-x+6

Step-by-step explanation:

That should work

The integer value of the given integers is 20.

According to the statement

we have given that the some integers values like a = 3, b = 2, c = 10 and we have to find the intresult = c *b it means integer result = c *b

So, For this purpose we know that the

An integer is a whole number (not a fractional number) that can be positive, negative, or zero.

And here integer a = 3 and b = 2 and c = 10 and we have to find the value of c *b then

intresult = c *b

Substitute the values in it then

intresult = 10 *2

intresult = 20.

So, the intresults is 20 from the given numbers.

Hence, The integer value of the given integers is 20.

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Question 17: B. A’ (1,2), B’ (3,2), C’ (3,5)

Translating 4 to the right means that you should add 4 to the x value of your coordinate point.

Question 18: C. (3,-5)

This is because reflecting over the x-axis would mean to move down the same amount of units above the x-axis the original point is (the original point is five units above the x-axis so you just move down five units). Look at the attached picture for more help.

Question 19: A. C’ (0,-2)

We can see that the triangle has been translated 1 unit to the right and 2 units up. This would mean you add 1 to the x-value of the coordinate and add 2 to the y-value of the coordinate. I can’t see point C clearly, but I’m guessing that it’s at (-1,-4). This would give point C’ as (0,-2)

Hope this helps! Let me know if you need more help! Have a fantastic day!

The area of the grass that will be watered is given by  800/9 pi ft^2.

What is the area of a circle?

The area of a circle of radius r is given by:

A = πr²

In this problem, a rotating sprinkler head sprays water as far as 20 feet, hence the radius is of r = 20 ft.

It covers a central angle of 80º, while an entire circle has 360º, hence the area of grass that will be watered corresponds to 80/360 = 2/9 of the area of the circle.

Hence the watered area in ft² is given by-

A = 2/9 π × (20)²

   = 800π/ 9

Therefore, the area of the grass that will be watered is given by  800/9 pi ft^2.

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Answer:

11.3 miles more than

Step-by-step explanation:

Looking at the graph, when x is 10 the y is 308. For the equation, if you make x 10, then y is 421. 421 is 113 more than 308. Jace travels 113 more than Jeriel on 10 gallons of gas. If you divide 113 by 10 (to get 1 gallon of gas), you would end up with 11.3 miles more than :)

The algebraic formula that represents the situation of the age difference between Fatimah and Nadia is x + 3 = y, where x, y > 0 and y > x.

Herein we have a situation where two people have different ages, Fatimah has an age such that she is 3 years younger than Nadia. Let be x and y variables that respesent the ages of Fatimah and Nadia, respectively. In summary, the word problem can be reduced into the following algebraic expression:

y - x = 3 (Expression that represents age difference between Fatimah and Nadia)

x + 3 = y, where x, y > 0 and y > x. (1)

The algebraic formula that represents the situation of the age difference between Fatimah and Nadia is x + 3 = y, where x, y > 0 and y > x.

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The unit rate of the proportional relationship y = 3x is 3

The proportional relationship is given as:

y = 3x

Divide both sides by x

y/x = 3

For a proportional relationship y/x = k;

The unit rate is 3

This means that the unit rate of the proportional relationship y = 3x is 3

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Answer:

0.213

Step-by-step explanation:

→ Convert into binomial information

x ~ B ( 12 , 0.4 )

→ Write down probability required

p ( x = 4 )

→ Evaluate

0.2128

Let's try solving the problem using the order of operations method, otherwise known as PEMDAS.

[tex]\begin{tabular}{c | l}Order of Operation & Required Operation \\\cline{1-2}1 & Parentheses () \\2 & Exponents e^{x} \\3 & Multiplication \times \\4 & Division \div \\5 & Addition + \\6 & Subtraction -\end{tabular}[/tex]

We are given this question :

[tex]\mathrm {\frac{7}{4} - 9 \div .08 + \frac{4}{5} - 7 \times .8}[/tex]

Since there are no parentheses or exponents, let's multiply.

[tex]\mathrm {\frac{7}{4} - 9 \div .08 + \frac{4}{5} - 5.6}[/tex]

The next step is to divide.

[tex]\mathrm {\frac{7}{4} - 112.5 + \frac{4}{5} - 5.6}[/tex]

After that, add.

[tex]\mathrm {\frac{7}{4} - 112.5 + 0.8 - 5.6}[/tex]

[tex]\mathrm {\frac{7}{4} - 111.7 - 5.6}[/tex]

Finally, subtract the remaining terms.

[tex]\mathrm {1.75 - 111.7 - 5.6}[/tex]

[tex]\mathrm {-109.95 - 5.6}[/tex]

[tex]\mathrm {-115.55}[/tex]

The final answer is -115.55.

I hope this helped solve the problem.

Good luck on your studies!

Answer:

-115.55

Step-by-step explanation:

7/4 -9÷ .08 + 4/5 -7 * .8

I would change fractions to decimals

1.75 - 9 ÷ .08  +.8 -7 * .8

Now using pemdas, multiply and divide from left to right

1.75 -112.5 +.8 -7 * .8

1.75 -112.5 +.8 -5.6

Now add and subtract from left to right

-110.75+.8 -5.6

-109.95-5.6

-115.55

From the table, the domain are all real numbers and they can be substituted for x to return a valid f(x) value:

A graph can be defined as a type of chart that's commonly used to graphically represent data on both the horizontal and vertical lines of a Cartesian coordinate, which are the x-axis and y-axis.

By critically observing the table (see attachment), we can logically deduce that relationship between the amount of ink and the size of the sign is modeled by this function:

f(x) = x²

From the table, the domain are all real numbers and they can be substituted for x to return a valid f(x) value:

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