A regular hexagon is inscribed in a circle of radius 2 units. In square units, what is the area of the hexagon

a) H0 = 15 m, is the initial height, the height of the rocket at time 0 s.

b) D = [0,5]

c) R = [0,35]

The set of inputs that a function will accept is known as the domain of the function in mathematics. The range of values that we are permitted to enter into our function is known as the domain of a function. The x values for a function like f make up this set (x). A function's range is the collection of values it can take as input. After we enter an x value, the function outputs this sequence of values.

Here, we have

a) H0 is the initial height. It means the height of the rocket at time 0 s.

This value is 15 m.

b) The domain is all values of t between 0 and 5 seconds.

D = [0,5]

c) The range is all values of height from 0 to 35 meters.

R = [0,35]

Hence, a) H0 = 15 m, is the initial height, the height of the rocket at time 0 s.

b) D = [0,5]

c) R = [0,35]

To learn more about domain visit:

brainly.com/question/26098895

#SPJ1

Complete question is: The graph H shows the height, in meters, of a rocket 1 seconds after it was launched.

a. Find H0). What does this value

represent?

b. Describe the domain of this function.

c. Describe the range of this function.

Answer:

Step-by-step explanation:

.

The initial force between the two charges is given by:

[tex]F=k\frac{q_{1} q_{2} }{d^2}[/tex]

where k is Coulomb's constant, q1 and q2 are the two charges, and d is their separation. Let's analyze now the other situations:

1. F

In this case, q1 is halved, q2 is doubled, but the distance between the charges remains d.

So, we have:

q'₁=q₁/2

q'₂=2q₂

d'=d

So, the new force is:

[tex]F'=k\frac{q'_{1}q'_{2} }{d^2} \\\\F'=k\frac{(\frac{q_{1} }{2})(\frac{q_{2} }{2}) }{d^2} \\\\F'=k\frac{q_{1}q_{2} }{d^2} =F[/tex]

So the force has not changed.

2. F/4

In this case, q1 and q2 are unchanged. The distance between the charges is doubled to 2d.

So, we have:

q'₁=q₁

q'₂=q₂

d'=2d

So, the new force is:

[tex]\\F'=k\frac{q'_{1} q'_{2} }{d^2} \\\\F'=k\frac{q_{1}q_{2} }{2d^2} \\\\F'=\frac{1}{4} k\frac{q_{1}q_{2} }{d^2} \\\\F'=\frac{F}{4}[/tex]

So the force has decreased by a factor of 4.

3. 6F

In this case, q1 is doubled and q2 is tripled. The distance between the charges remains d.

So, we have:

q'₁=2q₁

q'₂=3q₂

d'=d

So, the new force is:

[tex]F'=k\frac{q'_{1} q'_{2} }{d^2} \\\\F'=k\frac{2q_{1}3q_{2} }{d^2}\\ \\F'=6k\frac{q_{1}q_{2} }{d^2} =6F[/tex]

So the force has increased by a factor of 6.

To know more about the distance between charges:

https://brainly.com/question/12288272

#SPJ4

Answer:

1. F

2. F/4

3. 6F

The final integral is [tex]=5\left[x\arctan \left(\frac{1}{x}\right)-\left(-\frac{1}{2}\ln \left|1+x^2\right|\right)\right]_1^{\sqrt{3}}[/tex]

Numerical integrals are used to express concepts like volume, area, and displacement when infinitely small amounts of data are combined. Integral location is the integration process.

The signed area of the region in the plane that is circumscribed by the graph of a specific function between two points on the real line can be used to describe definitive integrals. Areas above the plane's horizontal axis are often positive, whereas those below it are typically negative.

[tex]\\\\\int _1^{\sqrt{3}}5\arctan \left(\frac{1}{x}\right)dx=\frac{5\left(2\sqrt{3}\ln \left(2\right)+2\pi -\sqrt{3}\pi \right)}{4\sqrt{3}}\quad \left(\mathrm{Decimal:\quad }\:2.34037\dots \right)\\\\=5\cdot \int _1^{\sqrt{3}}\arctan \left(\frac{1}{x}\right)dx\\\\=5\left[x\arctan \left(\frac{1}{x}\right)-\left(-\frac{1}{2}\ln \left|1+x^2\right|\right)\right]_1^{\sqrt{3}}x_{123} \\\\=5\left[x\arctan \left(\frac{1}{x}\right)-\left(-\frac{1}{2}\ln \left|1+x^2\right|\right)\right]_1^{\sqrt{3}}[/tex]

To know more about definite integral here: brainly.com/question/29974649#

#SPJ4

Correct Question:

[tex]\int _{\:1}^{\sqrt{3}}5\cdot \arctan \left(\frac{1}{x}\right)dx[/tex]

Yes, it is possible for a data set to have no mode.

A mode is the most common value in a data set, so if there are no observations that occur more than once, the data set would have no mode. For example, a data set of the numbers {1, 2, 3, 4, 5} would have no mode because none of the numbers appear more than once.

Additionally, a dataset can also have multiple modes, or a bimodal distribution, which means that there are two or more observations that occur with the same highest frequency. A dataset can have a multimodal distribution as well if it has more than two modes.

In summary, a dataset can have no mode if no observations occur more than once, or have multiple/multimodal modes if more than one observations occur with the same highest frequency.

To learn more about the dataset, visit:

brainly.com/question/22210584

#SPJ4

Therefore , the solution of the given problem of differential equations comes out to be  y = cos x + c.

Sequences in which the difference between succeeding terms is constant are known as arithmetic progressions. For instance, an arithmetic progression with a tolerance of 2 is the sequence 5, 7, 9, 11, 13, and so on. An arithmetic progression (A.P.) is a progression where the tolerance between two succeeding numbers is always the same. Arithmetic progression can be of two types: There are a finite number of terms in a finite geometric progression. The series' early, late, tolerance, and number of terms can be determined.

Here,

Given :dy/dx = x+1

dy = (x+1)dx

=>y = 1/2x² + x +c

dy/dx = -sinx

dy = -sinx dx

=> y = cos x + c

Therefore , the solution of the given problem of differential equations comes out to be  y = cos x + c.

To know more about differential equations visit:

brainly.com/question/28099315

#SPJ4

Yes , there can be a triangle that can have the side lengths as 10.2cm , 5.8cm and 4.5cm .

it is only possible to form a triangle , when the sum of the any two sides of the triangle is greater than the third side of triangle .

the side lengths of the triangle are given as : 10.2cm , 5.8cm and 4.5cm  ;

So , on adding any two side lengths and comparing it with third side ,

we get ;

⇒ 10.2 + 5.8 = 16 > 4.5 ; True

⇒ 5.8 + 4.5 = 10.3 > 10.2 ; True

⇒ 10.2 + 4.5 = 14.7 > 5.8 ;  True .

All the three sides follow the condition ,

Therefore , the given side lengths form a triangle .

Learn more about Triangle here

https://brainly.com/question/30238741

#SPJ4

The type of triangle that is given by the dimensions, is a Scalene triangle.

A scalene triangle has sides that are all measured differently. In such a triangle, no side will be the same length as any other side. Every interior angle in a scalene triangle is also unique.

The lengths of two of the three sides in an isosceles triangle are equal. The angles that are opposite the equal sides are therefore equal. An isosceles triangle, in other words, has two equal sides and two equal angles.

Each side of an equilateral triangle has an equal length. Each internal angle in this scenario will be 60 degrees in length. An equilateral triangle is often referred to as an equiangular triangle since its angles are equal.

The dimensions here are not the same which means that all the sides are not equal and so this is a scalene triangle.

Find out more on scalene triangles at https://brainly.com/question/8158071

#SPJ1

Answer:

Chebyshev's Theorem states that for any dataset with a mean and standard deviation, at least 1 - (1/k^2) of the data will lie within k standard deviations of the mean.

In this case, we're looking for households that have between 0 and 4 televisions, which is 4 - 0 = 4 - 2 = 2 standard deviations from the mean of 2 televisions.

So, using Chebyshev's Theorem, we can calculate that at least 1 - (1/2^2) = 1 - (1/4) = 3/4 or 75% of the households have between 0 and 4 televisions.

At least 75% of the households have between 0 and 4 televisions.

Different types of units are CGS system units, FPS system units, MKS system units and SI units.

The (CGS)centimetre-gram-second system of units is how this is expressed. The metric system employs the centimetre to represent length or distance, the gram as the fundamental unit to represent mass or weight, and the second to represent time. Although there are other units of measurement in the system, they are all derived from just a few of these.

The (FPS)foot-pound-second system of units is what this is in its entire form. In this metric system, the foot serves as the default unit of length, and the pound serves as the default unit of mass and force. Finally, time is represented by the second.

This system's full name is (MKS)meter, kilogram, and second. The measuring of physical quantities is indicated by the usage of this metric system. Here, a meter is used to indicate length and a kilogram to indicate mass. Prior to their redefinition, it was renowned for establishing the foundation for the SI units.

International System of Units(SI) is the lengthier abbreviation for the units. It is the most recent and contemporary variety of metric system in use today. It is frequently utilized as the reference unit of measurement. It primarily includes the following seven units of measurement: second, metre, kilogram, ampere, Kelvin, Mole and candela.

Learn more about SI units here:

https://brainly.com/question/28337624

#SPJ4

The direction of the ball at this point is <1/8, -4, 96/8>

The position vector of the ball can be found by taking the derivative of the rectangular equation with respect to time:

r(t) = <8t, -16t², 32t³>

To find the speed of the ball at the point where it has traveled 64 feet horizontally, we can use the magnitude of the velocity vector, which is the derivative of the position vector with respect to time:

v(t) = <8, -32t, 96t²>

|v(t)| =√(8² + (-32t)² + 96t⁴) = 8*√(1 + t² + 3t⁴)

We need to find the time t at which the ball has traveled 64 feet horizontally. We know that x = 8t, so we can set x = 64 and solve for t:

8t = 64

t = 8

At t = 8, the speed of the ball is:

|v(8)| = 8√(1 + 8² + 3(8⁴)) = 8√(65) = 8*8 = 64

To find the direction of the ball at this point, we can use the unit vector of the velocity vector:

v(t) = <8, -32t, 96t²> / |v(t)|

v(8) = <8, -256, 6144> / 64 = <1/8, -4, 96/8>

So the direction of the ball at this point is <1/8, -4, 96/8>

Learn more about position of vector here:

https://brainly.com/question/14552074

#SPJ4

Answer:

y = -2x + 13

Step-by-step explanation:

In order to write an equation of the line in slope-intercept form, we first have to look at the equation:

y = mx + b

We know that m represents slope, and b represents the y-intecept, in other words, what y is equal to when x is equal to zero.

We already have y and x, (4,5), and the slope of the line, since the two lines are parellel, they share the same slope. So now, we have to pulg those values into the equation and solve for b:

(4,5)

y = 5

x = 4

m = -2

y = mx + b

(5) = (-2)(4) + b

5 = -8 + b

13 = b

So, equation of the line in slope-intercept form that passes through point (4, 5), is y = -2x + 13

Remeber that you can always graph to check your work!

I hope this helps! :)

The solution to the system of equations is x = 3/2 and y = 11/2.

What is the linear equation?

The definition of a linear equation is an algebraic equation in which each term has an exponent of one and the graphing of the equation results in a straight line. An example of a linear equation is y=mx + b

We are given two equations:

y = 3x + 4

y = 7x – 2

We can set the two equations equal to each other and solve for x:

3x + 4 = 7x - 2

Subtracting 3x from both sides:

4 = 4x - 2

Adding 2 to both sides:

6 = 4x

Dividing both sides by 4:

x = 3/2

Now we can substitute this value of x back into either of the original equations to find the corresponding value of y. Using the first equation:

y = 3(3/2) + 4 = 9/2 + 4 = 11/2

Therefore, the solution to the system of equations is x = 3/2 and y = 11/2.

To learn more about the linear equation visit,

brainly.com/question/2030026

#SPJ1

For [tex]f(x)[/tex], the axis of symmetry is the vertical line passing through the vertex. Matching with vertex form, we see the vertex of the graph of [tex]f(x)[/tex] has coordinates [tex](4,2)[/tex]. Thus, the axis of symmetry has equation [tex]x=4[/tex].

Similarly, for [tex]h(x)[/tex], the axis of symmetry is the vertical line passing through the vertex. The vertex of the graph of a quadratic function is either the minimum or maximum point (it depends on the leading coefficient of the function). Here, there is a maximum point, which has coordinates [tex](-2,2)[/tex]. Thus, the axis of symmetry has equation [tex]x=-2[/tex].

Answer:

800 km/h

Step-by-step explanation:

speed = distance ÷ time

=1200km ÷ 1½

=800 km/h

Answer:

Step-by-step explanation:

It is difficult to determine the rule for the table without further context or information. However, based on the pattern in the table, it appears that the rule for generating the second number in each row is to add 2 to the first number in that row. The rule for generating the third number in each row is to add 6 to the second number in that row. The fourth number is the sum of the first and the third number in that row.

The inequalities to represent all of the constraints in Eric's problems using x for the number of adults and y for the number of children are as follows:

An inequality is a statement that compares two expressions using one of the following symbols: <, >, <=, >=, or ≠. The expressions being compared can be numbers, variables, or a combination of both.

The result of an inequality is either true or false. For example, the inequality 2x + 3y < 6 represents a set of ordered pairs (x,y) that satisfy the inequality. It describes all the points on a coordinate plane that fall under the solution set of the inequality.

From the inequalities above,

x + y <= 20 (maximum number of scuba divers) means that since the Lois Ann can only accommodate 20 scuba drivers, whether adults or children, their addition could be less than but not above 20

2x + y <= 30 (maximum number of tanks) means the capacity of Lois Ann is 30 tanks and the number of children is 10, and adult is 20, it implies that either all adults and all children or some adults participated twice (2x) plus children, it is their figure can be less than or equals to 30

20x + 10y <= 220 (maximum weight for scuba divers) implies that their entire weight whether adult or children cannot be more than 220

x, y >= 0 (non-negative number of adults and children) implies that no onee is undetermined of his placement as to whether such is adult or children.

Therefore, the correct answer is as given above

learn more about inequality: https://brainly.com/question/25275758

#SPJ1

The relationship between Doubling and halving is that in halving we simply half one of the factors and in doubling we double the other.

The Doubling and Halving is a technique that is commonly used in Multiplication of two numbers .

Let us understand the Relationship between Doubling and Halving with help of an example ;

Example : To solve 25×16, it is not that simple to directly multiply these ,

By using the Doubling and Halving method ,

we could double the number 25 to make it 50 and

then half the number 16 to make it 8.

So , the equivalent expression becomes , [tex]50\times8[/tex] ,which is much easier to solve , that is 400 .

Learn more about Doubling and Halving here

https://brainly.com/question/11328267

#SPJ4

Answer:First we need to simplify the left side of the equation:

12,5(3x-1)+132,4 = 12,5*3x - 12,5 + 132,4 = 37,5x + 120,9

Now we need to simplify the right side of the equation:

2,8-4x = 2,8 - 4x

Now we have to set the two sides equal:

37,5x + 120,9 = 2,8 - 4x

Now we have to move all the x terms to one side of the equation:

37,5x - 4x + 120,9 = 2,8

Next step is to combine like terms:

33,5x + 120,9 = 2,8

Subtracting 120.9 from both sides of the equation:

33,5x = -118.1

Dividing both sides by 33,5

x = -3,54

So the solution of the equation is x = -3,54

Step-by-step explanation:

Answer: The answer would be 745.5 yd.

Each lap is 250 yd, and Jasmine plans on running 3 laps, so 3*250 = 750 yd.

The answer is 745.5 yd, which is the closest to 750 yd.

Step-by-step explanation:

Answer:

The prime factors of 12 are 2 x 2 x 3.

So the composite factors of 12 are:

1, 2, 3, 4, 6 and 12.

The sum of all possible values for the common ratio is -1/2.

The formula for a convergent infinite geometric series is:  Sum  =  a / (1 - r)

where a = first term and r = common ratio.

Given that,

The first term = -3/2  =>   a = -3/2

Since it sums to twice the common ratio,  Sum = 2r.

Putting these together   --->   2r  =  (-3/2) / (1 - r)                      

multiplying both sides by 1 - r:

2r(1 - r)  =  -3/2                              

multiplying both sides by 2:

4r(1 - r)  =  -3                                

multiplying out the left-hand side:

4r - 4r2  =  -3                                  

rearranging the terms:

0  =  4r2 - 4r - 3                              

factor:

0  =  (2r - 3)(2r + 1)

Either  r = 3/2  or  r = -1/2

Since an infinite geometric series converges only when  -1 < r < r,  the possible answer 3/2 must be rejected.

Thus, r = -1/2

Therefore, the sum of all possible values for the common ratio is -1/2.

To know  more about ratio visit: brainly.com/question/13419413

#SPJ4

The probability that 75% or more of the women in the sample have been on a diet is 0.944.

The probability that 75% or more of the women in the sample have been on a diet can be calculated by using the binomial formula. The formula is P(X>=x) = 1 - P(X<x). The parameters in this case are as follows: n = 267, p = 0.7, and x = 201.5 (which is 75% of 267). Therefore, the probability that 75% or more of the women in the sample have been on a diet is 1 - P(X<201.5). Solving for this probability, P(X>=201.5) is 0.944. Therefore, the probability that 75% or more of the women in the sample have been on a diet is 0.944.

Learn more about probability here:

https://brainly.com/question/30034780

#SPJ4

Answer:

right angle

Step-by-step explanation:

Answer:

its 34

Step-by-step explanation:

Did it yesterday and got it right.

Answer:

r = 5

Step-by-step explanation:

calculate the slope m of the 2 given points and equate to - 2

using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (3, 2 ) and (x₂, y₂ ) = (r, - 2 )

m = [tex]\frac{-2-2}{r-3}[/tex] = [tex]\frac{-4}{r-3}[/tex]

equating to - 2 gives

[tex]\frac{-4}{r-3}[/tex] = - 2 ( multiply both sides by r - 3 to clear the fraction )

- 4 = - 2(r - 3) ← divide both sides by - 2 )

2 = r - 3 ( add 3 to both sides )

5 = r

To show that var(aX + bY + c) = a^2 var X + b^2 varY + 2ab cov(X, Y), we can start by using the definition of variance, which is var(X) = E[(X - E[X])^2], and the definition of covariance, which is cov(X, Y) = E[(X - E[X])(Y - E[Y])].

Variance is a measure of the spread of a random variable's possible values. It is defined as the expected value of the squared deviation of a random variable from its mean. For a random variable X, the variance is denoted as Var(X) or σ^2(X) and is calculated as:

Var(X) = E[(X - E[X])^2]

Using these definitions, we can write:

var(aX + bY + c) = E[(aX + bY + c - E[aX + bY + c])^2]

Using the properties of expectations and bilinearity, we can simplify this to:

var(aX + bY + c) = E[(a(X - E[X]) + b(Y - E[Y]))^2]

Expanding the square and using bilinearity again, we get:

var(aX + bY + c) = a^2 E[(X - E[X])^2] + b^2 E[(Y - E[Y])^2] + 2ab E[(X - E[X])(Y - E[Y])]

Since the expectations of (X - E[X])^2 and (Y - E[Y])^2 are equal to var(X) and var(Y) respectively, we can substitute these values into the above equation to get:

var(aX + bY + c) = a^2 var X + b^2 varY + 2ab cov(X,Y)

Therefore, we have shown that var(aX + bY + c) = a^2 var X + b^2 varY + 2ab cov(X,Y)

To know more about variance refer to:

brainly.com/question/10934442

#SPJ4

Answer:

8.5

Step-by-step explanation:

850/100

Answer:

[tex]8.5l[/tex]

Step-by-step explanation:

1cl = 10ml

850cl = 8500ml

1000ml= 1l

8500ml= 8.5l

You can use a compass and set its angle such that it the radius of the circle that it will draw is less than that of WX's length but longer than its half. Use it to make 4 arcs.

Making 4 arcs (2 arcs up and down from W and 2 arcs up and down from X which intersect the previous two arcs) with the circle of radius smaller than the length of  WX will give two points on a perpendicular bisector.

How to find the perpendicular bisector of a line segment with the help of a compass and a straightedge?

The construction steps are as follows:

Let the line segment to be bisected(divided into two equal parts) by a perpendicular line(that perpendicular bisecting line is called the perpendicular bisector of the given line segment) be WX

Take a compass and set its radius length smaller than the length of WX and longer than half of WX

Put the tip of the compass on W and make an arc upside of WX

Now make an arc downside of WX

Repeat the above two steps but now with the tip being on X such that two new arcs intersect the previous two arcs.

Use a straightedge and join both the points of intersection of arcs.

The obtained line is the perpendicular bisector of the line segment WX

Using the above method, we get the perpendicular bisector of WX  shown in the below-attached figure.

Thus,

Making 4 arcs (2 arcs up and down from W and 2 arcs up and down from X which intersect the previous two arcs) with a circle of radius smaller than the length of  WX will give two points on a perpendicular bisector.

Learn more about constructing perpendicular bisectors here:

brainly.com/question/14344702

You can use a compass and set its angle such - 1

The solution of the given quadratic equation are,

[tex]y = \frac{-11+\sqrt{41} }{4}, y = \frac{-11-\sqrt{41} }{4}[/tex].

What is quadratic equation?

Any equation in algebra that can be written in standard form as where x stands for an unknown value, where a, b, and c stand for known numbers, and where a ≠ 0 is true is known as a quadratic equation.

Consider, the given equation:

2y^2 + 11y + 10 = 0

Compare this equation with [tex]ay^2 + by + c = 0[/tex]

⇒  a = 2,  b = 11, c = 10

Consider, the quadratic formula

[tex]y = \frac{-b+-\sqrt{xb^2-4ac} }{2a}[/tex]

Plug the values of a, b, c in the quadratic formula.

⇒

[tex]y = \frac{-11+-\sqrt{11^2-4(2)(10)} }{2(2)} \\y = \frac{-11+-\sqrt{121-80} }{4}\\ y = \frac{-11+-\sqrt{41} }{4} \\y = \frac{-11+\sqrt{41} }{4}, y = \frac{-11-\sqrt{41} }{4}[/tex]

Hence, the solution of the given quadratic equation are,

[tex]y = \frac{-11+\sqrt{41} }{4}, y = \frac{-11-\sqrt{41} }{4}[/tex].

To learn more about quadratic equation, click on the link

https://brainly.com/question/1214333

#SPJ1

Mean has been affected most by the scores of these two students.

A bunch of scores is averaged to form the mean. The total scores were divided by the total scores. When population samples are tiny, the mean is susceptible to extreme scores.

When you add up all the individual scores and divide that total by the number of students, you obtain the mean, which is the arithmetic average score.

The average performance of a group of students on a test is represented by their mean scale score. A mean scale score is derived specifically by summing together the scores of each individual student and dividing that amount by the number of scores. It is additionally known as an average.

Know more about mean at:

https://brainly.com/question/1136789

#SPJ4

The radius of a wheel rolling on the ground is 80 centimeters. if the wheel rotates through an angle of 60. Therefore,  It move to 84 cm.

Circumference Of Circle:

The total length of the circle boundary. The circumference of a circle is the product of the constant π and the diameter of the circle. A person walking across a circular park or a circular table needs this measure of circumference. The circumference is a length value and its units are the same as the length units. A circle is a round closed figure with all endpoints equidistant from a fixed point called the center.

The formula for the circumference of a circle is expressed using the values ​​of the circle's radius 'r' and 'pi'. It is represented by the equation of circumference = 2πr. Using this perimeter formula, if you don't have a value for the radius, you can use the diameter to find it. To calculate the circumference is to use the formula circumference = π × diameter.

If you need to calculate the radius or diameter, consider the circumference of a circle and use the following formula:

                    Radius = circumference/2π

Now,

According to the Question:

If the radius is 80cm

and,  the circumference is 2×π×80cm.

If the wheel rotates by 60° then a fraction 60/360 (= 1/6) of the circumference moves over the ground.  

Therefore, the distance moved is

                     [tex]\frac{2*\pi*80 }{6}[/tex]

               = 83.77580

               ≈ 84 cm.

Learn more about Angle:

https://brainly.com/question/28451077

#SPJ4